# Posts Tagged scalar field

## Recent Postings from scalar field

### Why is the Dark Axion Mass $10^{-22}$ eV? [Cross-Listing]

Scalar field dark matter likely is able to solve all small-scale cosmology problems facing the cold dark matter (CDM), and has become an emerging contender to challenge the CDM. It however requires a particle mass $\sim 1 – 2 \times10^{-22}$eV. We find such an extremely small particle mass can naturally arise from a non-QCD axion mechanism, under fairly general assumptions that a few species of self-interacting light particles of comparable masses and a massless gauge boson decouple from the bright sector since the photon temperature exceeds 200 GeV, and the axion is the dominant dark matter. These assumptions also set the axion decay constant scale to several $\times 10^{16}$ GeV. Given the above axion mass range, we further pin down the dark-sector particles to consist of only one species of fermion and anti-fermion, likely right-handed neutrinos. With a mass around $92-128$ eV, the dark-sector particles may constitute a minority population of dark matter. If the gauge boson lives on SU(2), a dilute instanton gas can contribute about $2.5\%$ of the total relativistic relics in the cosmic microwave background radiation.

### An Alternative to Particle Dark Matter [Cross-Listing]

We propose an alternative to particle dark matter that borrows ingredients of MOdified Newtonian Dynamics (MOND) while adding new key components. The first new feature is a dark matter fluid, in the form of a scalar field with small equation of state and sound speed. This component is critical in reproducing the success of cold dark matter for the expansion history and the growth of linear perturbations, but does not cluster significantly on non-linear scales. Instead, the missing mass problem on non-linear scales is addressed by a modification of the gravitational force law. The force law approximates MOND at large and intermediate accelerations, and therefore reproduces the empirical success of MOND at fitting galactic rotation curves. At ultra-low accelerations, the force law reverts to an inverse-square-law, albeit with a larger Newton’s constant. This latter regime is important in galaxy clusters and is consistent with their observed isothermal profiles. We present an explicit relativistic theory in terms of two scalar fields. The first scalar field is governed by a Dirac-Born-Infeld action and behaves as a dark matter fluid on large scales. The second scalar field also has single-derivative interactions and mediates a fifth force that modifies gravity on non-linear scales. Both scalars are coupled to matter via an effective metric that depends locally on the fields. The form of this effective metric implies the equality of the two scalar gravitational potentials, which ensures that lensing and dynamical mass estimates agree.

### An Alternative to Particle Dark Matter

We propose an alternative to particle dark matter that borrows ingredients of MOdified Newtonian Dynamics (MOND) while adding new key components. The first new feature is a dark matter fluid, in the form of a scalar field with small equation of state and sound speed. This component is critical in reproducing the success of cold dark matter for the expansion history and the growth of linear perturbations, but does not cluster significantly on non-linear scales. Instead, the missing mass problem on non-linear scales is addressed by a modification of the gravitational force law. The force law approximates MOND at large and intermediate accelerations, and therefore reproduces the empirical success of MOND at fitting galactic rotation curves. At ultra-low accelerations, the force law reverts to an inverse-square-law, albeit with a larger Newton’s constant. This latter regime is important in galaxy clusters and is consistent with their observed isothermal profiles. We present an explicit relativistic theory in terms of two scalar fields. The first scalar field is governed by a Dirac-Born-Infeld action and behaves as a dark matter fluid on large scales. The second scalar field also has single-derivative interactions and mediates a fifth force that modifies gravity on non-linear scales. Both scalars are coupled to matter via an effective metric that depends locally on the fields. The form of this effective metric implies the equality of the two scalar gravitational potentials, which ensures that lensing and dynamical mass estimates agree.

### An Alternative to Particle Dark Matter [Cross-Listing]

We propose an alternative to particle dark matter that borrows ingredients of MOdified Newtonian Dynamics (MOND) while adding new key components. The first new feature is a dark matter fluid, in the form of a scalar field with small equation of state and sound speed. This component is critical in reproducing the success of cold dark matter for the expansion history and the growth of linear perturbations, but does not cluster significantly on non-linear scales. Instead, the missing mass problem on non-linear scales is addressed by a modification of the gravitational force law. The force law approximates MOND at large and intermediate accelerations, and therefore reproduces the empirical success of MOND at fitting galactic rotation curves. At ultra-low accelerations, the force law reverts to an inverse-square-law, albeit with a larger Newton’s constant. This latter regime is important in galaxy clusters and is consistent with their observed isothermal profiles. We present an explicit relativistic theory in terms of two scalar fields. The first scalar field is governed by a Dirac-Born-Infeld action and behaves as a dark matter fluid on large scales. The second scalar field also has single-derivative interactions and mediates a fifth force that modifies gravity on non-linear scales. Both scalars are coupled to matter via an effective metric that depends locally on the fields. The form of this effective metric implies the equality of the two scalar gravitational potentials, which ensures that lensing and dynamical mass estimates agree.

### An Alternative to Particle Dark Matter [Cross-Listing]

We propose an alternative to particle dark matter that borrows ingredients of MOdified Newtonian Dynamics (MOND) while adding new key components. The first new feature is a dark matter fluid, in the form of a scalar field with small equation of state and sound speed. This component is critical in reproducing the success of cold dark matter for the expansion history and the growth of linear perturbations, but does not cluster significantly on non-linear scales. Instead, the missing mass problem on non-linear scales is addressed by a modification of the gravitational force law. The force law approximates MOND at large and intermediate accelerations, and therefore reproduces the empirical success of MOND at fitting galactic rotation curves. At ultra-low accelerations, the force law reverts to an inverse-square-law, albeit with a larger Newton’s constant. This latter regime is important in galaxy clusters and is consistent with their observed isothermal profiles. We present an explicit relativistic theory in terms of two scalar fields. The first scalar field is governed by a Dirac-Born-Infeld action and behaves as a dark matter fluid on large scales. The second scalar field also has single-derivative interactions and mediates a fifth force that modifies gravity on non-linear scales. Both scalars are coupled to matter via an effective metric that depends locally on the fields. The form of this effective metric implies the equality of the two scalar gravitational potentials, which ensures that lensing and dynamical mass estimates agree.

