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Thermodynamics of Taub-NUT/Bolt-AdS Black Holes in Einstein-Gauss-Bonnet Gravity

Nov, 2008
16 pages
Published in:
  • Phys.Rev.D 79 (2009) 044002
e-Print:
DOI:
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20092013201720212024210
Abstract: (arXiv)
A revision of the existence of Taub-NUT/Bolt solutions in Einstein Gauss-Bonnet gravity with parameter α\alpha in 6-dimensions is done. We find that for all non-extremal NUT solutions of Einstein gravity with base factors B=S2×S2 \mathcal{B}=S^{2}\times S^{2} and B=CP2\mathcal{B}=\mathbb{CP}^{2}, there exist NUT solutions in Gauss-Bonnet gravity that contain these solutions in the limit of α→0\alpha \to 0. The investigation of thermodynamics of NUT/Bolt solutions for 6-dimensions is carried out. The Entropy and specific heat is calculated and it is shown that, in NUT solutions all thermodynamic quantities for both base spaces are related to each other by substituting \alpha^{\mathbb{CP}^{k}}=[(k+1)/k]\alpha ^{S^{2}\times% S^{2}\times >...S_{k}^{2}}. This relation is not true for Bolt solutions. A generalization of the thermodynamics of black holes to arbitrary even dimensions is made by new method on the basis of Gibbs-Duhamm relation and Gibbs free energy for NUT solutions. According to this method, the finite action in EGB is obtained from generalized finite action in Einstein gravity. Stability analysis is done by investigating the heat capacity and entropy in allowed range of α\alpha, Λ\Lambda and NN. For NUT solutions in dd-dimensions, there exist a stable phase at a narrow range of α\alpha, for both base factors. In Bolt solutions in 6-dimensions, the metric is completely stable for B=S2×S2\mathcal{B}=S^{2}\times S^{2}, and is completely unstable for B=CP2\mathcal{B}=\mathbb{CP}^{2} case.
  • 04.70.Bw
  • 04.70.Dy
  • 04.50.-h
  • 04.20.Jb
  • black hole: thermodynamics
  • Gauss-Bonnet term
  • stability
  • space-time: Taub-NUT
  • entropy
  • specific heat
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