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

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 anti–de 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.