Constraints on the Geometries of Black Holes in Classical and Semiclassical Gravity

TL;DR

This paper explores geometric constraints on static spherically symmetric black holes in classical and semiclassical gravity, revealing conditions under which zero temperature black holes can or cannot exist based on field types and sizes.

Contribution

It introduces new constraints on black hole geometries by analyzing curvature analyticity and semiclassical equations, highlighting the non-existence of zero temperature black holes in certain regimes.

Findings

Zero temperature black holes do not exist within certain size ranges.

The existence of black holes depends on the number and types of quantum fields.

Analyticity of curvature at the horizon constrains black hole geometries.

Abstract

Constraints on the geometries of static spherically symmetric black holes are obtained by requiring that the spacetime curvature be analytic at the event horizon. Further constraints are obtained by requiring that the semiclassical trace equation be satisfied in the case that only conformally invariant fields are present. It is found that there exists a range of sizes for which zero temperature black holes do not exist. The range depends on the number and types of quantized fields present.