Finite Black Hole Entropy and String Theory

TL;DR

This paper explores how string theory's maximum temperature and acceleration limits can regularize black hole entropy calculations, leading to a finite entropy consistent with the Bekenstein-Hawking formula.

Contribution

It introduces a natural cutoff in spacetime near black hole horizons based on string theory limits, providing a finite entropy derivation.

Findings

Finite black hole entropy consistent with Bekenstein-Hawking formula

Maximum acceleration imposes a cutoff near the horizon

String modes' entropy matches black hole entropy under certain conditions

Abstract

An accelerating observer sees a thermal bath of radiation at the Hawking temperature which is proportional to the acceleration. Also, in string theory there is a Hagedorn temperature beyond which one cannot go without an infinite amount of energy. Several authors have shown that in the context of Hawking radiation a limiting temperature for string theory leads to a limiting acceleration, which for a black hole implies a minimum distance from the horizon for an observer to remain stationary. We argue that this effectively introduces a cutoff in Rindler space or the Schwarzschild geometry inside of which accelerations would exceed this maximum value. Furthermore, this natural cutoff in turn allows one to define a finite entropy for Rindler space or a black hole as all divergences were occurring on the horizon. In all cases if a particular relationship exists between Newton's constant and the string tension then the entropy of the string modes agrees with the Bekenstein-Hawking formula.