Weak cosmic censorship conjecture in BTZ black holes with scalar fields

TL;DR

This paper investigates the weak cosmic censorship conjecture in BTZ black holes with scalar fields, confirming that extremal and near-extremal cases cannot be overspun, thus supporting the conjecture.

Contribution

It demonstrates the validity of the weak cosmic censorship conjecture in BTZ black holes through scalar field scattering, extending thermodynamic analysis to near-extremal cases.

Findings

Extremal and near-extremal BTZ black holes cannot be overspun.

The first law of thermodynamics is recovered in non-extremal cases.

The divergence of entropy variation is addressed in the analysis.

Abstract

The weak cosmic censorship conjecture in the near-extremal BTZ black hole has been tested by the test particles and fields. It was claimed that this black hole could be overspun. In this paper, we review the thermodynamics and weak cosmic censorship conjecture in BTZ black holes by the scattering of the scalar field. The first law of thermodynamics in the non-extremal BTZ black hole is recovered. For the extremal and near-extremal black holes, due to the divergence of the variation of the entropy, we test the weak cosmic censorship conjecture by evaluating the minimum values of the function $f$. Both of the extremal and near-extremal black holes cannot be overspun.