Effective Gravitational Equations Research Articles

Analytic and exponentially localized braneworld Reissner-Nordström-AdS solution: A top-down approach

In this work, we construct a five-dimensional spherically-symmetric, charged and asymptotically Anti-de Sitter black hole with its singularity being point-like and strictly localised on our brane. In addition, the induced brane geometry is described by a Reissner-Nordstr\"{o}m-(A)dS line-element. We perform a careful classification of the horizons, and demonstrate that all of them are exponentially localised close to the brane thus exhibiting a pancake shape. The bulk gravitational background is everywhere regular, and reduces to an AdS$_5$ spacetime right outside the black-hole event horizon. This geometry is supported by an anisotropic fluid with only two independent components, the energy density $\rho_E$ and tangential pressure $p_2$. All energy conditions are respected close to and on our brane, but a local violation takes place within the event horizon regime in the bulk. A tensor-vector-scalar field-theory model is built in an attempt to realise the necessary bulk matter, however, in order to do so, both gauge and scalar degrees of freedom need to turn phantom-like at the bulk boundary. The study of the junction conditions reveals that no additional matter needs to be introduced on the brane for its consistent embedding in the bulk geometry apart from its constant, positive tension. We finally compute the effective gravitational equations on the brane, and demonstrate that the Reissner-Nordstr\"{o}m-(A)dS geometry on our brane is caused by the combined effect of the five-dimensional geometry and bulk matter with its charge being in fact a tidal charge.

Braneworld gravity within non-conservative gravitational theory

We investigate the braneworld gravity starting from the non-conservative gravitational field equations in a five-dimensional bulk. The approach is based on the Gauss–Codazzi formalism along with the study of the braneworld consistency conditions. The effective gravitational equations on the brane are obtained and the constraint leading to a brane energy-momentum conservation is analyzed.

Cosmology and short-distance gravity

If the observed dark-energy density [Formula: see text] is interpreted as the net contribution of the energy density of the vacuum, [Formula: see text], and the corresponding vacuum length scale [Formula: see text] as the cutoff scale controlling the low-energy, effective field-theory limit of gravity, it follows that the conventional cosmological scenario based on the effective gravitational equations may be valid only up to the TeV energy scale. Such a possibility would be strongly disfavored by the existence of a relic background of primordial gravitational radiation of intensity compatible with present (or near future) experimental sensitivities.

Large-scale structure challenges dilaton gravity in a 5D brane scenario with AdS bulk

We study a theory of dilaton gravity in a five-dimensional brane scenario, with a non-minimal coupling of the dilaton to the matter content of the universe localized on the brane. The effective gravitational equations at the brane are derived in the Einstein frame in the covariant approach, addressing certain misconceptions in the literature. We then investigate whether the observed large-scale structure of the universe can exist on the brane in this dilaton gravity scenario with an exact anti de Sitter bulk, assuming that the matter energy–momentum tensor has the form of an inhomogeneous perfect fluid. The corresponding constraint on the spatial derivative of the matter energy density is derived, and subsequently quantified using the current limits resulting from searches for variation of the Newton's constant. By confronting it with the observational data from galaxy surveys, we show that up to scales of the order of 104 Mpc, the derived bound on the spatial derivative of the matter energy density does not allow for the existence of the large-scale structure as observed today. Thus, such a dilaton gravity brane scenario is ruled out.

Degravitation features in the cascading gravity model

We obtain the effective gravitational equations on the codimension-2 and codimension-1 branes in the cascading gravity model. We then apply our formulation to the cosmological case and obtain the effective Friedmann equations on the codimension-2 brane, which are generically given in terms of integro-differential equations. Adopting an approximation for which the thickness of the codimension-2 brane is much smaller than the Hubble horizon, we study the Minkowski and de Sitter codimension-2 brane solutions. Studying the cosmological solutions shows that the cascading model exhibits the features necessary for degravitation of the cosmological constant. We also show that only the branch which does not have the smooth limit to the self-accelerating branch in five-dimensional model in the absence of the bulk gravity can satisfy the null energy condition as the criterion of the stability. Note that our solutions are obtained in a different setup from that of the original cascading gravity model in the sense that the codimension-1 brane contains matter fields other than the pure tension.

Higher order dilaton gravity: brane equations of motion in the covariant formulation

Dilaton gravity with general brane localized interactions is investigated in this paper. Models with corrections up to arbitrary order in field derivatives are considered. Effective gravitational equations of motion at the brane are derived in the covariant approach. Dependence of such brane equations on the bulk quantities is also discussed. It is shown that the number of the bulk independent brane equations of motion depends strongly on the symmetries assumed for the model and for the background. Examples with two and four derivatives of the fields are presented in more detail.