### Extremal Hairy Black Holes

We consider a gravitating system consisting of a scalar field minimally coupled to gravity with a self-interacting potential and an U(1) electromagnetic field. Solving the coupled Einstein-Maxwell-scalar system we find exact hairy charged black hole solutions with the scalar field regular everywhere. We go to the zero temperature limit and we study the effect of the scalar field on the near horizon geometry of an extremal black hole. We find that except a critical value of the charge of the black hole there is also a critical value of the charge of the scalar field beyond of which the extremal black hole is destabilized. We study the thermodynamics of these solutions and we find that if the space is flat then at low temperature the Reissner-Nordstr\"om black hole is thermodynamically preferred, while if the space is AdS the hairy charged black hole is thermodynamically preferred at low temperature.

### Extremal Hairy Black Holes [Cross-Listing]

We consider a gravitating system consisting of a scalar field minimally coupled to gravity with a self-interacting potential and an U(1) electromagnetic field. Solving the coupled Einstein-Maxwell-scalar system we find exact hairy charged black hole solutions with the scalar field regular everywhere. We go to the zero temperature limit and we study the effect of the scalar field on the near horizon geometry of an extremal black hole. We find that except a critical value of the charge of the black hole there is also a critical value of the charge of the scalar field beyond of which the extremal black hole is destabilized. We study the thermodynamics of these solutions and we find that if the space is flat then at low temperature the Reissner-Nordstr\"om black hole is thermodynamically preferred, while if the space is AdS the hairy charged black hole is thermodynamically preferred at low temperature.

### Hadamard renormalized scalar field theory on anti-de Sitter space-time

We consider a real massive free quantum scalar field with arbitrary curvature coupling on $n$-dimensional anti-de Sitter space-time. We use Hadamard renormalization to find the vacuum expectation values of the quadratic field fluctuations and the stress-energy tensor, presenting explicit results for $n=2$ to $n=11$ inclusive.

### Geodesic structure of Janis-Newman-Winicour space-time

In the present paper we study the geodesic structure of the Janis-Newman-Winicour(JNW) space-time which contains a strong curvature naked singularity. This metric is an extension of the Schwarzschild geometry when a massless scalar field is included. We find that the strength parameter $\mu$ of the scalar field effects on the geodesic structure of the JNW space-time. By solving the geodesic equation and analyzing the behavior of effective potential, we investigate all geodesic types of the test particle and the photon in the JNW space-time. At the same time we simulate all the geodesic orbits corresponding to the energy levels of the effective potential in the JNW space-time.

### Higher Order Lagrangians inspired in the Pais-Uhlenbeck Oscillator and their cosmological applications [Cross-Listing]

We study higher derivative terms associated to an scalar field cosmology. We consider a coupling between the scalar field and the geometry inspired in the Pais-Uhlenbeck oscillator given by $\alpha\partial_{\mu}\partial^{\mu}\phi\partial_{\nu}\partial^{\nu}\phi.$ We investigate the cosmological dynamics in a phase space. For $\alpha>0$ we provide conditions for the stability of de Sitter solutions. For $\alpha<0,$ which is the portion of the parameter space where the crossing of the phantom divide $w_{DE}=-1$ and the cyclic behavior are possible, we present regions in the parameter space where the ghost has benign or malicious behavior, according to Smilga’s classification.

### Higher Order Lagrangians inspired in the Pais-Uhlenbeck Oscillator and their cosmological applications [Cross-Listing]

We study higher derivative terms associated to an scalar field cosmology. We consider a coupling between the scalar field and the geometry inspired in the Pais-Uhlenbeck oscillator given by $\alpha\partial_{\mu}\partial^{\mu}\phi\partial_{\nu}\partial^{\nu}\phi.$ We investigate the cosmological dynamics in a phase space. For $\alpha>0$ we provide conditions for the stability of de Sitter solutions. For $\alpha<0,$ which is the portion of the parameter space where the crossing of the phantom divide $w_{DE}=-1$ and the cyclic behavior are possible, we present regions in the parameter space where the ghost has benign or malicious behavior, according to Smilga’s classification.

### Higher Order Lagrangians inspired in the Pais-Uhlenbeck Oscillator and their cosmological applications

We study higher derivative terms associated to an scalar field cosmology. We consider a coupling between the scalar field and the geometry inspired in the Pais-Uhlenbeck oscillator given by $\alpha\partial_{\mu}\partial^{\mu}\phi\partial_{\nu}\partial^{\nu}\phi.$ We investigate the cosmological dynamics in a phase space. For $\alpha>0$ we provide conditions for the stability of de Sitter solutions. For $\alpha<0,$ which is the portion of the parameter space where the crossing of the phantom divide $w_{DE}=-1$ and the cyclic behavior are possible, we present regions in the parameter space where the ghost has benign or malicious behavior, according to Smilga’s classification.

