4-dimensional spacetimes from 2-dimensional conformal null data

TL;DR

This paper explores a classical analogue of the holographic principle in general relativity, establishing a correspondence between certain 4D spacetimes and 2D conformal fields on null boundaries, particularly for black hole spacetimes.

Contribution

It demonstrates a partial classical holographic correspondence for vacuum Petrov type D spacetimes with Killing tensors, linking bulk gravity to boundary conformal fields.

Findings

Establishes a one-to-one correspondence for specific spacetimes

Links bulk gravitational data to boundary conformal scalar fields

Focuses on astrophysical black hole spacetimes

Abstract

In this paper we investigate whether the holographic principle proposed in string theory has a classical counterpart in general relativity theory. We show that there is a partial correspondence: at least in the case of vacuum Petrov type D spacetimes that admit a non-trivial Killing tensor, which encompass all the astrophysical black hole spacetimes, there exists a one to one correspondence between gravity in bulk and a two dimensional classical conformal scalar field on a null boundary.