Petrov Classification and holographic reconstruction of spacetime

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 conserv...

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Bibliographic Details
Published in:arXiv.org 2018-04
Main Authors: Gath, Jakob, Mukhopadhyay, Ayan, Petkou, Anastasios C, Petropoulos, P Marios, Siampos, Konstantinos
Format: Article
Language:English
Subjects:
Classification
Cotton
Mathematical analysis
Spacetime
Tensors
Vorticity
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1506.04813