### Myers-Perry black holes with scalar hair and a mass gap

We construct a family of asymptotically flat, rotating black holes with scalar hair and a regular horizon, within five dimensional Einstein’s gravity minimally coupled to a complex, massive scalar field doublet. These solutions are supported by rotation and have no static limit. They are described by their mass $M$, two equal angular momenta $J_1=J_2\equiv J$ and a conserved Noether charge $Q$, measuring the scalar hair. For vanishing horizon size the solutions reduce to five dimensional boson stars. In the limit of vanishing Noether charge density, the scalar field becomes point-wise arbitrarily small and the geometry becomes, locally, arbitrarily close to that of a specific set of Myers-Perry black holes (MPBHs); but there remains a global difference with respect to the latter, manifest in a finite mass gap. Thus, the scalar hair never becomes a linear perturbation of MPBHs. This is a qualitative difference when compared to Kerr black holes with scalar hair~\cite{Herdeiro:2014goa}. Whereas the existence of the latter can be anticipated in linear theory, from the existence of scalar bound states on the Kerr geometry (i.e. scalar clouds), the hair of these MPBHs is intrinsically non-linear.

### Myers-Perry black holes with scalar hair and a mass gap [Cross-Listing]

We construct a family of asymptotically flat, rotating black holes with scalar hair and a regular horizon, within five dimensional Einstein’s gravity minimally coupled to a complex, massive scalar field doublet. These solutions are supported by rotation and have no static limit. They are described by their mass $M$, two equal angular momenta $J_1=J_2\equiv J$ and a conserved Noether charge $Q$, measuring the scalar hair. For vanishing horizon size the solutions reduce to five dimensional boson stars. In the limit of vanishing Noether charge density, the scalar field becomes point-wise arbitrarily small and the geometry becomes, locally, arbitrarily close to that of a specific set of Myers-Perry black holes (MPBHs); but there remains a global difference with respect to the latter, manifest in a finite mass gap. Thus, the scalar hair never becomes a linear perturbation of MPBHs. This is a qualitative difference when compared to Kerr black holes with scalar hair~\cite{Herdeiro:2014goa}. Whereas the existence of the latter can be anticipated in linear theory, from the existence of scalar bound states on the Kerr geometry (i.e. scalar clouds), the hair of these MPBHs is intrinsically non-linear.

### Emergent Cosmology, Inflation and Dark Energy from Spontaneous Breaking of Scale Invariance

A new class of gravity-matter models defined in terms of two independent non-Riemannian volume forms (alternative generally covariant integration measure densities) on the space-time manifold are studied in some detail. These models involve an additional R^2 (square of the scalar curvature) term as well as scalar matter field potentials of appropriate form so that the pertinent action is invariant under global Weyl-scale symmetry. Scale invariance is spontaneously broken upon integration of the equations of motion. After performing transition to the physical Einstein frame we obtain: (i) An effective potential for the scalar field with two flat regions which allows for a unified description of both early universe inflation as well as of present dark energy epoch; (ii) For a definite parameter range the model possesses a non-singular "emergent universe" solution which describes an initial phase of evolution that precedes the inflationary phase.

### Emergent Cosmology, Inflation and Dark Energy from Spontaneous Breaking of Scale Invariance [Cross-Listing]

A new class of gravity-matter models defined in terms of two independent non-Riemannian volume forms (alternative generally covariant integration measure densities) on the space-time manifold are studied in some detail. These models involve an additional R^2 (square of the scalar curvature) term as well as scalar matter field potentials of appropriate form so that the pertinent action is invariant under global Weyl-scale symmetry. Scale invariance is spontaneously broken upon integration of the equations of motion. After performing transition to the physical Einstein frame we obtain: (i) An effective potential for the scalar field with two flat regions which allows for a unified description of both early universe inflation as well as of present dark energy epoch; (ii) For a definite parameter range the model possesses a non-singular "emergent universe" solution which describes an initial phase of evolution that precedes the inflationary phase.

### Emergent Cosmology, Inflation and Dark Energy from Spontaneous Breaking of Scale Invariance [Replacement]

A new class of gravity-matter models defined in terms of two independent non-Riemannian volume forms (alternative generally covariant integration measure densities) on the space-time manifold are studied in some detail. These models involve an additional R^2 (square of the scalar curvature) term as well as scalar matter field potentials of appropriate form so that the pertinent action is invariant under global Weyl-scale symmetry. Scale invariance is spontaneously broken upon integration of the equations of motion. After performing transition to the physical Einstein frame we obtain: (i) An effective potential for the scalar field with two flat regions which allows for a unified description of both early universe inflation as well as of present dark energy epoch; (ii) For a definite parameter range the model possesses a non-singular "emergent universe" solution which describes an initial phase of evolution that precedes the inflationary phase.

### Emergent Cosmology, Inflation and Dark Energy from Spontaneous Breaking of Scale Invariance [Replacement]

A new class of gravity-matter models defined in terms of two independent non-Riemannian volume forms (alternative generally covariant integration measure densities) on the space-time manifold are studied in some detail. These models involve an additional R^2 (square of the scalar curvature) term as well as scalar matter field potentials of appropriate form so that the pertinent action is invariant under global Weyl-scale symmetry. Scale invariance is spontaneously broken upon integration of the equations of motion. After performing transition to the physical Einstein frame we obtain: (i) An effective potential for the scalar field with two flat regions which allows for a unified description of both early universe inflation as well as of present dark energy epoch; (ii) For a definite parameter range the model possesses a non-singular "emergent universe" solution which describes an initial phase of evolution that precedes the inflationary phase.

### Bouncing scalar field cosmology in the polymeric minisuperspace picture

We study a cosmological setup consisting of a FRW metric as the background geometry with a massless scalar field in the framework of classical polymerization of a given dynamical system. To do this, we first introduce the polymeric representation of the quantum operators. We then extend the corresponding process to reach a transformation which maps any classical variable to its polymeric counterpart. It is shown that such a formalism has also an analogue in terms of the symplectic structure, i.e., instead of applying polymerization to the classical Hamiltonian to arrive its polymeric form, one can use a new set of variables in terms of which Hamiltonian retains its form but now the corresponding symplectic structure gets a new deformed functional form. We show that these two methods are equivalent and by applying of them to the scalar field FRW cosmology see that the resulting scale factor exhibits a bouncing behavior from a contraction phase to an expanding era. Since the replacing of the big bang singularity by a bouncing behavior is one of the most important predictions of the quantum cosmological theories, we may claim that our polymerized classical model brings with itself some signals from quantum theory.

