Null infinity and extremal horizons in AdS-CFT

TL;DR

This paper explores the relationship between null infinity on the boundary of AdS spacetimes and extremal horizons in the bulk, showing how boundary geometry influences bulk near-horizon structures and stress tensor decay.

Contribution

It demonstrates that boundary null infinity can extend into extremal horizons in the bulk, with the near-horizon geometry determined by the boundary's large-scale behavior.

Findings

Bulk near-horizon geometry is fixed by boundary null infinity.

Boundary stress tensor must decay in a specific way at null infinity.

Static bulk duals with extremal horizons imply Poincare-AdS near-horizon geometry.

Abstract

We consider AdS gravity duals to CFT on background spacetimes with a null infinity. Null infinity on the conformal boundary may extend to an extremal horizon in the bulk. For example it does so for Poincare-AdS, although does not for planar Schwarzschild-AdS. If null infinity does extend into an extremal horizon in the bulk, we show that the bulk near-horizon geometry is determined by the geometry of the boundary null infinity. Hence the `infra-red' geometry of the bulk is fixed by the large scale behaviour of the CFT spacetime. In addition the boundary stress tensor must have a particular decay at null infinity. As an application, we argue that for CFT on asymptotically flat backgrounds, any static bulk dual containing an extremal horizon extending from the boundary null infinity, must have the near-horizon geometry of Poincare-AdS. We also discuss a class of boundary null infinity that cannot extend to a bulk extremal horizon, although we give evidence that they can extend to an analogous null surface in the bulk which possesses an associated scale-invariant `near-geometry'.