Quantum Backreaction on Three-Dimensional Black Holes and Naked Singularities

TL;DR

This paper analytically studies how quantum scalar fields influence three-dimensional rotating spacetimes, revealing effects like horizon growth, singularity formation, and quantum censorship of naked singularities.

Contribution

It provides the first analytical investigation of quantum backreaction on rotating BTZ geometries, showing horizon formation and singularity shielding due to quantum effects.

Findings

Quantum effects increase the event horizon and ergosphere size.

Quantum effects induce a curvature singularity at the Cauchy horizon.

Quantum effects create a horizon shielding naked singularities.

Abstract

We analytically investigate backreaction by a quantum scalar field on two rotating Ba\~nados-Teitelboim-Zanelli (BTZ) geometries: that of a black hole and that of a naked singularity. In the former case, we explore the quantum effects on various regions of relevance for a rotating black hole space-time. We find that the quantum effects lead to a growth of both the event horizon and the radius of the ergosphere, and to a reduction of the angular velocity, compared to the unperturbed values. Furthermore, they give rise to the formation of a curvature singularity at the Cauchy horizon and show no evidence of the appearance of a superradiant instability. In the case of a naked singularity, we find that quantum effects lead to the formation of a horizon that shields it, thus supporting evidence for the r\^ole of quantum mechanics as a cosmic censor in nature.