Black holes that are too cold to respect cosmic censorship

Abstract

In this essay it is proved that there are black holes that are dangerously cold. In particular, by analyzing the emission spectra of highly charged black holes we reveal the fact that near-extremal black holes whose Bekenstein-Hawking temperatures lie in the regime $T_{\text{BH}}\lesssim m^6_e/e^3$ may turn into horizonless naked singularities, thus violating the cosmic censorship principle, if they emit a photon with the characteristic thermal energy $\omega=O(T_{\text{BH}})$ [here $\{m_e,e\}$ are respectively the proper mass and the electric charge of the electron, the lightest charged particle]. We therefore raise here the conjecture that, in the yet unknown quantum theory of gravity, the temperatures of well behaved black-hole spacetimes are fundamentally bounded from below by the relation $T_{\text{BH}}\gtrsim m^6_e/e^3$.