Overcharging dilaton black holes in 2+1 dimensions to extremality and beyond

TL;DR

This paper demonstrates that in 2+1 dimensional charged dilaton black holes, it is possible to overcharge and reach or surpass extremality using test particles, violating cosmic censorship and thermodynamic laws.

Contribution

It shows that charged dilaton black holes in 2+1 dimensions can be overcharged and driven beyond extremality, unlike other black hole types, challenging existing conjectures.

Findings

Overcharging is possible for extremal and nearly extremal black holes.

Nearly extremal black holes can be driven to and beyond extremality.

No phase transitions prevent naked singularity formation.

Abstract

We test whether static charged dilaton black holes in 2+1 dimensions can be turned into naked singularities, by sending in test particles from infinity. We derive that overcharging is possible and generic for both extremal and nearly extremal black holes. Our analysis also imply that nearly extremal charged dilaton black holes can be continuously driven to extremality and beyond, unlike nearly extremal Ba\u{n}ados-Teitelboim-Zanelli, Kerr and Reissner-Nordstr\"{o}m black holes which are overspun or overcharged by a discrete jump. Thus the weak form of the cosmic censorship conjecture and the third law of black hole thermodynamics are both violated in the interaction of charged dilaton black holes in 2+1 dimensions, with test particles. We also derive that there exists no points where the heat capacity vanishes or diverges in the transition from black holes to naked singularities. The phase transitions that could potentially prevent the formation of naked singularities do not occur.