Reconstructing Minkowski Space-Time

TL;DR

This paper advances the holographic duality understanding for Minkowski space-time by analyzing linear gravitational perturbations and reconstructing the space-time from boundary data, focusing on de Sitter reductions and black hole information encoding.

Contribution

It develops a method to reconstruct Ricci-flat Minkowski space-time from holographic data by analyzing linear gravitational perturbations and their reduction to de Sitter space equations.

Findings

Reduction of Minkowski perturbations to de Sitter field equations

Identification of boundary data for gravitational fields

Encoding of black hole mass in holographic data

Abstract

Minkowski space is a physically important space-time for which the finding an adequate holographic description is an urgent problem. In this paper we develop further the proposal made in hep-th/0303006 for the description as a duality between Minkowski space-time and a Conformal Field Theory defined on the boundary of the light-cone. We focus on the gravitational aspects of the duality. Specifically, we identify the gravitational holographic data and provide the way Minkowski space-time (understood in more general context as a Ricci-flat space) is reconstructed from the data. In order to avoid the complexity of non-linear Einstein equations we consider linear perturbations and do the analysis for the perturbations. The analysis proceeds in two steps. We first reduce the problem in Minkowski space to an infinite set of field equations on de Sitter space one dimension lower. These equations are quite remarkable: they describe massless and massive gravitons in de Sitter space. In particular, the partially massless graviton appears naturally in this reduction. In the second step we solve the graviton field equations and identify the holographic boundary data. Finally, we consider the asymptotic form of the black hole space-time and identify the way the information about the mass of the static gravitational configuration is encoded in the holographic data.