Four-dimensional anti–de Sitter toroidal black holes from a three-dimensional perspective: Full complexity

Abstract

The dimensional reduction of black hole solutions in four-dimensional (4D) general relativity is performed and new 3D black hole solutions are obtained. Considering a 4D spacetime with one spacelike Killing vector, it is possible to split the Einstein-Hilbert-Maxwell action with a cosmological term in terms of 3D quantities. Definitions of quasilocal mass and charges in 3D spacetimes are reviewed. The analysis is then particularized to the toroidal charged rotating antide Sitter black hole. The reinterpretation of the fields and charges in terms of a three-dimensional point of view is given in each case, and the causal structure analyzed.

A Reissner-Nordström+Λ Black Hole in the Friedman-Robertson-Walker Universe

“…The dimensional reduction of black hole solutions in 4D general relativity is done and new 3D black hole solutions with an isotropic event horizon are obtained by Zanchin et al [4]. Such event horizon is a typical characteristic of black hole and is an important study in our research too.…”

“…The metric (1) [considering spherical and planar (2+1)-dimensional black holes as [4], [5]] can be written in the form, where we take,…”

Are ultra-spinning Kerr-Sen-AdS$_4$ black holes always super-entropic ?

“…Next, we want to investigate the conformal boundary of the ultraspinning Kerr-Sen-AdS 4 black hole. Multiplying the metric (13) with the conformal factor l 2 /r 2 and taking the r → ∞ limit, we find that the boundary metric has the form…”

“…For example, in the five-dimensional asymptotically flat spacetimes, apart from the well-known black hole [2] which has the horizon topology of a round S 3 sphere, the black ring [3] owns the S 2 × S 1 horizon topology, while a rotating black lens solution [4] has the horizon topology of a lens-space L(n, 1). On the other hand, if the spacetime is considered to be asymptotically nonflat, it has been found that especially for the four-dimensional anti-de Sitter (AdS) spacetime, the Einstein equation also admits topological solutions with their event horizons being Riemann surfaces of any genus, namely, planar, toroidal and hyperbolic horizons [5][6][7][8][9][10][11][12][13][14][15][16][17][18], and rotating black string solutions in all dimensions [19]. Higher dimensional spacetimes can have even more rich horizon topologies; for instance, the event horizons of the ddimensional asymptotically AdS black holes are also possible to be the Einstein manifolds with positive, zero, or negative curvature [20].…”

Spherical and planar three-dimensional anti-de Sitter black holes

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The technique of dimensional reduction was used in a recent paper [1] where a three-dimensional (3D) Einstein-Maxwell-Dilaton theory was built from the usual fourdimensional (4D) Einstein-Maxwell-Hilbert action for general relativity. Starting from a class of 4D toroidal black holes in asymptotically anti-de Sitter (AdS) spacetimes several 3D black holes were obtained and studied in such a context.

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