### Combined cosmological tests of a bivalent tachyonic dark energy scalar field model

A recently investigated tachyonic scalar field dark energy dominated universe exhibits a bivalent future: depending on initial parameters can run either into a de Sitter exponential expansion or into a traversable future soft singularity followed by a contraction phase. We also include in the model (i) a tiny amount of radiation, (ii) baryonic matter ($\Omega _{b}h^{2}=0.022161$, where the Hubble constant is fixed as $h=0.706$) and (iii) cold dark matter (CDM). Out of a variety of six types of evolutions arising in a more subtle classification, we identify two in which in the past the scalar field effectively degenerates into a dust (its pressure drops to an insignificantly low negative value). These are the evolutions of type IIb converging to de Sitter and type III hitting the future soft singularity. We confront these background evolutions with various cosmological tests, including the supernova type Ia Union 2.1 data, baryon acoustic oscillation distance ratios, the $Omh^{2}$ diagnostic and the cosmic microwave background (CMB) acoustic scale. We determine a subset of the evolutions of both types which at 1$\sigma$ confidence level are consistent with all of these cosmological tests. At perturbative level we derive the CMB temperature power spectrum to find the best agreement with the Planck data for $\Omega _{CDM}=0.22$. The fit is as good as for the $\Lambda$CDM model at high multipoles, but the power remains slightly overestimated at low multipoles, for both types of evolutions. The rest of the CDM is effectively generated by the tachyonic field, which in this sense acts as a combined dark energy and dark matter model.

### Combined cosmological tests of a bivalent tachyonic dark energy scalar field model [Cross-Listing]

A recently investigated tachyonic scalar field dark energy dominated universe exhibits a bivalent future: depending on initial parameters can run either into a de Sitter exponential expansion or into a traversable future soft singularity followed by a contraction phase. We also include in the model (i) a tiny amount of radiation, (ii) baryonic matter ($\Omega _{b}h^{2}=0.022161$, where the Hubble constant is fixed as $h=0.706$) and (iii) cold dark matter (CDM). Out of a variety of six types of evolutions arising in a more subtle classification, we identify two in which in the past the scalar field effectively degenerates into a dust (its pressure drops to an insignificantly low negative value). These are the evolutions of type IIb converging to de Sitter and type III hitting the future soft singularity. We confront these background evolutions with various cosmological tests, including the supernova type Ia Union 2.1 data, baryon acoustic oscillation distance ratios, the $Omh^{2}$ diagnostic and the cosmic microwave background (CMB) acoustic scale. We determine a subset of the evolutions of both types which at 1$\sigma$ confidence level are consistent with all of these cosmological tests. At perturbative level we derive the CMB temperature power spectrum to find the best agreement with the Planck data for $\Omega _{CDM}=0.22$. The fit is as good as for the $\Lambda$CDM model at high multipoles, but the power remains slightly overestimated at low multipoles, for both types of evolutions. The rest of the CDM is effectively generated by the tachyonic field, which in this sense acts as a combined dark energy and dark matter model.

### Dynamic C-metrics in (Gauged) Supergravities

We construct an exact time-dependent charged dilaton C-metric in four-dimensional ${\cal N}=4$ gauged supergravity. The scalar field drives the time evolution by transferring energy to the black holes, thereby causing their masses to increase and their acceleration to decrease. The values of the electric/magnetic and scalar charges determine three regions of potential time evolution. This solution holographically describes a strongly-coupled three-dimensional conformal field theory on the background of an evolving black hole. We also find new static charged dilaton C-metrics, which arise in four-dimensional Einstein-Maxwell-dilaton theories whose scalar potential can be expressed in terms of a superpotential.

### Varying-Alpha and K-Essence [Cross-Listing]

We introduce a model which allows the fine structure constant (alpha) to vary throughout space and time due to a coupling to a scalar field with a non-canonical kinetic structure. This provided a new extension of the Bekenstein-Sandvik-Barrow-Magueijo model of alpha variations. The background cosmology is studied in detail using dynamical systems techniques for a scalar field of ghost condensate type. We show generically that if the kinetic terms are chosen to allow an accelerated late-time attractor for the expansion scale factor then alpha will not asymptote to a constant at late times.

### Varying-Alpha and K-Essence [Cross-Listing]

We introduce a model which allows the fine structure constant (alpha) to vary throughout space and time due to a coupling to a scalar field with a non-canonical kinetic structure. This provided a new extension of the Bekenstein-Sandvik-Barrow-Magueijo model of alpha variations. The background cosmology is studied in detail using dynamical systems techniques for a scalar field of ghost condensate type. We show generically that if the kinetic terms are chosen to allow an accelerated late-time attractor for the expansion scale factor then alpha will not asymptote to a constant at late times.

### Varying-Alpha and K-Essence

We introduce a model which allows the fine structure constant (alpha) to vary throughout space and time due to a coupling to a scalar field with a non-canonical kinetic structure. This provided a new extension of the Bekenstein-Sandvik-Barrow-Magueijo model of alpha variations. The background cosmology is studied in detail using dynamical systems techniques for a scalar field of ghost condensate type. We show generically that if the kinetic terms are chosen to allow an accelerated late-time attractor for the expansion scale factor then alpha will not asymptote to a constant at late times.

