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The Komar integral relation of Einstein gravity is generalized to Lovelock theories of gravity.
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1994
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J. Crisostomo, R. Troncoso and J. Zanelli, “Black hole scan,” Phys. Rev. D 62
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R. Aros, M. Contreras, R. Olea, R. Troncoso and J. Zanelli, “Conserved charges for gravity with locally AdS asymptotics,” Phys. Rev. Lett. 84
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R. Aros, M. Contreras, R. Olea, R. Troncoso and J. Zanelli, “Conserved charges for even dimensional asymptotically AdS gravity theories,” Phys. Rev. D 62
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In this and subsequent examples, we will be concerned primarily with the structure of the results and will not try to determine the overall normalization factors necessary to get precise agreement with other definitions of the mass
Cited in the paper.
Other presriptions have been put forth for computing a finite Komar-type mass for asymptotically AdS spacetimes without requiring an infinite background subtraction. In the construction of references [ 14 , 15 ] a surface term is added to the Einstein-Hilbert action with Λ ≠ 0 \Lambda\neq 0 in even dimensions. The computation of the Noether charge associated with the time translation Killing vector in a first order formalism then gives a finite result. This construction also holds for the subclass of Lovelock theories having a unique negative curvature vacuum. Reference [ 16 ] (see also earlier papers cited therein) regularizes the computation of the Euclidean Lovelock action with asymptotically AdS boundary conditions via the addition of boundary terms depending on the extrinsic curvature. This procedure also yields finite Noether charges. This method holds for all dimensions and Lovelock theories having only negative curvature vacua. The formalisms of these two constructions are sufficiently different from that of the present paper to make a comparison of the results difficult. It is worth noting that the prescription presented here holds in a wider range of settings, i.e
Cited in the paper.
Note that ω ( 0 ) a b \omega^{(0)ab} defined in this way is related to ω a b \omega^{ab} from section ( 5
Cited in the paper.
2007
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B. D. Chowdhury, S. Giusto and S. D. Mathur, “A microscopic model for the black hole - black string phase transition,” Nucl. Phys. B 762
2007
Later among the works it cites.