Constraints on Black Holes in Classical and Semiclassical Theories of Gravity

TL;DR

This paper investigates the geometric constraints on static spherically symmetric black holes, especially zero temperature ones, using conditions of curvature analyticity and semiclassical trace equations, revealing non-existence within certain size ranges.

Contribution

It introduces new constraints on black hole geometries in classical and semiclassical gravity, particularly regarding zero temperature solutions with conformally invariant fields.

Findings

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

Constraints depend on the number and type of conformally invariant quantum fields.

Analyticity of curvature at the horizon imposes significant geometric restrictions.

Abstract

Constraints on the geometry of a static spherically symmetric black hole are obtained by requiring the spacetime curvature to be analytic at the event horizon. For a zero temperature black hole further constraints are obtained by also requiring that the semiclassical trace equation be satisfied when conformally invariant fields are present. It is found that zero temperature black holes whose sizes lie within a certain range do not exist. The range depends on the numbers and types of conformally invariant quantized fields that are present.