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

The technique of dimensional reduction was used in a recent paper (Zanchin V T, Kleber A and Lemos J P S 2002 Phys. Rev. D 66 064022) where a three-dimensional (3D) Einstein–Maxwell–dilaton theory was built from the usual four-dimensional (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. In the present work we choose a particular case of the 3D action which presents Maxwell field, dilaton field and an extra scalar field, besides gravity field and a negative cosmological constant, and obtain new 3D static black hole solutions whose horizons may have spherical or planar topology. We show that there is a 3D static spherically symmetric solution analogous to the 4D Reissner–Nordstrom–AdS black hole, and obtain other new 3D black holes with planar topology. From the static spherical solutions, new rotating 3D black holes are also obtained and analysed in some detail.