Black Holes in Cosmological Backgrounds

Abstract

Black hole physics has been one of the most active areas of research in general relativity. A great deal of information has been gathered on the structure of black holes and physical phenomena that take place in their spacetimes. These spacetimes, such as those associated with the Schwarzschild and Kerr black holes, are time-independent and asymptotically flat. Time symmetry is equivalent to the requirement that the spacetime admit a global timelike Killing vector field. In a totally realistic model, however, the black hole should be imbedded in or associated with a cosmological background. In such a scenario, neither of the above two conditions would be valid. Being part of an expanding universe, the black hole would cease to be time independent, i.e., the spacetime will no longer admit a timelike Killing vector field. Furthermore, spacetime would become cosmological and non-flat at large distances from the black hole. Very little has been done in exploring such black holes. It is not at all unlikely that the structure and properties of these black holes may differ significantly, or even drastically, from the ones that have been studied. Even in the case of the latter it is well known that the introduction of rotation, i.e., the passage from the non-rotating, spherically symmetric Schwarzschild to the rotating Kerr black hole, brings about profound changes. For instance, in the case of the Schwarzschild black hole the timelike Killing vector becomes null (static limit) on the black hole which is itself a null surface (Killing event horizon) [1]. On the other hand, in the case of the Kerr black hole the stationary limit at which the timelike Killing vector becomes null does not coincide with the event horizon which is required to be a null surface. However, Kerr spacetime admits a globally hypersurface orthogonal, irrotational timelike vector field which does become null on the event horizon[2]. The separation of the stationary limit from the event horizon and the consequent existence of the ergosphere in between lead to several interesting phenomena such as the Penrose process and superradiance. Similarly, phenomena that occur in the Schwarzschild spacetime may not take place in the Kerr spacetime, for instance the generation of gravitational synchrotron radiation. In the same manner, the introduction of the cosmic background may radically transform the physics of black holes.