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Holographic stress-energy tensor near the Cauchy horizon inside a rotating black hole

Akihiro Ishibashi1,*, Kengo Maeda2,†, and Eric Mefford3,‡

  • 1Department of Physics, Kindai University, Higashi-Osaka 577-8502, Japan
  • 2Faculty of Engineering, Shibaura Institute of Technology, Saitama 330-8570, Japan
  • 3Department of Physics, University of California, Santa Barbara, California 93106, USA

  • *akihiro@phys.kindai.ac.jp
  • †maeda302@sic.shibaura-it.ac.jp
  • ‡mefford@physics.ucsb.edu
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Phys. Rev. D 96, 024005 – Published 10 July, 2017

DOI: https://doi.org/10.1103/PhysRevD.96.024005

Abstract

We investigate a stress-energy tensor for a conformal field theory (CFT) at strong coupling inside a small five-dimensional rotating Myers-Perry black hole with equal angular momenta by using the holographic method. As a gravitational dual, we perturbatively construct a black droplet solution by applying the “derivative expansion” method, generalizing the work of Haddad [Classical Quantum Gravity 29, 245001 (2012)] and analytically compute the holographic stress-energy tensor for our solution. We find that the stress-energy tensor is finite at both the future and past outer (event) horizons and that the energy density is negative just outside the event horizons due to the Hawking effect. Furthermore, we apply the holographic method to the question of quantum instability of the Cauchy horizon since, by construction, our black droplet solution also admits a Cauchy horizon inside. We analytically show that the null-null component of the holographic stress-energy tensor negatively diverges at the Cauchy horizon, suggesting that a singularity appears there, in favor of strong cosmic censorship.

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Phys. Rev. D 96, 024005– Published 10 July, 2017
  • Received 4 April 2017
Article part of CHORUS

© 2017 American Physical Society

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