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Black ring entropy from the Weyl tensor |
Ze-Wei Zhao1, Chun-Kai Yu1,2, Nan Li1( ) |
1. Department of Physics, College of Sciences, Northeastern University, Shenyang 110819, China
2. Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China |
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Abstract A black ring is an asymptotically flat vacuum solution of the n-dimensional Einstein equations with an event horizon of topology S1×Sn−3. In this study, a connection between the black ring entropy and the Weyl tensor Cμνλρ is explored by interpreting the Weyl scalar invariant CμνλρCμνλρ as the entropy density in five-dimensional space-time. It is shown that the proper volume integral of CμνλρCμνλρ for a neutral black ring is proportional to the black ring entropy in the thin-ring limit. Similar calculations are extended to more general cases: a black string, a black ring with two angular momenta, and a black ring with a cosmological constant. The proportionality is also found to be valid for these complex black objects at the leading order.
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| Keywords
black ring
Weyl tensor
entropy
Penrose conjecture
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Corresponding Author(s):
Nan Li
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Issue Date: 25 May 2018
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