The mass formula for an exotic BTZ black hole

TL;DR

This paper introduces a mass formula for exotic BTZ black holes, demonstrating that their energy is represented by angular momentum and confirming no violation of cosmic censorship during energy extraction processes.

Contribution

It proposes a new mass formula for exotic BTZ black holes and clarifies their energy representation, ensuring consistency with thermodynamics and cosmic censorship.

Findings

The total energy of exotic BTZ black holes is represented by angular momentum.

The mass formula prevents violation of weak cosmic censorship.

Thermodynamics relates only to the black hole's mass, not other energy forms.

Abstract

An exotic Banados-Teitelboim-Zanelli (BTZ) black hole has an angular momentum larger than its mass in three dimension (3D), which suggests the possibility that cosmic censorship could be violated if angular momentum is extracted by the Penrose process. In this paper, we propose a mass formula for the exotic BTZ black hole and show no violation of weak cosmic censorship in the gedanken process above by understanding properly its mass formula. Unlike the other black holes, the total energy of the exotic BTZ black hole is represented by the angular momentum instead of the mass, which supports a basic point of view that the same geometry should be determined by the same energy in 3D general relativity whose equation of motion can be given either by normal 3D Einstein gravity or by exotic 3D Einstein gravity. However, only the mass of the exotic black hole is related to the thermodynamics and other forms of energy are "dumb", which is consistent with the earlier thermodynamic analysis about exotic black holes.