Quantum backreaction for overspinning BTZ geometries

TL;DR

This paper investigates the quantum backreaction effects on overspinning BTZ geometries with naked singularities, finding that the semiclassical equations cannot be solved perturbatively, indicating severe singularity issues.

Contribution

It extends semiclassical analysis to overspinning BTZ geometries and reveals the non-renormalizability of the stress-energy tensor in this context.

Findings

Semiclassical backreaction cannot be perturbatively solved for overspinning BTZ.

The stress-energy tensor is non-renormalizable in this setting.

Naked singularities in overspinning geometries are more severe than conical ones.

Abstract

We examine the semiclassical backreaction of a conformally coupled scalar field on an overspinning BTZ geometry. This extends the work done on a similar problem for ($2+1$)- AdS geometries of the BTZ family with $|M|>|J|$. The overspinning classical solutions corresponds to $|M|<|J|$ and possess a naked singularity at $r=0$. Using the renormalized quantum stress-energy tensor for a conformally coupled scalar field on such a spacetime, we obtain the semiclassical Einstein equations, which we attempt to solve perturbatively. We show that the stress-energy tensor is non-renormalizable in this approach, and consequently the perturbative solution to the semiclassical equations in the overspinning case does not exist. This could be an indication of the fact that the naked singularity at the center of an overspinning geometry is of a more severe nature than the conical singularity found in the same family of BTZ geometries.