Positivity Conditions for Generalised Schwarzschild Space-Times

TL;DR

This paper investigates how positivity conditions influence static, spherically symmetric deformations of Schwarzschild space-times, with implications for classical and quantum black hole models.

Contribution

It systematically analyzes the effects of various physicality conditions on space-time deformations and explores minimal realizations of stress-energy tensors in quantum black hole models.

Findings

Positivity conditions constrain space-time deformations.

Universal applicability to classical and quantum models.

Concrete models of quantum black holes discussed.

Abstract

We analyse the impact of positivity conditions on static spherically symmetric deformations of the Schwarzschild space-time. The metric is taken to satisfy, at least asymptotically, the Einstein equation in the presence of a non-trivial stress-energy tensor, on which we impose various physicality conditions. We systematically study and compare the impact of these conditions on the space-time deformations. The universal nature of our findings applies to both classical and quantum metric deformations with and without event horizons. We further discuss minimal realisations of the asymptotic stress energy tensor in terms of physical fields. Finally, we illustrate our results by discussing concrete models of quantum black holes.