Large D Limit of General Relativity

Abstract

General Relativity simplifies dramatically in the infinite limit of the spacetime dimension, D. This is because gravitational fields by a black hole are confined in very near region of the black hole horizon at the large D limit. The scales of this confinement are 1/D times smaller than the black hole horizon radius. Then the gravitational fields by a black hole can be integrated out in the Einstein equations by using 1/D expansion, and, as a result, the effective theory of the black hole emerges at the large D limit. This effective theory describes instabilities of various back holes and their non-linear time evolutions in a simple form.