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

Abstract

Abstract The semi-classical Hawking evaporation process of Reissner–Nordström black holes is analyzed. It is shown that this quantum mechanism may turn a near-extremal black-hole spacetime with $$T_{\text {BH}}\lesssim \hbar ^2/G^2M^3$$ TBH≲ħ2/G2M3 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 $$T_{\text {BH}}\gtrsim \hbar ^2/G^2M^3$$ TBH≳ħ2/G2M3 .