Quantum Fluctuations from Thermal Fluctuations in Jacobson Formalism

TL;DR

This paper explores how thermal fluctuations influence quantum fluctuations in black hole geometry within Jacobson's thermodynamic approach to gravity, especially as black holes shrink and quantum effects become significant.

Contribution

It proposes a method to derive quantum fluctuations of spacetime from thermal fluctuations, extending Jacobson's formalism to include quantum effects at small black hole scales.

Findings

Thermal fluctuations increase as black holes become smaller.

Quantum effects dominate at small black hole sizes.

Thermal fluctuations can be linked to quantum geometric fluctuations.

Abstract

In the Jacobson formalism general relativity is obtained from thermodynamics. This is done by using the Bekenstein-Hawking entropy-area relation. However, as a black holes will gets smaller, its temperature will increase. This will cause the thermal fluctuations to also increase, and these will in turn correct the Bekenstein-Hawking entropy-area relation. Furthermore, with the reduction in the size of the black hole, quantum effects will also start to dominate. Just as the general relativity can be obtained from thermodynamics in the Jacobson formalism, we propose that the quantum fluctuations to the geometry can be obtained from thermal fluctuations.