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

Details Non-Existence of Black Holes in Certain $Λ<0$ Spacetimes Non-Existence of Black Holes in Certain $Λ<0$ Spacetimes

2002-12-19

arxiv.org/abs/gr-qc/0212079v2

Class.Quant.Grav. 20 (2003) 1635-1648

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

17 pages, Latex. Typos corrected, minor changes to the text. Accepted for publication in Classical and Quantum Gravity

Scientific paper

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.

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