  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.
