Conserved Charges for Gravity with Locally Anti–de Sitter Asymptotics

Abstract

Abstract.A new formula for the conserved charges in 3+1 gravity for spacetimes with local AdS asymptotic geometry is proposed. It is shown that requiring the action to have an extremum for this class of asymptotia sets the boundary term that must be added to the Lagrangian as the Euler density with a fixed weight factor. The resulting action gives rise to the mass and angular momentum as Noether charges associated to the asymptotic Killing vectors without requiring specification of a reference background in order to have a convergent expression. A consequence of this definition is that any negative constant curvature spacetime has vanishing Noether charges. These results remain valid in the limit of vanishing cosmological constant.

Gravitational energy of Kerr and Kerr anti-de Sitter space-times in the teleparallel geometry

“…On the other hand in our paper the background spacetime is the Minkowski spacetime that is characterized by the total absence of energy and for which our energy expression vanishes. The result presented in [33] in the limite l → ∞, differently from that presented here for the energy expression, reduces to m that is the same obtained with Komar's charge. Moreover, as remarked by Faddeev [34], an expression for gravitational energy must vanish only in the absence of matter and gravitational field; consequently when the metric is that of the Minkowski spacetime.…”

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

“…The same action was also used in [22,23] for the derivation of the conserved current associated with a vector field.…”

“…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.…”

“…Two immediate guesses naturally can be formulated. Either the construction [22,23] is fundamentally inconsistent, then it is necessary to find the source of the inconsistency. Or, if this result is nevertheless consistent, then perhaps one can improve it in such a way that from an invariant Lagrangian, by using covariant manipulations, one would be able to derive invariant conserved quantities.…”

Boson stars with negative cosmological constant

“…It consists in adding an Euler (boundary-)term to the gravitational action [52]. The purpose is to guarantee that the action reaches an extremum for solutions which are locally AdS at the boundary.…”