Rotating charged black strings and three-dimensional black holes

Stationary black holes in a generalized three-dimensional theory of gravity

“…[17], where the three-dimensional gravity theory was obtained through dimensional reduction from four-dimensional General Relativity with one Killing vector field. This solution was further generalized to include charge [18]. Some of these black hole solutions were also analysed in ref.…”

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

“…Moreover, A i couples to Ψ through kinetic terms, whereas A i couples through potential terms. Both gauge charges can be obtained by the Gauss law, adapted to non-asymptotically flat stationary spacetimes and to the presence of the dilaton [29,31] (see also [11,12])…”

“…Then the conjecture says that if one has, e.g., a 10-dimensional type IIB supergravity, compactified into a BTZ × S 3 × T 4 spacetime, the BTZ in the bulk corresponds to a thermal state in the boundary CFT [19]. It is also possible to embed the 4D toroidal black holes [11,12] in a higher-D string theory such that they can be interpreted as the near horizon structures of an M2 brane rotating in extra dimensions [20]. Now, in order to find solutions in a given dimension, n say, one usually starts from the action of gravity theory with the generic dilaton and gauge vector couplings in that dimension, derives the corresponding equations of motion, tries an ansatz for the solution and then finally from the differential equations finds the black hole solutions compatible with the ansatz.…”

“…For instance, upon reducing 4D Einstein-Maxwell theory with Λ and with one spatial Killing vector it was shown in [11,12] that it gives rise to a 3D Brans-Dicke-Maxwell theory with its own black hole, which when reinterpreted back in 4D is a black hole with a toroidal horizon. One can then naturally extend the whole set to Brans-Dicke theories [13,14].…”

“…It is our aim to apply the dimensional reduction technique to construct 3D black holes from the 4D toroidal AdS black holes [11,12]. Sect.…”