Black Holes, Entropy Bound and Causality Violation

Abstract

The gravity/gauge theory duality has provided us a way of studying QCD at short distances from straightforward calculations in classical general relativity. Among numerous results obtained so far, one of the most striking is the universality of the ratio of the shear viscosity to the entropy density. For all gauge theories with Einstein gravity dual, this ratio is \eta/s=1/4\pi. However, in general higher-curvature gravity theories, including two concrete models under discussion - the Gauss-Bonnet gravity and the (Riemann)^2 gravity - the ratio \eta/s can be smaller than 1/4\pi (thus violating the conjecture bound), equal to 1/4\pi or even larger than 1/4\pi. As we probe spacetime at shorter distances, there arises an internal inconsistency in the theory, such as a violation of microcausality, which is correlated with a classical limit on black hole entropy.