A quantum bound on the thermodynamic description of gravity

TL;DR

This paper investigates the limits of thermodynamic descriptions of black holes, providing evidence that quantum effects cause the first law of thermodynamics to fail in the low-temperature regime of near-extremal black holes.

Contribution

It introduces a quantum bound indicating the breakdown of thermodynamic laws for near-extremal black holes at low temperatures.

Findings

Thermodynamic description breaks down at low black hole temperatures.

Quantum effects invalidate the first law in the near-extremal regime.

A specific temperature-radius bound for the breakdown is established.

Abstract

The seminal works of Bekenstein and Hawking have revealed that black holes have a well-defined thermodynamic description. In particular, it is often stated in the physical literature that black holes, like mundane physical systems, obey the first law of thermodynamics: $\Delta S=\Delta E/T_{\text{BH}}$, where $T_{\text{BH}}$ is the Bekenstein-Hawking temperature of the black hole. In the present work we test the regime of validity of the thermodynamic description of gravity. In particular, we provide compelling evidence that, due to quantum effects, the first law of thermodynamics breaks down in the low-temperature regime $T_{\text{BH}}\times r_{\text{H}}\lesssim ({{\hbar}/{r_{\text{H}}}})^2$ of near-extremal black holes (here $r_{\text{H}}$ is the radius of the black-hole horizon).