Black-hole evaporation, cosmic censorship, and a quantum lower bound on the Bekenstein-Hawking temperature

TL;DR

This paper investigates how quantum effects in black hole evaporation could violate cosmic censorship and proposes a quantum lower bound on the Bekenstein-Hawking temperature to prevent such violations.

Contribution

It introduces a conjecture that quantum gravity enforces a lower bound on black hole temperature, ensuring cosmic censorship is not violated during evaporation.

Findings

Quantum evaporation can turn near-extremal black holes into naked singularities.

A lower bound on Bekenstein-Hawking temperature is proposed to preserve cosmic censorship.

The bound is given by T_BH ≥ ħ² / G² M³.

Abstract

The semi-classical Hawking evaporation process of Reissner-Nordstr\"om black holes is analyzed. It is shown that this quantum mechanism may turn a near-extremal black-hole spacetime with $T_{\text{BH}}\lesssim \hbar^2/G^2M^3$ into an horizonless naked singularity, thus violating the Penrose cosmic censorship conjecture. It is therefore conjectured that, within the framework of a self-consistent quantum theory of gravity, the Bekenstein-Hawking temperature should be bounded from below by the simple relation $T_{\text{BH}}\gtrsim \hbar^2/G^2M^3$.