The large D limit of General Relativity

TL;DR

This paper explores the behavior of General Relativity in the limit of infinitely many dimensions, revealing simplified dynamics and developing an effective theory for black hole phenomena, with analytical results on scalar absorption and black brane instability.

Contribution

It introduces a leading-order effective theory for black hole dynamics at large D and provides analytical calculations for scalar absorption and black brane instability.

Findings

Simplification of General Relativity at large D

Analytical scalar absorption probability calculation

Accurate results for black brane instability

Abstract

General Relativity simplifies dramatically in the limit that the number of spacetime dimensions D is infinite: it reduces to a theory of non-interacting particles, of finite radius but vanishingly small cross sections, which do not emit nor absorb radiation of any finite frequency. Non-trivial black hole dynamics occurs at length scales that are 1/D times smaller than the horizon radius, and at frequencies D times larger than the inverse of this radius. This separation of scales at large D, which is due to the large gradient of the gravitational potential near the horizon, allows an effective theory of black hole dynamics. We develop to leading order in 1/D this effective description for massless scalar fields and compute analytically the scalar absorption probability. We solve to next-to-next-to-leading order the black brane instability, with very accurate results that improve on previous approximations with other methods. These examples demonstrate that problems that can be formulated in an arbitrary number of dimensions may be tractable in analytic form, and very efficiently so, in the large D expansion.