Linear dilaton black holes
Abstract
We present new solutions to Einstein-Maxwell-dilaton-axion (EMDA) gravity in four dimensions describing black holes which asymptote to the linear dilaton background. In the nonrotating case they can be obtained as the limiting geometry of dilaton black holes. The rotating solutions (possibly endowed with a NUT parameter) are constructed using a generating technique based on the $\mathrm{Sp}(4,R)$ duality of the EMDA system. In a certain limit (with no event horizon present) our rotating solutions coincide with supersymmetric Israel-Wilson-Perj\`es type dilaton-axion solutions. In the presence of an event horizon supersymmetry is broken. The temperature of the static black holes is constant, and their mass does not depend on it, so the heat capacity is zero. We investigate geodesics and wave propagation in these spacetimes and find superradiance in the rotating case. Because of the nonasymptotically flat nature of the geometry, certain modes are reflected from infinity; in particular, all superradiant modes are confined. This leads to a classical instability of the rotating solutions. The nonrotating linear dilaton black holes are shown to be stable against spherical perturbations.