4-dimensional spacetimes from 2-dimensional conformal null data

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 2-dimensional classical conformal scalar field on a null boundary.