Counterterm method in Lovelock theory and horizonless solutions in dimensionally continued gravity

Dehghani, M.; Bostani, N.; Sheykhi, Ahmad

doi:10.1103/physrevd.73.104013

Cited by 53 publications

(39 citation statements)

References 71 publications

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“…In Lovelock theory, for each Euler density of orderk in n dimension space-time, only terms withk < n exist in the equations of motion [22]. Therefore, the solutions of the Einstein-Gauss-Bonnet theory are in n ≥ 5 dimensions.…”

Section: Action and Field Equationsmentioning

confidence: 99%

Einstein-Gauss-Bonnet traversable wormholes satisfying the weak energy condition

2015

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In this paper, we explore higher-dimensional asymptotically flat wormhole geometries in the framework of Gauss-Bonnet (GB) gravity and investigate the effects of the GB term, by considering a specific radial-dependent redshift function and by imposing a particular equation of state. This work is motivated by previous assumptions that wormhole solutions were not possible for the k = 1 and α < 0 case, where k is the sectional curvature of an (n − 2)-dimensional maximally symmetric space, and α is the Gauss-Bonnet coupling constant. However, we emphasize that this discussion is purely based on a nontrivial assumption that is only valid at the wormhole throat, and cannot be extended to the entire radial-coordinate range. In this work, we provide a counterexample to this claim, and find for the first time specific solutions that satisfy the weak energy condition throughout the entire spacetime, for k = 1 and α < 0. In addition to this, we also present other wormhole solutions which alleviate the violation of the WEC in the vicinity of the wormhole throat.

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Section: Action and Field Equationsmentioning

confidence: 99%

Einstein-Gauss-Bonnet traversable wormholes satisfying the weak energy condition

2015

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“…However for the case of a boundary with zero curvature [ R abcd (γ) = 0], it is quite straightforward. This is because all curvature invariants are zero except for a constant, and so the only possible boundary counterterm is one proportional to the volume of the boundary regardless of the number of dimensions [14,21]:…”

Section: Conserved Quantitiesmentioning

confidence: 99%

“…The second integral in Eq. (3) is a boundary term which is chosen such that the variational principle is well defined [14,20,21]. In this integral…”

Section: Field Equationsmentioning

confidence: 99%

Spacetimes with longitudinal and angular magnetic fields in third order Lovelock gravity

Dehghani

Bostani

2007

Phys. Rev. D

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We obtain two new classes of magnetic brane solutions in third order Lovelock gravity. The first class of solutions yields an (n + 1)-dimensional spacetime with a longitudinal magnetic field generated by a static source. We generalize this class of solutions to the case of spinning magnetic branes with one or more rotation parameters. These solutions have no curvature singularity and no horizons, but have a conic geometry. For the spinning brane, when one or more rotation parameters are nonzero, the brane has a net electric charge which is proportional to the magnitude of the rotation parameters, while the static brane has no net electric charge. The second class of solutions yields a spacetime with an angular magnetic field. These solutions have no curvature singularity, no horizon, and no conical singularity. Although the second class of solutions may be made electrically charged by a boost transformation, the transformed solutions do not present new spacetimes. Finally, we use the counterterm method in third order Lovelock gravity and compute the conserved quantities of these spacetimes. * email address: mhd@shirazu.ac.ir

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“…Though this corresponds to a very particular case, this term is yet enough to regularize the conserved charges for horizonless extended solutions in these theories [49]. The last term of the eq.…”

Section: Jhep10(2007)028mentioning

confidence: 99%

Counterterms in dimensionally continued AdS gravity

Mišković¹,

Olea²

2007

J. High Energy Phys.

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We revise two regularization mechanisms for Lovelock gravity with AdS asymptotics. The first one corresponds to the Dirichlet counterterm method, where local functionals of the boundary metric are added to the bulk action on top of a Gibbons-Hawking-Myers term that defines the Dirichlet problem in gravity. The generalized Gibbons-Hawking term can be found in any Lovelock theory following the Myers' procedure to achieve a well-posed action principle for a Dirichlet boundary condition on the metric, which is proved to be equivalent to the Hamiltonian formulation for a radial foliation of spacetime. In turn, a closed expression for the Dirichlet counterterms does not exist for a generic Lovelock gravity. The second method supplements the bulk action with boundary terms which depend on the extrinsic curvature (Kounterterms), and whose explicit form is independent of the particular theory considered. In this paper, we use Dimensionally Continued AdS Gravity (Chern-Simons-AdS in odd and Born-Infeld-AdS in even dimensions) as a toy model to perform the first explicit comparison between both regularization prescriptions. This can be done thanks to the fact that, in this theory, the Dirichlet counterterms can be readily integrated out from the divergent part of the Dirichlet variation of the action. The agreement between both procedures at the level of the boundary terms suggests the existence of a general property of any Lovelock-AdS gravity: intrinsic counterterms are generated as the difference between the Kounterterm series and the corresponding GibbonsHawking-Myers term.

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Counterterm method in Lovelock theory and horizonless solutions in dimensionally continued gravity

Cited by 53 publications

References 71 publications

Einstein-Gauss-Bonnet traversable wormholes satisfying the weak energy condition

Einstein-Gauss-Bonnet traversable wormholes satisfying the weak energy condition

Spacetimes with longitudinal and angular magnetic fields in third order Lovelock gravity

Counterterms in dimensionally continued AdS gravity

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