Singularity resolution in spherically reduced 2D semiclassical gravity with negative central charge

TL;DR

This paper demonstrates that reversing the sign of the central charge in 2D semiclassical gravity models removes curvature singularities, resulting in horizonless, asymptotically flat geometries, and discusses the physical implications of negative central charges.

Contribution

It shows that negative central charges in 2D dilaton gravity eliminate singularities, providing new insights into quantum backreaction effects and their physical significance.

Findings

Negative central charge removes curvature singularity.

Resulting geometry is horizonless and asymptotically flat.

Findings align with similar results in the CGHS model.

Abstract

We analyze the semiclassical Schwarzschild geometry in the Boulware quantum state in the framework of two-dimensional (2D) dilaton gravity. The classical model is defined by the spherical reduction of Einstein's gravity sourced with conformal scalar fields. The expectation value of the stress-energy tensor in the Boulware state is singular at the classical horizon of the Schwarzschild spacetime, but when backreaction effects are considered, previous results have shown that the 2D geometry is horizonless and described by a non-symmetric wormhole with a curvature singularity on the other side of the throat. In this work we show that reversing the sign of the central charge of the conformal matter removes the curvature singularity of the 2D backreacted geometry, which happens to be horizonless and asymptotically flat. This result is consistent with a similar analysis recently performed for the CGHS model. We also argue the physical significance of negative central charges in conformal anomalies from a four-dimensional perspective.