Constraints on Black Holes in Classical and Semiclassical Theories of Gravity

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. Typeset using REVT E X I. INTRODUCTION One of the unanswered questions in semiclassical gravity is how quantized fields alter the spacetime geometry near the event horizon of a black hole. This is important because the thermodynamic properties of a black hole are determined by the geometry at the event horizon. Some work has been done to answer this question using linearized semiclassical gravity and either analytical approximations or numerical co..