Nonsupersymmetric attractors

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 nonsupersymmetric 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 N 1 supersymmetry, as well as nonsupersymmetric black holes in theories with N 2 supersymmetry. Similar results are also obtained for extremal black holes in asymptotically anti-de Sitter space and in higher dimensions.

supersymmetric black attractors in six and seven dimensions

“…where 49) and where Ω b a and P I a are given by 50) together with similar relation for Ω J I and P a I . Using (7.48), we can write down the Maurer-Cartan eqs for the dressed charge.…”

“…Notice by the way that there are different ways to derive the gauge invariant effective scalar potential V ef f of the 6D N = 2 supersymmetric BPS black objects [34,48,49,50].…”

Black holes and black strings of N = 2, d = 5 supergravity in the H-FGK formalism

“…Now, defining for convenience ϕ 0 ≡ 1, we can write 34) and taking into account the normalization at spatial infinity, we find that…”

“…The entropy, given by eq. (2.41), takes the explicit form 34) and the mass, given by eq. (2.39) becomes…”

Non-supersymmetric Attractors in Symmetric Coset Spaces

“…In 2005, Sen showed that all extremal black holes, both supersymmetric and non-supersymmetric (non-BPS), exhibit attractor behavior [2]: it is a result of the near-horizon geometry of extremal black holes, rather than supersymmetry. Since then, non-BPS attractors have been a very active field of research (see for instance [3,4,5,6,7,8,9,10,11,12,13,14,15]). In particular, a microstate counting for certain non-BPS black holes was proposed in [16].…”