Order In Metric Perturbations Research Articles

The energy–momentum complex in non-local gravity

In General Relativity, the issue of defining the gravitational energy contained in a given spatial region is still unresolved, except for particular cases of localized objects where the asymptotic flatness holds for a given spacetime. In principle, a theory of gravity is not self-consistent, if the whole energy content is not uniquely defined in a specific volume. Here, we generalize the Einstein gravitational energy–momentum pseudotensor to non-local theories of gravity where analytic functions of the non-local integral operator [Formula: see text] are taken into account. We apply the Noether theorem to a gravitational Lagrangian, supposed invariant under the one-parameter group of diffeomorphisms, that is, the infinitesimal rigid translations. The invariance of non-local gravitational action under global translations leads to a locally conserved Noether current, and thus, to the definition of a gravitational energy–momentum pseudotensor, which is an affine object transforming like a tensor under affine transformations. Furthermore, the energy–momentum complex remains locally conserved, thanks to the non-local contracted Bianchi identities. The continuity equations for the gravitational pseudotensor and the energy–momentum complex, taking into account both gravitational and matter components, can be derived. Finally, the weak field limit of pseudotensor is performed to lowest order in metric perturbation in view of astrophysical applications.

Self-supporting wormholes with a massive vector field

In this paper we consider a massive vector field in the background of a space-time obtained by certain Z2 quotient of the BTZ black hole. We analyse the back reaction of the matter field on the space-time geometry up to first order in metric perturbation. The expectation value of the stress-energy tensor can be computed exactly by considering its pull-back onto the covering space. Upon a suitable choice of the boundary condition on the vector field around a non-contractible cycle of the quotient manifold it is possible to obtain the average energy on a null geodesic to be negative there by resulting a traversable wormhole.

Brane dynamics from the first law of entanglement

In this note, we study the first law of entanglement in a boundary conformal field theory (BCFT) dual to warped AdS cut off by a brane. Exploiting the symmetry of boundary-centered half-balls in the BCFT, and using Wald’s covariant phase space formalism in the presence of boundaries, we derive constraints from the first law for a broad range of covariant bulk Lagrangians. We explicitly evaluate these constraints for Einstein gravity, and find a local equation on the brane which is precisely the Neumann condition of Takayanagi [6] at linear order in metric perturbations. This is analogous to the derivation of Einstein’s equations from the first law of entanglement entropy. This machinery should generalize to give local linearized equations of motion for higher-derivative bulk gravity with additional fields.

Does nonlocal gravity yield divergent gravitational energy-momentum fluxes?

Energy-momentum conservation requires the associated gravitational fluxes on an asymptotically flat spacetime to scale as $1/r^2$, as $r \to \infty$, where $r$ is the distance between the observer and the source of the gravitational waves. We expand the equations-of-motion for the Deser-Woodard nonlocal gravity model up to quadratic order in metric perturbations, to compute its gravitational energy-momentum flux due to an isolated system. The contributions from the nonlocal sector contains $1/r$ terms proportional to the acceleration of the Newtonian energy of the system, indicating such nonlocal gravity models may not yield well-defined energy fluxes at infinity. In the case of the Deser-Woodard model, this divergent flux can be avoided by requiring the first and second derivatives of the nonlocal distortion function $f[X]$ at $X=0$ to be zero, i.e., $f'[0] = 0 = f''[0]$. It would be interesting to investigate whether other classes of nonlocal models not involving such an arbitrary function can avoid divergent fluxes.

Beyond the linear-order relativistic effect in galaxy clustering: Second-order gauge-invariant formalism

We present the second-order general relativistic description of the observed galaxy number density in a cosmological framework. The observed galaxy number density is affected by the volume and the source effects, both of which arise due to the mismatch between physical and observationally inferred quantities such as the redshift, the angular position, the volume, and the luminosity of the observed galaxies. These effects are computed to the second order in metric perturbations without choosing a gauge condition or adopting any restrictions on vector and tensor perturbations, extending the previous linear-order calculations. Paying particular attention to the second-order gauge transformation, we explicitly isolate unphysical gauge modes and construct second-order gauge-invariant variables. Moreover, by constructing second-order tetrads in the observer's rest frame, we clarify the relation between the physical and the parametrized photon wavevectors. Our second-order relativistic description will provide an essential tool for going beyond the power spectrum in the era of precision measurements of galaxy clustering. We discuss potential applications and extensions of the second-order relativistic description of galaxy clustering.