Non-Existence of Black Holes in Certain $\Lambda<0$ Spacetimes

TL;DR

This paper proves that under certain conditions, static regular black holes cannot exist in spacetimes with negative cosmological constant and specific topological properties, supporting conjectures related to AdS/CFT correspondence.

Contribution

The paper establishes a general non-existence theorem for static regular black holes in certain negatively curved spacetimes with infinite fundamental group, extending previous results and supporting the positive mass conjecture.

Findings

No static regular black holes with infinite fundamental group in these spacetimes.

Ruling out negative mass AdS black holes with Ricci flat scri.

Supporting the positive mass conjecture in specific cases.

Abstract

Assuming certain asymptotic conditions, we prove a general theorem on the non-existence of static regular (i.e., nondegenerate) black holes in spacetimes with a negative cosmological constant, given that the fundamental group of space is infinite. We use this to rule out the existence of regular negative mass AdS black holes with Ricci flat scri. For any mass, we also rule out a class of conformally compactifiable static black holes whose conformal infinity has positive scalar curvature and infinite fundamental group, subject to our asymptotic conditions. In a limited, but important, special case our result adds new support to the AdS/CFT inspired positive mass conjecture of Horowitz and Myers.