Black hole solution in third order Lovelock gravity has no Gauss-Bonnet limit
arXiv:1311.4911 · doi:10.1103/PhysRevD.88.087503
Abstract
We revisit the spherically symmetric third order Lovelock black hole solution in 7-dimensions. We show that the general solution for the metric function does not admit the Gauss-Bonnet (GB) limit. This is not expected due to the linear superposition of the second (GB) and third order Lovelock Lagrangians in the general action. It is found that the two branches of the GB solutions are indeed the limit of the other two complex solutions of the field equations in the third order Lovelock gravity. These two complex solutions could not be accepted as the solutions of the Einstein's field equations which are supposed to be real values function on entire real r- axis. A new solution which is only valid if the third order Lovelock parameter is small is introduced which can be considered as the natural extension of the general relativity (GR) to the third order Lovelock modified theory of gravity. We also generalize the discussion to the higher dimensional third order Lovelock gravity coupled to the matter sources with cosmological constant.
4 pages, 1 figure. Final version published in Phys. Rev. D
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Cited by in corpus (7)
- P-V Criticality of Topological Black Holes in Lovelock-Born-Infeld Gravity
- Higher-dimensional thin-shell wormholes in third-order Lovelock gravity
- Criticality and extended phase space thermodynamics of AdS black holes in higher curvature massive gravity
- Non-extended phase space thermodynamics of Lovelock AdS black holes in grand canonical ensemble
- Effects of Lovelock gravity on the Joule-Thomson expansion
- Symmetry Breaking Vacua in Lovelock Gravity
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