Energy issue for a class of modified higher order gravity black hole solutions

Cognola, Guido; Gorbunova, O.; Sebastiani, Lorenzo; Zerbini, Sergio

doi:10.1103/physrevd.84.023515

Cited by 70 publications

(72 citation statements)

References 81 publications

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“…This model has been extensively studied, and static black hole solutions have been found [40][41][42]. The corresponding topological black hole solutions have been investigated in [43][44][45][46].…”

Section: Discussionmentioning

confidence: 99%

Thermodynamics of topological black holes inR2gravity

et al. 2015

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We study topological black hole solutions of the simplest quadratic gravity action and we find that two classes are allowed. The first is asymptotically flat and mimics the Reissner-Nordström solution, while the second is asymptotically de Sitter or anti-de Sitter. In both classes, the geometry of the horizon can be spherical, toroidal or hyperbolic. We focus in particular on the thermodynamical properties of the asymptotically anti-de Sitter solutions and we compute the entropy and the internal energy with Euclidean methods. We find that the entropy is positive-definite for all horizon geometries and this allows to formulate a consistent generalized first law of black hole thermodynamics, which keeps in account the presence of two arbitrary parameters in the solution.The two-dimensional thermodynamical state space is fully characterized by the underlying scale invariance of the action and it has the structure of a projective space. We find a kind of duality between black holes and other objects with the same entropy in the state space. We briefly discuss the extension of our results to more general quadratic actions. *

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Section: Discussionmentioning

confidence: 99%

Thermodynamics of topological black holes inR2gravity

et al. 2015

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“…In Ref. [24], for a particular class of BH solutions, an identification for the BH energy has been proposed, as a quantity proportional to the unique constant of integration which appears in the explicit solutions of FðRÞ-modified gravity models in vacuum. This identification was achieved by making use of a derivation of the first law of black hole thermodynamics from the equations of motion of FðRÞ gravity, by independently evaluating the entropy via the Wald method [25] and the Hawking temperature [26] via quantum mechanical methods in curved space-times.…”

Section: Introductionmentioning

confidence: 99%

Topological electro-vacuum solutions in extended gravity

et al. 2012

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Spherically symmetric static topological black hole solutions associated with some extended higher order gravitational models in the presence of a Maxwell-field are derived by means of simple Lagrangian method, based on spherically symmetric reduction. Some new topological black hole solutions are presented and the validity of the First Law is investigated, and in these cases an expression for the energy is provided.Comment: 17 pages, published versio

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“…Some interesting work has also been done in Refs. [8][9][10] where general topological solutions in Weyl gravity were investigated. The particular case of cylindrically symmetric solutions in Weyl gravity has been considered in Refs.…”

Section: Introductionmentioning

confidence: 99%