Effective gravitational equations on brane world with induced gravity described by f(R) term

In this article we study a generalization of Dvali-Gabadadze-Porrati scenarios, where the effective theory of gravity induced on the brane is given by a f(R) term. We obtain the effective gravitational equations and the effective FLRW cosmologicalequation on the brane of this model. We show that thisgeneralization has also two regime, a 5D regime a low energiesthat has a self-accelerated branch of interest for cosmology and a4D regime at high energies that it is described a modifiedgravitational theory.

Effective gravitational equations induced by quantum effects of a scalar field in the Bianchi type IX spaces

The effective gravitational equations induced by quantum effects of a scalar field in the Bianchi type IX space-time are derived in the present work. The curvature tensor components and their combinations are calculated in the Bianchi type IX spaces. To estimate a one-loop effective action, the asymptotic Schwinger-DeWitt perturbative formula with consideration of terms up to the second order is used. Quantum corrections involve the fourth-order derivative of the metric; as a consequence, the background gravitational action also includes terms up to the fourth-order derivatives of the metric.

Low energy effective gravitational equations on a Gauss-Bonnet brane

We present effective gravitational equations at low energies in a ${Z}_{2}$-symmetric braneworld with the Gauss-Bonnet term. Our derivation is based on the geometrical projection approach, and we solve iteratively the bulk geometry using the gradient expansion scheme. Although the original field equations are quite complicated due to the presence of the Gauss-Bonnet term, our final result clearly has the form of the Einstein equations plus correction terms, which is simple enough to handle. As an application, we consider homogeneous and isotropic cosmology on the brane. We also comment on the holographic interpretation of bulk gravity in the Gauss-Bonnet braneworld.

Effective gravitational equations on a brane world with induced gravity

We present the effective equations to describe the four-dimensional gravity of a brane world, assuming that a five-dimensional bulk spacetime satisfies the Einstein equations and gravity is confined on the $Z_2$ symmetric brane. Applying this formalism, we study the induced-gravity brane model first proposed by Dvali, Gabadadze and Porrati. In a generalization of their model, we show that an effective cosmological constant on the brane can be extremely reduced in contrast to the case of the Randall-Sundrum model even if a bulk cosmological constant and a brane tension are not fine-tuned.

Brane gravity at low energy

Four dimensional gravity in the low energy limit of a higher dimensional theory has been expected to be a (generalized) Brans-Dicke theory. A subtle point in brane world scenarios is that the system of four dimensional effective gravitational equations is not closed due to bulk gravitational waves and bulk scalars. Nonetheless, weak gravity on the brane can be analyzed completely. We reexamine the theory of weak brane gravity using gauge-invariant gravitational and scalar perturbations around a background warped geometry with a bulk scalar between two flat branes. We obtain a simple condition for the radion stabilization in terms of the scalar field potentials. We show that for general potentials of the scalar field which provides radion stabilization and a general conformal transformation to a frame in which matter on the branes are minimally coupled to the metric, 4-dimensional Einstein gravity, not BD gravity, is restored at low energies on either brane. In contrast, in RS brane world scenario without a bulk scalar, low energy gravity is a BD one. We conjecture that in general brane world scenarios with more than one scalar field one will again encounter the situation that low energy gravity is not described by the Einstein theory. Equipped with the weak gravity results, we discuss the properties of 4D brane gravitational equations, in particular, the value and sign of 4D Newton gravitational coupling.

The Einstein equations on the 3-brane world

We carefully investigate the gravitational equations of the brane world, in which all the matter forces except gravity are confined on the 3-brane in a 5-dimensional spacetime with ${Z}_{2}$ symmetry. We derive the effective gravitational equations on the brane, which reduce to the conventional Einstein equations in the low energy limit. From our general argument we conclude that the first Randall-Sundrum-type theory predicts that the brane with a negative tension is an antigravity world and hence should be excluded from the physical point of view. Their second-type theory where the brane has a positive tension provides the correct signature of gravity. In this latter case, if the bulk spacetime is exactly anti--de Sitter spacetime, generically the matter on the brane is required to be spatially homogeneous because of the Bianchi identities. By allowing deviations from anti--de Sitter spacetime in the bulk, the situation will be relaxed and the Bianchi identities give just the relation between the Weyl tensor and the energy momentum tensor. In the present brane world scenario, the effective Einstein equations cease to be valid during an era when the cosmological constant on the brane is not well defined, such as in the case of the matter dominated by the potential energy of the scalar field.