Petrov type I Condition and Rindler Fluid in Vacuum Einstein-Gauss-Bonnet Gravity

TL;DR

This paper demonstrates that the Petrov type I condition applies to vacuum Einstein-Gauss-Bonnet gravity solutions up to second order and allows for the correct derivation of the Rindler fluid stress tensor and transport coefficients.

Contribution

It extends the Petrov type I condition framework to Einstein-Gauss-Bonnet gravity, linking it to the dual Rindler fluid and its transport properties.

Findings

Petrov type I condition holds up to second order in Einstein-Gauss-Bonnet gravity.

Stress tensor of Rindler fluid can be recovered with correct transport coefficients.

Condition applies on finite cutoff hypersurfaces in vacuum Einstein-Gauss-Bonnet gravity.

Abstract

Recently the Petrov type I condition is introduced to reduce the degrees of freedom in the extrinsic curvature of a timelike hypersurface to the degrees of freedom in the dual Rindler fluid in Einstein gravity. In this paper we show that the Petrov type I condition holds for the solutions of vacuum Einstein-Gauss-Bonnet gravity up to the second order in the relativistic hydrodynamic expansion. On the other hand, if imposing the Petrov type I condition and Hamiltonian constraint on a finite cutoff hypersurface, the stress tensor of the relativistic Rindler fluid in vacuum Einstein-Gauss-Bonnet gravity can be recovered with correct first order and second order transport coefficients.