Conserved charges for even dimensional asymptotically AdS gravity theories

Aros, Rodrigo; Contreras, Mauricio; Olea, Rodrigo; Troncoso, Ricardo; Zanelli, Jorge

doi:10.1103/physrevd.62.044002

Cited by 126 publications

(180 citation statements)

References 25 publications

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“…The charges are then given as the integration on Σ (the boundary of spatial section) that is parametrized by ϕ m , 37) where σ denotes the determinant of the metric σ nm (that satisfies √ −h = N Σ √ σ) and ξ i is an asymptotic Killing vector. It can be verified, with the help of some of the identities extensively used above, that the conserved quantity (4.37) agrees with the charge obtained by the Noether theorem in differential forms language [47], and provides the correct mass for Born-Infeld-AdS black holes [7,50].…”

Section: Jhep10(2007)028mentioning

confidence: 73%

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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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Section: Jhep10(2007)028mentioning

confidence: 73%

“…This comes as a natural generalization of a strategy used for Einstein-Hilbert-AdS in any even dimension [47,48]. In this way, the total action is…”

Section: Jhep10(2007)028mentioning

confidence: 99%

Counterterms in dimensionally continued AdS gravity

Mišković¹,

Olea²

2007

J. High Energy Phys.

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“…A different approach has been proposed recently for locally AdS 4 asymptotically geometries and generalized in [53] for asymptotically AdS 2n spacetimes (see also [54]). It consists in adding an Euler (boundary-)term to the gravitational action [52].…”

Section: The Mass and The Boundary Stress Tensormentioning

confidence: 99%

Boson stars with negative cosmological constant

2003

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We consider boson star solutions in a D-dimensional, asymptotically anti-de Sitter spacetime and investigate the influence of the cosmological term on their properties. We find that for D > 4 the boson star properties are close to those in four dimensions with a vanishing cosmological constant. A different behavior is noticed for the solutions in the three dimensional case. We establish also the non-existence of static, spherically symmetric black holes with a harmonically time-dependent complex scalar field in any dimension greater than two.

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“…One of the motivations for the current study can be formulated as ''understanding Komar.' ' Another motivation is related to the interesting work of Aros et al [22,23] who have proposed a new conserved quantity for asymptotically anti-de Sitter (AdS) spacetimes. Actually, their result appeared both surprising and confusing to us.…”

Section: Introductionmentioning

confidence: 99%

Invariant conserved currents in gravity theories with local Lorentz and diffeomorphism symmetry

2006

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We discuss conservation laws for gravity theories invariant under general coordinate and local Lorentz transformations. We demonstrate the possibility to formulate these conservation laws in many covariant and noncovariant(ly looking) ways. An interesting mathematical fact underlies such a diversity: there is a certain ambiguity in a definition of the (Lorentz-) covariant generalization of the usual Lie derivative. Using this freedom, we develop a general approach to the construction of invariant conserved currents generated by an arbitrary vector field on the spacetime. This is done in any dimension, for any Lagrangian of the gravitational field and of a (minimally or nonminimally) coupled matter field. A development of the ''regularization via relocalization'' scheme is used to obtain finite conserved quantities for asymptotically nonflat solutions. We illustrate how our formalism works by some explicit examples.

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Conserved charges for even dimensional asymptotically AdS gravity theories

Cited by 126 publications

References 25 publications

Counterterms in dimensionally continued AdS gravity

Counterterms in dimensionally continued AdS gravity

Boson stars with negative cosmological constant

Invariant conserved currents in gravity theories with local Lorentz and diffeomorphism symmetry

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