### Asymptotic properties of solutions of the Maxwell Klein Gordon equation with small data [Cross-Listing]

We prove peeling estimates for the small data solutions of the Maxwell Klein Gordon equations with non-zero charge and with a non-compactly supported scalar field, in $(3+1)$ dimensions. We obtain the same decay rates as in an earlier work by Lindblad and Sterbenz, but giving a simpler proof. In particular we dispense with the fractional Morawetz estimates for the electromagnetic field, as well as certain space-time estimates. In the case that the scalar field is compactly supported we can avoid fractional Morawetz estimates for the scalar field as well. All of our estimates are carried out using the double null foliation and in a gauge invariant manner.

### Rotating black holes with scalar hair in three dimensions [Cross-Listing]

We examine the first law of thermodynamics in (2+1)-dimensional rotating hairy black holes and find that the first law of black hole thermodynamics can be protected when the scalar field parameter $B$ is constrained to relate to the black hole size. We disclose the Hawking-Page phase transition between the hairy black holes and the pure thermal radiation. Moreover, we find that the free energies of the rotating hairy black holes depend on the ratio between the horizon size to the scalar field parameter $B$. We also compare the free energies for the hairy black hole and the BTZ black hole when they have the same temperature and angular momentum, and find that when this ratio is large, the BTZ black hole has smaller free energy which is a thermodynamically more preferred phase; but when the ratio is small, the hairy black hole has smaller free energy and there exists the possibility for the BTZ black hole to dress up scalar field and become hairy.

### Rotating black holes with scalar hair in three dimensions

We examine the first law of thermodynamics in (2+1)-dimensional rotating hairy black holes and find that the first law of black hole thermodynamics can be protected when the scalar field parameter $B$ is constrained to relate to the black hole size. We disclose the Hawking-Page phase transition between the hairy black holes and the pure thermal radiation. Moreover, we find that the free energies of the rotating hairy black holes depend on the ratio between the horizon size to the scalar field parameter $B$. We also compare the free energies for the hairy black hole and the BTZ black hole when they have the same temperature and angular momentum, and find that when this ratio is large, the BTZ black hole has smaller free energy which is a thermodynamically more preferred phase; but when the ratio is small, the hairy black hole has smaller free energy and there exists the possibility for the BTZ black hole to dress up scalar field and become hairy.

### $(2+1)$-dimensional charged black holes with scalar hair in Einstein-Power-Maxwell Theory [Cross-Listing]

We obtain an exact static solution to Einstein-Power-Maxwell (EPM) theory in $(2+1)$ dimensional AdS spacetime, in which the scalar field couples to gravity in a non-minimal way. After considering the scalar potential, a stable system leads to a constraint on the power parameter $k$ of Maxwell field. The solution contains a curvature singularity at the origin and is non-conformally flat. The horizon structures are identified, which indicates the physically acceptable lower bound of mass in according to the existence of black hole solutions. Especially for the cases with $k>1$, the lower bound is negative, thus there exist scalar black holes with negative mass. The null geodesics in this spacetime are also discussed in detail. They are divided into five models, which are made up of the cases with the following geodesic motions: no-allowed motion, the circular motion, the elliptic motion and the unbounded spiral motion.

### $(2+1)$-dimensional charged black holes with scalar hair in Einstein-Power-Maxwell Theory [Replacement]

We obtain an exact static solution to Einstein-Power-Maxwell (EPM) theory in $(2+1)$ dimensional AdS spacetime, in which the scalar field couples to gravity in a non-minimal way. After considering the scalar potential, a stable system leads to a constraint on the power parameter $k$ of Maxwell field. The solution contains a curvature singularity at the origin and is non-conformally flat. The horizon structures are identified, which indicates the physically acceptable lower bound of mass in according to the existence of black hole solutions. Especially for the cases with $k>1$, the lower bound is negative, thus there exist scalar black holes with negative mass. The null geodesics in this spacetime are also discussed in detail. They are divided into five models, which are made up of the cases with the following geodesic motions: no-allowed motion, the circular motion, the elliptic motion and the unbounded spiral motion.

### $(2+1)$-dimensional charged black holes with scalar hair in Einstein-Power-Maxwell Theory [Replacement]

We obtain an exact static solution to Einstein-Power-Maxwell (EPM) theory in $(2+1)$ dimensional AdS spacetime, in which the scalar field couples to gravity in a non-minimal way. After considering the scalar potential, a stable system leads to a constraint on the power parameter $k$ of Maxwell field. The solution contains a curvature singularity at the origin and is non-conformally flat. The horizon structures are identified, which indicates the physically acceptable lower bound of mass in according to the existence of black hole solutions. Especially for the cases with $k>1$, the lower bound is negative, thus there exist scalar black holes with negative mass. The null geodesics in this spacetime are also discussed in detail. They are divided into five models, which are made up of the cases with the following geodesic motions: no-allowed motion, the circular motion, the elliptic motion and the unbounded spiral motion.

### $(2+1)$-dimensional charged black holes with scalar hair in Einstein-Power-Maxwell Theory

We obtain an exact static solution to Einstein-Power-Maxwell (EPM) theory in $(2+1)$ dimensional AdS spacetime, in which the scalar field couples to gravity in a non-minimal way. After considering the scalar potential, a stable system leads to a constraint on the power parameter $k$ of Maxwell field. The solution contains a curvature singularity at the origin and is non-conformally flat. The horizon structures are identified, which indicates the physically acceptable lower bound of mass in according to the existence of black hole solutions. Especially for the cases with $k>1$, the lower bound is negative, thus there exist scalar black holes with negative mass. The null geodesics in this spacetime are also discussed in detail. They are divided into five models, which are made up of the cases with the following geodesic motions: no-allowed motion, the circular motion, the elliptic motion and the unbounded spiral motion.

