Petrov Classification and holographic reconstruction of spacetime

TL;DR

This paper presents a method to reconstruct exact four-dimensional Einstein spacetimes of specific algebraic types using boundary data and the Weyl tensor, extending beyond traditional hydrodynamic approximations.

Contribution

It introduces an explicit approach for holographic reconstruction of algebraically special spacetimes from boundary conditions, including non-hydrodynamic modes.

Findings

Reconstruction of Robinson-Trautman spacetimes of arbitrary Petrov class.

Extension to Plebanski-Demianski Petrov D family with non-zero vorticity.

Method captures modes beyond hydrodynamic derivative expansion.

Abstract

Using the asymptotic form of the bulk Weyl tensor, we present an explicit approach that allows us to reconstruct exact four-dimensional Einstein spacetimes which are algebraically special with respect to Petrov's classification. If the boundary metric supports a traceless, symmetric and conserved complex rank-two tensor, which is related to the boundary Cotton and energy-momentum tensors, and if the hydrodynamic congruence is shearless, then the bulk metric is exactly resummed and captures modes that stand beyond the hydrodynamic derivative expansion. We illustrate the method when the congruence has zero vorticity, leading to the Robinson-Trautman spacetimes of arbitrary Petrov class, and quote the case of non-vanishing vorticity, which captures the Plebanski-Demianski Petrov D family.