Horizon Holography

TL;DR

This work introduces horizon holography, proposing that holographic data on a horizon suffices to reconstruct bulk fields and the spacetime metric, and shows that the near-horizon optical metric is locally AdS-like with a conformal structure on the horizon. By deriving horizon-based two-point functions and identifying asymptotic conformal symmetries, the paper extends AdS/CFT intuition to horizons, while demonstrating that conformal weights are complex and that the dual horizon theory, if it exists, would be non-unitary. The authors provide a constructive, order-by-order reconstruction scheme for both scalar fields and the bulk metric purely from horizon data, and show that non-spherical horizons yield a new class of GR solutions whose horizon entropy remains S_BH=A_Σ/(4G). These results offer a framework to connect horizon thermodynamics and quantum aspects of gravity with a holographic perspective, while outlining key differences and open questions relative to standard AdS/CFT.

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.