Gravitational Collapse and Black Hole Thermodynamics In Braneworld Scenario

TL;DR

This paper explores gravitational collapse in a braneworld scenario with an extra timelike dimension, deriving a bouncing FLRW interior, analyzing black hole thermodynamics with bulk-brane effects, and proposing a statistical entropy model.

Contribution

It introduces a new model of gravitational collapse in a braneworld with an extra timelike dimension, deriving a bouncing interior solution and extending black hole thermodynamics.

Findings

Derived a bouncing FLRW interior solution matching a corrected Schwarzschild exterior.

Extended black hole thermodynamics to include bulk-brane corrections and an extra work term.

Proposed a statistical mechanics model for entropy that differs from geometrical entropy by a constant.

Abstract

We examine the dynamics of the gravitational collapse in a 4-dim Lorentzian brane embedded in a 5-dim bulk with an extra timelike dimension. By considering the collapse of pure dust on the brane we derive a bouncing FLRW interior solution and match it with a corrected Schwarzschild exterior geometry. In the physical domain considered for the parameters of the solution, the analytical extension is built, exhibiting an exterior event horizon and a Cauchy horizon, analogous to the Reissner-Nordstr\"om solution. For such an exterior geometry we examine the effects of the bulk-brane corrections in the Hawking radiation. In this scenario the model extends Bekenstein's black hole geometrical thermodynamics for quasi-extremal configurations, with an extra work term in the laws associated with variations of the brane tension. We also propose a simple statistical mechanics model for the entropy of the bouncing collapsed matter by quantizing its fluctuations and constructing the associated partition function. This entropy differs from the geometrical entropy by an additive constant proportional to the area of the extremal black hole and satisfies an analogous first law of thermodynamics. A possible connection between both entropies is discussed.