# Posts Tagged initial boundary

## Recent Postings from initial boundary

### Dependence of acoustic surface gravity on geometric configuration of matter for axisymmetric background flow in Schwarzschild metric [Cross-Listing]

In black hole evaporation process, the mass of the hole anti-correlates with the Hawking temperature enabling us to infer that the smaller mass holes will have higher surface gravity. For analogue Hawking effects, however, the acoustic surface gravity is determined by the local value of the dynamical velocity of the stationary background fluid flow and the speed of propagation of the characteristic perturbation embedded in the background fluid, as well as their space derivatives evaluated along the direction normal to the acoustic horizon, respectively. The mass of the analogue system – whether classical or quantum – does not directly contribute to extremise the value of the associated acoustic surface gravity. For general relativistic axisymmetric background fluid flow in the Schwarzschild metric, we show that the initial boundary conditions describing such axisymmetrically accreting matter flow influence the maximization scheme of the acoustic surface gravity as well as the corresponding characteristic temperature. Aforementioned background flow onto astrophysical black hole can assume three distinct geometric configurations. Identical set of initial boundary conditions can lead to entirely different phase space behaviour of the stationary flow solutions, as well as the salient features of the associated relativistic acoustic geometry. It is thus important to investigate how the acoustic surface gravity for the aforementioned classical analogue system gets influenced by the geometric configuration of the stationary axisymmetric matter flow described by various astrophysically relevant thermodynamic equations of state. Our work is useful to study the effect of gravity on the non-conventional classical features in Hawking like effect in a dispersive medium as is expected to be observed in the limit of a strong dispersion relation.

### Dependence of acoustic surface gravity on geometric configuration of matter for axisymmetric background flow in Schwarzschild metric [Replacement]

In black hole evaporation process, the mass of the hole anti-correlates with the Hawking temperature enabling us to infer that the smaller mass holes will have higher surface gravity. For analogue Hawking effects, however, the acoustic surface gravity is determined by the local value of the dynamical velocity of the stationary background fluid flow and the speed of propagation of the characteristic perturbation embedded in the background fluid, as well as their space derivatives evaluated along the direction normal to the acoustic horizon, respectively. The mass of the analogue system – whether classical or quantum – does not directly contribute to extremise the value of the associated acoustic surface gravity. For general relativistic axisymmetric background fluid flow in the Schwarzschild metric, we show that the initial boundary conditions describing such axisymmetrically accreting matter flow influence the maximization scheme of the acoustic surface gravity as well as the corresponding characteristic temperature. Aforementioned background flow onto astrophysical black hole can assume three distinct geometric configurations. Identical set of initial boundary conditions can lead to entirely different phase space behaviour of the stationary flow solutions, as well as the salient features of the associated relativistic acoustic geometry. It is thus important to investigate how the acoustic surface gravity for the aforementioned classical analogue system gets influenced by the geometric configuration of the stationary axisymmetric matter flow described by various astrophysically relevant thermodynamic equations of state. Our work is useful to study the effect of gravity on the non-conventional classical features in Hawking like effect in a dispersive medium as is expected to be observed in the limit of a strong dispersion relation.

### Dependence of acoustic surface gravity on geometric configuration of matter for axisymmetric background flow in Schwarzschild metric [Replacement]

In black hole evaporation process, the mass of the hole anti-correlates with the Hawking temperature enabling us to infer that the smaller mass holes will have higher surface gravity. For analogue Hawking effects, however, the acoustic surface gravity is determined by the local value of the dynamical velocity of the stationary background fluid flow and the speed of propagation of the characteristic perturbation embedded in the background fluid, as well as their space derivatives evaluated along the direction normal to the acoustic horizon, respectively. The mass of the analogue system – whether classical or quantum – does not directly contribute to extremise the value of the associated acoustic surface gravity. For general relativistic axisymmetric background fluid flow in the Schwarzschild metric, we show that the initial boundary conditions describing such axisymmetrically accreting matter flow influence the maximization scheme of the acoustic surface gravity as well as the corresponding characteristic temperature. Aforementioned background flow onto astrophysical black hole can assume three distinct geometric configurations. Identical set of initial boundary conditions can lead to entirely different phase space behaviour of the stationary flow solutions, as well as the salient features of the associated relativistic acoustic geometry. It is thus important to investigate how the acoustic surface gravity for the aforementioned classical analogue system gets influenced by the geometric configuration of the stationary axisymmetric matter flow described by various astrophysically relevant thermodynamic equations of state. Our work is useful to study the effect of gravity on the non-conventional classical features in Hawking like effect in a dispersive medium as is expected to be observed in the limit of a strong dispersion relation.