### Two scalar field cosmology: Conservation laws and exact solutions [Cross-Listing]

We consider the two scalar field cosmology in a FRW spatially flat spacetime where the scalar fields interact both in the kinetic part and the potential. We apply the Noether point symmetries in order to define the interaction of the scalar fields. We use the point symmetries in order to write the field equations in the normal coordinates and we find that the Lagrangian of the field equations which admits at least three Noether point symmetries describes linear Newtonian systems. Furthermore, by using the corresponding conservation laws we find exact solutions of the field equations. Finally, we generalize our results to the case of N scalar fields interacting both in their potential and their kinematic part in a flat FRW background.

### Two scalar field cosmology: Conservation laws and exact solutions

We consider the two scalar field cosmology in a FRW spatially flat spacetime where the scalar fields interact both in the kinetic part and the potential. We apply the Noether point symmetries in order to define the interaction of the scalar fields. We use the point symmetries in order to write the field equations in the normal coordinates and we find that the Lagrangian of the field equations which admits at least three Noether point symmetries describes linear Newtonian systems. Furthermore, by using the corresponding conservation laws we find exact solutions of the field equations. Finally, we generalize our results to the case of N scalar fields interacting both in their potential and their kinematic part in a flat FRW background.

### Two scalar field cosmology: Conservation laws and exact solutions [Cross-Listing]

We consider the two scalar field cosmology in a FRW spatially flat spacetime where the scalar fields interact both in the kinetic part and the potential. We apply the Noether point symmetries in order to define the interaction of the scalar fields. We use the point symmetries in order to write the field equations in the normal coordinates and we find that the Lagrangian of the field equations which admits at least three Noether point symmetries describes linear Newtonian systems. Furthermore, by using the corresponding conservation laws we find exact solutions of the field equations. Finally, we generalize our results to the case of N scalar fields interacting both in their potential and their kinematic part in a flat FRW background.

### Black hole hair in generalized scalar-tensor gravity: An explicit example [Cross-Listing]

In a recent Letter we have shown that in shift-symmetric Horndeski theory the scalar field is forced to obtain a nontrivial configuration in black hole spacetimes, unless a linear coupling with the Gauss-Bonnet invariant is tuned away. As a result, black holes generically have hair in this theory. In this companion paper, we first review our argument and discuss it in more detail. We then present actual black hole solutions in the simplest case of a theory with the linear scalar-Gauss-Bonnet coupling. We generate exact solutions numerically for a wide range of values of the coupling and also construct analytic solutions perturbatively in the small coupling limit. Comparison of the two types of solutions indicates that non-linear effects that are not captured by the perturbative solution lead to a finite area, as opposed to a central, singularity. Remarkably, black holes have a minimum size, controlled by the length scale associated with the scalar-Gauss-Bonnet coupling. We also compute some phenomenological observables for the numerical solution for a wide range of values of the scalar-Gauss-Bonnet coupling. Deviations from the Schwarzschild geometry are generically very small.

### Black hole hair in generalized scalar-tensor gravity: An explicit example

In a recent Letter we have shown that in shift-symmetric Horndeski theory the scalar field is forced to obtain a nontrivial configuration in black hole spacetimes, unless a linear coupling with the Gauss-Bonnet invariant is tuned away. As a result, black holes generically have hair in this theory. In this companion paper, we first review our argument and discuss it in more detail. We then present actual black hole solutions in the simplest case of a theory with the linear scalar-Gauss-Bonnet coupling. We generate exact solutions numerically for a wide range of values of the coupling and also construct analytic solutions perturbatively in the small coupling limit. Comparison of the two types of solutions indicates that non-linear effects that are not captured by the perturbative solution lead to a finite area, as opposed to a central, singularity. Remarkably, black holes have a minimum size, controlled by the length scale associated with the scalar-Gauss-Bonnet coupling. We also compute some phenomenological observables for the numerical solution for a wide range of values of the scalar-Gauss-Bonnet coupling. Deviations from the Schwarzschild geometry are generically very small.

### Black hole hair in generalized scalar-tensor gravity: An explicit example [Cross-Listing]

In a recent Letter we have shown that in shift-symmetric Horndeski theory the scalar field is forced to obtain a nontrivial configuration in black hole spacetimes, unless a linear coupling with the Gauss-Bonnet invariant is tuned away. As a result, black holes generically have hair in this theory. In this companion paper, we first review our argument and discuss it in more detail. We then present actual black hole solutions in the simplest case of a theory with the linear scalar-Gauss-Bonnet coupling. We generate exact solutions numerically for a wide range of values of the coupling and also construct analytic solutions perturbatively in the small coupling limit. Comparison of the two types of solutions indicates that non-linear effects that are not captured by the perturbative solution lead to a finite area, as opposed to a central, singularity. Remarkably, black holes have a minimum size, controlled by the length scale associated with the scalar-Gauss-Bonnet coupling. We also compute some phenomenological observables for the numerical solution for a wide range of values of the scalar-Gauss-Bonnet coupling. Deviations from the Schwarzschild geometry are generically very small.

### Thermodynamics of AdS Black Holes in Einstein-Scalar Gravity

We study the thermodynamics of $n$-dimensional static asymptotically AdS black holes in Einstein gravity coupled to a scalar field with a potential admitting a stationary point with an AdS vacuum. Such black holes with non-trivial scalar hair can exist provided that the mass-squared of the scalar field is negative, and above the Breitenlohner-Freedman bound. We use the Wald procedure to derive the first law of thermodynamics for these black holes, showing how the scalar hair (or charge) contributes non-trivially in the expression. We show in general that the black hole mass can be deduced by isolating an integrable contribution to the (non-integrable) variation of the Hamiltonian arising in the Wald construction, and that this is consistent with the mass calculated using the renormalised holographic stress tensor and also, in those cases where it is defined, with the mass calculated using the conformal method of Ashtekar, Magnon and Das. Similar arguments can also be given for the smooth solitonic solutions in these theories. Neither the black hole nor the soliton solutions can be constructed explicitly, and we carry out a numerical analysis to demonstrate their existence and to provide approximate checks on some of our thermodynamic results.

