4-Dimensional black holes from Kaluza-Klein theories

Abstract

In this paper we consider generalizations in 4 dimensions of the Einstein-Maxwell equations which typically arise from Kaluza-Klein theories. We specify conditions such that stationary solutions lead to non-linear σ-models for symmetric spaces. Using both this group theoretic structure and some properties of harmonic maps we are able to generalize many of the known existence and uniqueness theorems for black holes in Einstein-Maxwell theory to this more general setting.

Non-supersymmetric Attractors in Symmetric Coset Spaces

“…The technique of studying stationary configurations of 4D supergravities by dimensionally reducing the 4D theories to 3D non-linear σ-models coupled to gravity was described in the pioneering work [24]. The 3D moduli space for 4D N = 2 supergravity coupled to n V vector-multiplets is well-studied, for example in [25,26,27,28].…”

Black Holes in Supergravity

“…Although the numerator group G for a timelike reduction is the same as that obtained in a spacelike reduction, the divisor group H * for a timelike reduction is a noncompact form of the spacelike divisor group H [2]. A consequence of this H → H * change and the dualization of vectors is the appearance of negative-sign kinetic terms for some 3D scalars.…”

“…The search for supergravity solutions with assumed Killing symmetries can be recast as a Kaluza-Klein problem [1,2,3]. To see this, consider a 4D theory with a nonlinear bosonic symmetry G 4 (e.g.…”

“…Breitenlohner, Gibbons and Maison [2] proved that if G is simple, all the nonextremal single-black-hole solutions of a given theory lie on the H * orbit of a Kerr solution. Moreover, all static solutions regular outside the horizon with a charge matrix satisfying Tr C 2 > 0 lie on the H * -orbit of a Schwarzschild solution.…”

“…Branes and their intersections, as well as their worldvolume modes and attached string modes, are key elements in phenomenological approaches to the marriage of string theory with particle physics phenomenology. The related study of nonsingular and horizon-free BPS gravitational solitons is also central to the "fuzzball" proposal of BPS solutions as candidate black-hole quantum microstates.The search for supergravity solutions with assumed Killing symmetries can be recast as a Kaluza-Klein problem [1,2,3]. To see this, consider a 4D theory with a nonlinear bosonic symmetry G 4 (e.g.…”