Entropy Bound and Causality Violation in Higher Curvature Gravity

TL;DR

This paper explores how higher curvature corrections in gravity theories, such as Gauss-Bonnet and Riemann squared terms, can lead to causality violations and affect black hole entropy, challenging established bounds like the viscosity-to-entropy ratio.

Contribution

It demonstrates the connection between curvature corrections, causality violations, and entropy bounds in modified gravity theories, providing insights into quantum gravity effects.

Findings

Higher curvature terms can violate microcausality.

Such theories can have a lower shear viscosity to entropy ratio.

Results suggest possible violations of the $ ext{eta}/s$ bound in extreme conditions.

Abstract

In any quantum theory of gravity we do expect corrections to Einstein gravity to occur. Yet, at fundamental level, it is not apparent what the most relevant corrections are. We argue that the generic curvature square corrections present in lower dimensional actions of various compactified string theories provide a natural passage between the classical and quantum realms of gravity. The Gauss-Bonnet and $({\rm Riemann})^2$ gravities, in particular, provide concrete examples in which inconsistency of a theory, such as, a violation of microcausality, and a classical limit on black hole entropy are correlated. In such theories the ratio of the shear viscosity to the entropy density, $\eta/s$, can be smaller than for a boundary conformal field theory with Einstein gravity dual. This result is interesting from the viewpoint that the nuclear matter or quark-gluon plasma produced (such as at RHIC) under extreme densities and temperatures may violate the conjectured bound $\eta/s\ge 1/4\pi$, {\it albeit} marginally so.