### Thermodynamics of AdS Black Holes in Einstein-Scalar Gravity [Cross-Listing]

We study the thermodynamics of $n$-dimensional static asymptotically AdS black holes in Einstein gravity coupled to a scalar field with a potential admitting a stationary point with an AdS vacuum. Such black holes with non-trivial scalar hair can exist provided that the mass-squared of the scalar field is negative, and above the Breitenlohner-Freedman bound. We use the Wald procedure to derive the first law of thermodynamics for these black holes, showing how the scalar hair (or charge) contributes non-trivially in the expression. We show in general that the black hole mass can be deduced by isolating an integrable contribution to the (non-integrable) variation of the Hamiltonian arising in the Wald construction, and that this is consistent with the mass calculated using the renormalised holographic stress tensor and also, in those cases where it is defined, with the mass calculated using the conformal method of Ashtekar, Magnon and Das. Similar arguments can also be given for the smooth solitonic solutions in these theories. Neither the black hole nor the soliton solutions can be constructed explicitly, and we carry out a numerical analysis to demonstrate their existence and to provide approximate checks on some of our thermodynamic results.

### Three-dimensional black holes with conformally coupled scalar and gauge fields

We consider three-dimensional gravity with negative cosmological constant in the presence of a scalar and an Abelian gauge field. Both fields are conformally coupled to gravity, the scalar field through a nonminimal coupling with the curvature and the gauge field by means of a Lagrangian given by a power of the Maxwell one. A sixth-power self-interaction potential, which does not spoil conformal invariance is also included in the action. Using a circularly symmetric ansatz, we obtain black hole solutions dressed with the scalar and gauge fields, which are regular on and outside the event horizon. These charged hairy black holes are asymptotically anti-de Sitter spacetimes. The mass and the electric charge are computed by using the Regge-Teitelboim Hamiltonian approach. If both leading and subleading terms of the asymptotic condition of the scalar field are present, a boundary condition that functionally relates them is required for determining the mass. Since the asymptotic form of the scalar field solution is defined by two integration constants, the boundary condition may or may not respect the asymptotic conformal symmetry. An analysis of the temperature and entropy of these black holes is presented. The temperature is a monotonically increasing function of the horizon radius as expected for asymptotically anti-de Sitter black holes. However, restrictions on the parameters describing the black holes are found by requiring the entropy to be positive, which, given the nonminimal coupling considered here, does not follow the area law.

### Three-dimensional black holes with conformally coupled scalar and gauge fields [Cross-Listing]

We consider three-dimensional gravity with negative cosmological constant in the presence of a scalar and an Abelian gauge field. Both fields are conformally coupled to gravity, the scalar field through a nonminimal coupling with the curvature and the gauge field by means of a Lagrangian given by a power of the Maxwell one. A sixth-power self-interaction potential, which does not spoil conformal invariance is also included in the action. Using a circularly symmetric ansatz, we obtain black hole solutions dressed with the scalar and gauge fields, which are regular on and outside the event horizon. These charged hairy black holes are asymptotically anti-de Sitter spacetimes. The mass and the electric charge are computed by using the Regge-Teitelboim Hamiltonian approach. If both leading and subleading terms of the asymptotic condition of the scalar field are present, a boundary condition that functionally relates them is required for determining the mass. Since the asymptotic form of the scalar field solution is defined by two integration constants, the boundary condition may or may not respect the asymptotic conformal symmetry. An analysis of the temperature and entropy of these black holes is presented. The temperature is a monotonically increasing function of the horizon radius as expected for asymptotically anti-de Sitter black holes. However, restrictions on the parameters describing the black holes are found by requiring the entropy to be positive, which, given the nonminimal coupling considered here, does not follow the area law.

### Scalar and Electromagnetic Quasinormal modes of Extended black hole in F(R) gravity

In this paper we study the scalar and electromagnetic perturbations of an extended black hole in F(R) gravity. The quasinormal modes in two cases are evaluated and studied their behavior by plotting graphs in each case. To study the quasinormal mode, we use the third order WKB method. The present study shows that the absolute value of imaginary part of complex quasinormal modes increases in both cases, thus the black hole is stable against these perturbations. As the mass of the scalar field increases the imaginary part of the frequency decreases. Thus damping slows down with increasing mass of the scalar field.

### A Stochasticity Threshold in Holography and and the Instability of AdS

We give strong numerical evidence that a self-interacting probe scalar field in AdS, with only a few modes turned on initially, will undergo fast thermalization only if it is above a certain energetic threshold. Below the threshold the energy stays close to constant in a few modes for a very long time instead of cascading quickly. This indicates the existance of a Strong Stochasticity Threshold (SST) in holography. The idea of SST is familiar from certain statistical mechanical systems, and we suggest that it exists also in AdS gravity. This would naturally reconcile the generic non-linear instability of AdS observed by Bizon and Rostworowski, with the Fermi-Pasta-Ulam-Tsingou-like quasi-periodocity noticed recently for some classes of initial conditions. We show that our simple set-up captures many of the relevant features of the full gravity-scalar system.

