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Abstract

The Bekenstein – Hawking entropy for the spherical symmetric gravitational collapse, conformal field theory and the Gauss-Bonnet index

In this talk I briefly present some old and new results physically motivated by the ansatz of Verlinde based on the Cardy formula, an exact result in 2D CFT, as a consequence of the “duality” (global symmetry for CFT (and string). First, I give a resumé of previous work on ADS3 in 3D, which is dual to CFT2 on the boundary (horizon of a Black Hole in 3D). The role of the trace anomaly and the (related) Casimir effect is at the base of surface (Hawking) entropy SH and of the saturation of Bekenstein bound. Therefore, I will apply the mentioned Verlinde ansatz which connects the CFT with a FLWR universe.. I then evaluate in a simple way the Hubble entropy for a spherical collapsing object, SH showing that itnever reachs the Bekenstein-Hawking SBH black hole entropy, by using the already mentioned Verlinde ansatz. But I will show how this problem can be solved using those powerful methods. In fact SBH is equal to SH at the Schwarzschild radius RS.for a generic Black Hole. Finally I will make some comments on the “topological” origin of the area law for Black Holes and the physical properties of the “phase transition”.

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