Kaluza-Klein gravity

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-linearσ-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.

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$4$-dimensional black holes from Kaluza-Klein theories

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.

Non-supersymmetric attractors

Recent work has demonstrated an attractor mechanism for extremal rotating black holes subject to the assumption of a near-horizon SO(2,1) symmetry. We prove the existence of this symmetry for any extremal black hole with the same number of rotational symmetries as known four and five dimensional solutions (including black rings). The result is valid for a general two-derivative theory of gravity coupled to abelian vectors and uncharged scalars, allowing for a non-trivial scalar potential. We prove that it remains valid in the presence of higher-derivative corrections. We show that SO(2,1)-symmetric near-horizon solutions can be analytically continued to give SU(2)-symmetric black hole solutions. For example, the near-horizon limit of an extremal 5D Myers-Perry black hole is related by analytic continuation to a non-extremal cohomogeneity-1 Myers-Perry solution.

https://iopscience.iop.org/article/10.1088/0264-9381/24/16/012/pdf

Near-horizon symmetries of extremal black holes

All stationary, spherically symmetric solutions of Jordan's unified theory of gravity and electromagnetism are constructed. Conditions for the solutions are given to represent black holes with nonvanishing mass, electric and magnetic charge.

P. Dobiasch

Papers

Stationary, Spherically Symmetric Solutions of Jordan's Unified Theory of Gravity and Electromagnetism