Brane-world cosmology with black strings

Abstract

We consider the simplest scenario when black strings / cigars penetrate the cosmological brane. As a result, the brane has a Swiss-cheese structure, with Schwarzschild black holes immersed in a Friedmann-Lema\^ıtre-Robertson-Walker brane. There is no dark radiation in the model, the cosmological regions of the brane are characterized by a cosmological constant $\Lambda$ and flat spatial sections. Regardless of the value of $\Lambda$, these brane-world universes forever expand and forever decelerate. The totality of source terms in the modified Einstein equation sum up to a dust, establishing a formal equivalence with the general relativistic Einstein-Straus model. However in this brane-world scenario with black strings the evolution of the cosmological fluid strongly depends on $\Lambda$. For $\Lambda \le 0$ it has positive energy density $\rho$ and negative pressure $p$ and at late times it behaves as in the Einstein-Straus model. For (not too high) positive values of $\Lambda$ the cosmological evolution begins with positive $\rho$ and negative $p$, but this is followed by an epoch with both $\rho$ and $p$ positive. Eventually, $\rho$ becomes negative, while $p$ stays positive. A similar evolution is present for high positive values of $\Lambda$, however in this case the evolution ends in a pressure singularity, accompanied by a regular behaviour of the cosmic acceleration. This is a novel type of singularity appearing in brane-worlds.

6 pages, 4 figures; expanded version, references added, to appear in Physical Review D

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• Strong gravitational lensing by braneworld black holes
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• Braneworld black holes in cosmology and astrophysics
• Detecting extra dimensions with gravity wave spectroscopy: the black string brane-world
• Statefinders, higher-order energy conditions and sudden future singularities
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• Braneworld gravitational collapse from a radiative bulk
• Dilatonic Equation of Hydrostatic Equilibrium and Neutron Star Structure
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