On Black Hole Scalar Hair in Asymptotically Anti de Sitter Spacetimes

TL;DR

This paper analyzes the emergence of scalar hair on black holes in asymptotically Anti de Sitter spacetimes, highlighting differences from flat spacetime and implications for the ADS/CFT correspondence.

Contribution

It demonstrates the conditions under which Schwarzschild Anti de Sitter black holes become unstable and develop scalar hair, revealing new insights into black hole solutions in AdS spaces.

Findings

Hairy black hole solutions exist in AdS with scalar fields.

Schwarzschild AdS black holes can become unstable under certain conditions.

Implications for the ADS/CFT correspondence are discussed.

Abstract

The unexpected discovery of hairy black hole solutions in theories with scalar fields simply by considering asymptotically Anti de-Sitter, rather than asymptotically flat, boundary conditions is analyzed in a way that exhibits in a clear manner the differences between the two situations. It is shown that the trivial Schwarzschild Anti de Sitter becomes unstable in some of these situations, and the possible relevance of this fact for the ADS/CFT conjecture is pointed out.