Black Holes in Infinite Dimensions

Sammanfattning: The description of a black hole in the limit of very large number of spacetime dimensions D simplifies considerably. When D approaches infinity, the gravitational field lines of force are infinitely dispersed among the infite number of spacetime directions. This implies that outside the near-horizon region of the black hole the background spacetime will be flat, while the gravitational field will be strongly localized near the horizon. Thus, we can attempt to replace the black hole by a sphere cut off at the horizon in an empty background. In this project we attempt to obtain the physical conditions that the sphere has to meet in order to be able to reproduce the dynamics of the black hole when embedded in the empty background. This is described in the effective equation that we derive starting from the Einstein equations. Finally, we apply our results to take a look at ’black droplets’, black holes localized at the boundary of AdS and extending a finite distance into the bulk.