The black ring entropy from the Weyl tensor

Abstract

A black ring is an asymptotically flat vacuum solution of the Einstein equations with an event horizon of topology $S^1\times S^2$. A connection between the black ring entropy and its Weyl tensor $C_{\mu \nu \lambda \rho }$ is explored by interpreting the Weyl scalar invariant $C_{\mu \nu \lambda \rho }{C}^{\mu \nu \lambda \rho }$ as the entropy density in 5-dimensional space-time. We calculate the proper volume integral of $C_{\mu \nu \lambda \rho }{C}^{\mu \nu \lambda \rho }$ for a neutral black ring and prove that it is proportional to the entropy of a thin black ring. Similar calculations are extended to more general cases: the black string, the black ring with two angular momenta, and the black ring with a cosmological constant. The proportionality still maintains or is valid at least at the leading order.

9 pages

References in corpus (2)

• Black ring with two angular momenta
• Naked singularities and the Weyl Curvature Hypothesis