Holography with Timelike Bulk Hypersurfaces

TL;DR

This paper introduces a novel holographic principle that extends the traditional lightsheet-based approach to include entropy constraints on timelike bulk hypersurfaces, supported by a classical proof.

Contribution

It proposes a new holographic framework involving timelike hypersurfaces and provides a classical proof based on a local entropy condition.

Findings

The new holographic principle constrains entropy on timelike hypersurfaces.

A classical proof validates the proposed entropy bound.

Extends holography beyond lightlike surfaces.

Abstract

We propose a new version of holographic principle. This proposal extends the holographic principle based on the lightsheet to the one constraining the entropy passing through bulk hypersurface of timelike geodesics by the boundary area divided by 4G. We give a proof of the proposal in the classical regime based on a simple local entropy condition.