Horizon Holography

TL;DR

This paper explores a holographic correspondence at black hole and de Sitter horizons, revealing conformal symmetries and reconstructing bulk spacetime from horizon data, suggesting a new perspective on horizon physics.

Contribution

It introduces a holographic framework relating horizon data to bulk spacetime, including new solutions with non-spherical horizons and horizon conformal symmetry analysis.

Findings

Identifies a conformal symmetry at horizons similar to AdS/CFT.

Reconstructs bulk metrics from horizon data, including non-spherical horizons.

Discusses horizon entropy and potential links to conformal field theories.

Abstract

A holographic correspondence between data on horizon and space-time physics is investigated. We find similarities with the AdS/CFT correspondence, based on the observation that the optical metric near the horizon describes a Euclidean asymptotically anti-de Sitter space. This picture emerges for a wide class of static space-times with a non-degenerate horizon, including Schwarzschild black holes as well as de Sitter space-time. We reveal a asymptotic conformal symmetry at the horizon. We compute the conformal weights and 2-point functions for a scalar perturbation and discuss possible connections with a (non-unitary) conformal field theory located on the horizon. We then reconstruct the scalar field and the metric from the data given on the horizon. We show that the solution for the metric in the bulk is completely determined in terms of a specified metric on the horizon. From the General Relativity point of view our solutions present a new class of space-time metrics with non-spherical horizons. The horizon entropy associated with these solutions is also discussed.