### Upper Bound for Diameter of Cosmological Black Holes and Nonexistence of Black Strings

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The diameter of the apparent horizon, defined by the distance between furthest points on the horizon, in spacetimes with a positive cosmological constant $\varLambda$ has been investigated. It is established that the diameter of the apparent horizon on the totally umbilic partial Cauchy surface cannot exceed $2\pi/\sqrt{3\varLambda}$. Then, it is argued that arbitrary long black strings cannot be formed in our universe.