### The role of axisymmetric flow configuration in the estimation of the analogue surface gravity and related Hawking like temperature [Cross-Listing]

For axially symmetric flow of dissipationless inhomogeneous fluid onto a non rotating astrophysical black hole under the influence of a generalized pseudo-Schwarzschild gravitational potential, we investigate the influence of the background flow configuration on determining the salient features of the corresponding acoustic geometry. The acoustic horizon for the aforementioned flow structure has been located and the corresponding acoustic surface gravity $\kappa$ as well as the associated analogue Hawking temperature $T_{\rm AH}$ has been calculated {\it analytically}. The dependence of $\kappa$ on the flow geometry as well as on the nature of the back ground black hole space time (manifested through the nature of the pseudo-Schwarzschild potential used) has been discussed. Dependence of the value of $\kappa$ on various initial boundary conditions governing the dynamic and the thermodynamic properties of the background fluid flow has also been studied.

### On Spin Dependence of Relativistic Acoustic Geometry [Cross-Listing]

This work makes the first ever attempt to understand the influence of the black hole background space-time in determining the fundamental properties of the embedded relativistic acoustic geometry. To accomplish such task, the role of the spin angular momentum of the astrophysical black hole (the Kerr parameter $a$ — a representative feature of the background black hole metric) in estimating the value of the acoustic surface gravity (the representative feature of the corresponding analogue space time) has been investigated for axially symmetric inflow of hydrodynamic fluid onto a rotating black hole. Since almost all astrophysical black holes are supposed to posses some degree of intrinsic rotation, the influence of the Kerr parameter on classical analogue models is very important to understand. For certain values of the initial boundary conditions describing the aforementioned flow, more than one acoustic horizons, namely two black hole type and one white hole type, may form, where the surface gravity may become formally infinite at the acoustic white hole. The connection between the corresponding analogue Hawking temperature with astrophysically relevant observables associated with the spectral signature has been discussed.

### Inflation and the cosmological constant [Replacement]

A particular compensation-type solution of the main cosmological constant problem has been proposed recently, with two massless vector fields dynamically canceling an arbitrary cosmological constant \Lambda. The naive expectation is that such a compensation mechanism does not allow for the existence of an inflationary phase in the very early Universe. However, it is shown that certain initial boundary conditions on the vector fields can in fact give rise to an inflationary phase.

### Hysteresis effects and diagnostics of the shock formation in low angular momentum axisymmetric accretion in the Kerr metric

The secular evolution of the purely general relativistic low angular momentum accretion flow around a spinning black hole is shown to exhibit hysteresis effects. This confirms that a stationary shock is an integral part of such an accretion disc in the Kerr metric. The equations describing the space gradient of the dynamical flow velocity of the accreting matter have been shown to be equivalent to a first order autonomous dynamical systems. Fixed point analysis ensures that such flow must be multi-transonic for certain astrophysically relevant initial boundary conditions. Contrary to the existing consensus in the literature, the critical points and the sonic points are proved not to be isomorphic in general. Homoclinic orbits for the flow flow possessing multiple critical points select the critical point with the higher entropy accretion rate, confirming that the entropy accretion rate is the degeneracy removing agent in the system. However, heteroclinic orbits are also observed for some special situation, where both the saddle type critical points of the flow configuration possesses identical entropy accretion rate. Topologies with heteroclinic orbits are thus the only allowed non removable degenerate solutions for accretion flow with multiple critical points, and are shown to be structurally unstable. Depending on suitable initial boundary conditions, a homoclinic trajectory can be combined with a standard non homoclinic orbit through an energy preserving Rankine-Hugoniot type of stationary shock. An effective Lyapunov index has been proposed to analytically confirm why certain class of transonic flow can not accommodate shock solutions even if it produces multiple critical points. (Abridged)

### Behaviour of relativistic black hole accretion sufficiently close to the horizon

This work introduces a novel formalism to investigate the role of the spin of astrophysical black holes in determining the behaviour of matter falling onto such accretors. Equations describing the general relativistic hydrodynamic accretion flow in the Kerr metric are formulated, and stationary solutions for such flow equations are provided. The accreting matter may become multi-transonic, allowing a stationary shock to form for certain initial boundary conditions. Such a shock determines the disc geometry and can drive strong outflows. The properties of matter extremely close to the event horizon are studied as a function of the Kerr parameter, leading to the possibility of detecting a new spectral signature of black hole spin.