Non-Supersymmetric Attractors

TL;DR

This paper demonstrates that the attractor mechanism, previously associated with supersymmetric black holes, also applies to non-supersymmetric extremal black holes in various theories and spacetime backgrounds, broadening its scope.

Contribution

It establishes the conditions under which the attractor mechanism works for non-supersymmetric extremal black holes using an effective potential approach.

Findings

Attractor mechanism applies to non-supersymmetric extremal black holes.

Conditions for attractor behavior are expressed via an effective potential.

Results extend to asymptotically Anti-de Sitter space and higher dimensions.

Abstract

We consider theories with gravity, gauge fields and scalars in four-dimensional asymptotically flat space-time. By studying the equations of motion directly we show that the attractor mechanism can work for non-supersymmetric extremal black holes. Two conditions are sufficient for this, they are conveniently stated in terms of an effective potential involving the scalars and the charges carried by the black hole. Our analysis applies to black holes in theories with ${\cal N} \le 1$ supersymmetry, as well as non-supersymmetric black holes in theories with ${\cal N} = 2$ supersymmetry. Similar results are also obtained for extremal black holes in asymptotically Anti-de Sitter space and in higher dimensions.