### Quantum Corrections in Galileons from Matter Loops

Galileon interactions represent a class of effective field theories that have received much attention since their inception. They can be treated in their own right as scalar field theories with a specific global shift and Galilean symmetry or as a descendant of a more fundamental theory like massive gravity. It is well known that the Galileon theories are stable under quantum corrections thanks to the non-renormalization theorem which is not due to the symmetry unlike the misconceptions claimed in the literature. We consider different covariant couplings of this Galileon scalar field with the matter field: the conformal coupling, the disformal coupling and the longitudinal coupling. We compute the one-loop quantum corrections to the Galileon interactions from the coupling to the external matter fields. In all the considered cases of covariant couplings we show that the terms generated by one-loop matter corrections not only renormalize the Galileon interactions but also give rise to higher order derivative ghost interactions. These new interactions come at a scale suppressed by the original classical coupling scale.

### Quantum Corrections in Galileons from Matter Loops [Replacement]

Galileon interactions represent a class of effective field theories that have received much attention since their inception. They can be treated in their own right as scalar field theories with a specific global shift and Galilean symmetry or as a descendant of a more fundamental theory like massive gravity. It is well known that the Galileon theories are stable under quantum corrections thanks to the non-renormalization theorem which is not due to the symmetry unlike the misconceptions claimed in the literature. We consider different covariant couplings of this Galileon scalar field with the matter field: the conformal coupling, the disformal coupling and the longitudinal coupling. We compute the one-loop quantum corrections to the Galileon interactions from the coupling to the external matter fields. In all the considered cases of covariant couplings we show that the terms generated by one-loop matter corrections not only renormalize the Galileon interactions but also give rise to higher order derivative ghost interactions. These new interactions come at a scale suppressed by the original classical coupling scale.

### Quantum Corrections in Galileons from Matter Loops [Replacement]

Galileon interactions represent a class of effective field theories that have received much attention since their inception. They can be treated in their own right as scalar field theories with a specific global shift and Galilean symmetry or as a descendant of a more fundamental theory like massive gravity. It is well known that the Galileon theories are stable under quantum corrections thanks to the non-renormalization theorem which is not due to the symmetry unlike the misconceptions claimed in the literature. We consider different covariant couplings of this Galileon scalar field with the matter field: the conformal coupling, the disformal coupling and the longitudinal coupling. We compute the one-loop quantum corrections to the Galileon interactions from the coupling to the external matter fields. In all the considered cases of covariant couplings we show that the terms generated by one-loop matter corrections not only renormalize the Galileon interactions but also give rise to higher order derivative ghost interactions. These new interactions come at a scale suppressed by the original classical coupling scale.

### How chameleons core dwarfs with cusps

The presence of a scalar field that couples nonminimally and universally to matter can enhance gravitational forces on cosmological scales while restoring general relativity in the Solar neighborhood. In the intermediate regime, kinematically inferred masses experience an additional radial dependence with respect to the underlying distribution of matter, which is caused by the increment of gravitational forces with increasing distance from the Milky Way center. The same effect can influence the internal kinematics of subhalos and cause cuspy matter distributions to appear core-like. Specializing to the chameleon model as a worked example, we demonstrate this effect by tracing the scalar field from the outskirts of the Milky Way halo to its interior, simultaneously fitting observed velocity dispersions of chemo-dynamically discriminated red giant populations in the Fornax and Sculptor dwarf spheroidals. Whereas in standard gravity these observations suggest that the matter distribution of the dwarfs is cored, we find that in the presence of a chameleon field the assumption of a cuspy Navarro-Frenk-White profile becomes perfectly compatible with the data. Importantly, chameleon models also predict the existence of slopes between two stellar subcomponents that in Newtonian gravity would be interpreted as a depletion of matter in the dwarf center. Hence, an observation of such an apparently pathological scenario may serve as a smoking gun for the presence of a chameleon field or a similar modification of gravity, independent of baryonic feedback effects. In general, measuring the dynamic mass profiles of the Milky Way dwarfs provides stronger constraints than those inferred from the screening scale of the Solar System since these are located at greater distances from the halo center.

### Galileons and strong gravity [Cross-Listing]

In the context of a cubic Galileon model in which the Vainshtein mechanism suppresses the scalar field interactions with matter, we study low-density stars with slow rotation and static relativistic stars. We develop an expansion scheme to find approximated solutions inside the Vainshtein radius, and show that deviations from General Relativity (GR), while considering rotation, are also suppressed by the Vainshtein mechanism. In a quadratic coupling model, in which the scalarisation effect can significantly enhance deviations from GR in normal scalar tensor gravity, the Galileon term successfully suppress the large deviations away from GR. Moreover, using a realistic equation of state, we construct solutions for a relativistic star, and show that deviations from GR are more suppressed for higher density objects. However, we found that the scalar field solution ceases to exist above a critical density, which roughly corresponds to the maximum mass of a neutron star. This indicates that, for a compact object described by a polytropic equation of state, the configuration that would collapse into a black hole cannot support a non-trivial scalar field.

### Galileons and strong gravity

In the context of a cubic Galileon model in which the Vainshtein mechanism suppresses the scalar field interactions with matter, we study low-density stars with slow rotation and static relativistic stars. We develop an expansion scheme to find approximated solutions inside the Vainshtein radius, and show that deviations from General Relativity (GR), while considering rotation, are also suppressed by the Vainshtein mechanism. In a quadratic coupling model, in which the scalarisation effect can significantly enhance deviations from GR in normal scalar tensor gravity, the Galileon term successfully suppress the large deviations away from GR. Moreover, using a realistic equation of state, we construct solutions for a relativistic star, and show that deviations from GR are more suppressed for higher density objects. However, we found that the scalar field solution ceases to exist above a critical density, which roughly corresponds to the maximum mass of a neutron star. This indicates that, for a compact object described by a polytropic equation of state, the configuration that would collapse into a black hole cannot support a non-trivial scalar field.