Bekenstein-Hawking entropy in expanding universes from black hole theorems

TL;DR

This paper extends the Bekenstein-Hawking entropy formula to expanding universes using black hole theorems, proposing a modified entropy expression that accounts for cosmic expansion and exploring implications for primordial inflation.

Contribution

It introduces a new entropy formulation for black holes in expanding universes, linking it to the equation of state and potential cosmological implications.

Findings

Modified Bekenstein-Hawking entropy for expanding universes

Relation between entropy and Hubble radius

Potential connection to primordial inflation mechanisms

Abstract

We show that the use of suitable theorems for black hole formation in Friedmann expanding universes leads to a modification of the Bekenstein-Hawking entropy. By adopting an argument similar to the original Bekenstein one, we write down the expression for the Bekenstein-Hawking entropy suitable for non-static isotropic expanding universes together with the equation of state of a black hole. This equation can be put in a form similar to the one of an ideal gas but with a factor depending on the Hubble radius. Moreover, we give some argument on a possible relation between our entropy expression and the Cardy-Verlinde one. Finally, we explore the possibility that primordial inflation is due to black hole evaporation in our context.