Two-dimensional dilaton gravity and spacetimes with finite curvature at the horizon away from the Hawking temperature

TL;DR

This paper demonstrates that in dilaton gravity, static solutions with finite horizon curvature can exist at temperatures different from the Hawking temperature, featuring a 'singularity without singularity' due to dilaton-gravity coupling divergence.

Contribution

It introduces static dilaton gravity solutions with finite horizon curvature at arbitrary temperatures, including zero, where the horizon remains regular despite quantum field divergences.

Findings

Hawking radiation is absent in these solutions.

The horizon's curvature remains finite from outside measurement.

Spacetimes are geodesically incomplete with diverging dilaton-gravity coupling.

Abstract

It is shown that static solutions with a finite curvature at the horizon may exist in dilaton gravity at temperatures $T\neq T_{H}$ (including T=0) where $T_{H} $is the Hawking one. Hawking radiation is absent and the state of a system represents thermal excitation over the Boulware vacuum. The horizon remains unattainable for a observer because of thermal divergences in the stress-energy of quantum fields there. However, the curvature at the horizon is finite, when measured from outside, since these divergences are compensated by those in gradients of a dilaton field. Spacetimes under consideration are geodesically incomplete and the coupling between dilaton and gravity diverges at the horizon, so we have ''singularity without singularity''.