Quasi-topological Gravities on General Spherically Symmetric Metric

TL;DR

This paper develops a class of quasi-topological gravity theories that do not affect equations of motion for static spherically symmetric metrics, highlighting their potential effects on perturbations and holographic properties.

Contribution

The authors construct higher-order quasi-topological gravity theories up to quintic order that vanish on general static spherically symmetric metrics, extending their applicability.

Findings

Higher order terms vanish on non-stationary spherically symmetric metrics.

Theories are quasi-topological on a broader class of metrics.

Calculated holographic shear viscosity in Einstein-scalar setup.

Abstract

In this work we study a more restricted class of quasi-topological gravity theories where the higher curvature terms have no contribution to the equation of motion on general static spherically symmetric metric where $g_{tt} g_{rr} \ne \mathrm{constant}$. We construct such theories up to quintic order in Riemann tensor and observe an important property of these theories: the higher order term in the Lagrangian vanishes identically when evaluated on the most general non-stationary spherically symmetric metric ansatz. This not only signals the higher terms could only have non-trivial effects when considering perturbations, but also makes the theories quasi-topological on a much wider range of metrics. As an example of the holographic effects of such theories, we consider a general Einstein-scalar theory and calculate it's holographic shear viscosity.