Stationary black holes and attractor mechanism Original Research Article

We investigate the symmetries of the near horizon geometry of extremal stationary black hole in four-dimensional Einstein gravity coupled to Abelian gauge fields and neutral scalars. Careful consideration of the equations of motion and the boundary conditions at the horizon imply that the near horizon geometry has image isometry. This compliments the rotating attractors proposal of that had assumed the presence of this isometry. The extremal solutions are classified into two families differentiated by the presence or absence of an ergo-region. We also comment on the attractor mechanism of both branches.