Universal Property of Quantum Gravity implied by Bekenstein-Hawking Entropy and Boltzmann formula

TL;DR

This paper proposes that quantum gravity universally exhibits repulsive behavior at the Planck scale, based on thermodynamic principles and the Bekenstein-Hawking entropy, independent of specific models.

Contribution

It introduces a model-independent universal property of quantum gravity derived from black hole thermodynamics and the Boltzmann formula, suggesting repulsive gravity at the Planck scale.

Findings

Universal property implies repulsive gravity at Planck length

Stationary black holes as thermal equilibrium states require this property

Possible correction to Einstein's equation at quantum gravity scale

Abstract

We search for a universal property of quantum gravity. By "universal", we mean the independence from any existing model of quantum gravity (such as the super string theory, loop quantum gravity, causal dynamical triangulation, and so on). To do so, we try to put the basis of our discussion on theories established by some experiments. Thus, we focus our attention on thermodynamical and statistical-mechanical basis of the black hole thermodynamics: Let us assume that the Bekenstein-Hawking entropy is given by the Boltzmann formula applied to the underlying theory of quantum gravity. Under this assumption, the conditions justifying Boltzmann formula together with uniqueness of Bekenstein-Hawking entropy imply a reasonable universal property of quantum gravity. The universal property indicates a repulsive gravity at Planck length scale, otherwise stationary black holes can not be regarded as thermal equilibrium states of gravity. Further, in semi-classical level, we discuss a possible correction of Einstein equation which generates repulsive gravity at Planck length scale. (This article is bease on ref.[4] (Entropy 13(2011)1611-1647), but the conclusion in sec.4 is modified from ref.[4].)