Background Metric Research Articles

Kaluza-Klein Multidimensional Models with Ricci-Flat Internal Spaces: The Absence of the KK Particles

We consider a multidimensional Kaluza-Klein (KK) model with a Ricci-flat internal space, for example, a Calabi-Yau manifold. We perturb this background metrics by a system of gravitating masses, for example, astrophysical objects such as our Sun. We suppose that these masses are pressureless in the external space but they have relativistic pressure in the internal space. We show that metric perturbations do not depend on coordinates of the internal space and gravitating masses should be uniformly smeared over the internal space. This means, first, that KK modes corresponding to the metric fluctuations are absent and, second, particles should be only in the ground quantum state with respect to the internal space. In our opinion, these results look very unnatural. According to statistical physics, any nonzero temperature should result in fluctuations, that is, in KK modes. We also get formulae for the metric correction terms which enable us to calculate the gravitational tests: the deflection of light, the time-delay of the radar echoes, and the perihelion advance.

Are different approaches to constructing initial data for binary black hole simulations of the same astrophysical situation equivalent?

Initial data for numerical evolutions of binary-black holes have been dominated by "conformally flat" (CF) data (i.e., initial data where the conformal background metric is chosen to be flat) because they are easy to construct. However, CF initial data cannot simulate nearly extremal spins, while more complicated "conformally curved" initial data (i.e., initial data in which the background metric is \emph{not} explicitly chosen to be flat), such as initial data where the spatial metric is chosen to be proportional to a weighted superposition of two Kerr-Schild (SKS) black holes can. Here we establish the consistency between the astrophysical results of these two initial data schemes for nonspinning binary systems. We evolve the inspiral, merger, and ringdown of two equal-mass, nonspinning black holes using SKS initial data and compare with an analogous simulation using CF initial data. We find that the resultant gravitational-waveform phases agree to within $\delta \phi \lesssim 10^{-2}$ radians and the amplitudes agree to within $\delta A/A \lesssim 5 \times 10^{-3}$, which are within the numerical errors of the simulations. Furthermore, we find that the final mass and spin of the remnant black hole agree to one part in $10^{5}

Tension in the void: cosmic rulers strain inhomogeneous cosmologies

New constraints on inhomogeneous Lemaȋtre-Tolman-Bondi (LTB) models alternative to Dark Energy are presented, focusing on adiabatic profiles with space-independent Big Bang and baryon fraction. The Baryon Acoustic Oscillation (BAO) scale at early times is computed in terms of the asymptotic value and then projected to different redshifts by following the geodesics of the background metric. Additionally, a model-independent method to constraint the local expansion rate using a prior on supernovae luminosity is presented. Cosmologies described by an adiabatic GBH matter profile with Ωout = 1 and Ωout ⩽ 1 are investigated using a Markov Chain Monte Carlo analysis including the latest BAO data from the WiggleZ collaboration and the local expansion rate from the Hubble Space Telescope, together with Union2 type Ia supernovae data and the position and height of the Cosmic Microwave Background acoustic peaks. The addition of BAO data at higher redshifts increases considerably their constraining power and represents a new drawback for this type of models, yielding a value of the local density parameter Ωin≳0.2 which is 3σ apart from the value Ωin≲0.15 found using supernovae. The situation does not improve if the asymptotic flatness assumption is dropped, and a Bayesian analysis shows that constrained GBH models are ruled out at high confidence. We emphasize that these are purely geometric probes, that only recently have become sufficiently constraining to independently rule out the whole class of adiabatic LTB models.

Localization of matter fields in the 5D standing wave braneworld

We investigate the localization problem of matter fields within the 5D standing wave braneworld. In this model the brane emits anisotropic waves into the bulk with different amplitudes along different spatial dimensions. We show that in the case of increasing warp factor there exist the pure gravitational localization of all kinds of quantum and classical particles on the brane. For classical particles the anisotropy of the background metric is hidden, brane fields exhibit standard Lorentz symmetry in spite of anisotropic nature of the primordial 5D metric.

Density versus chemical potential in holographic probe theories

We study the relationship between charge density ($\ensuremath{\rho}$) and chemical potential ($\ensuremath{\mu}$) for an array of Lorentz-invariant $3+1$-dimensional holographic field theories with the minimal structure of a conserved charge. In all cases, at large density, the relationship is well-modeled by a power-law behavior of the form $\ensuremath{\rho}\ensuremath{\propto}{\ensuremath{\mu}}^{\ensuremath{\alpha}}$. For the minimal ingredients of a gravitational field and a probe $U(1)$ gauge field in the bulk, we find general constraints $\ensuremath{\alpha}=1$ for the Maxwell action and $\ensuremath{\alpha}>1$ for the Born-Infeld case, for general background metrics. We show that the constraint $\ensuremath{\alpha}\ensuremath{\ge}1$ can also be understood directly in the field theory from thermodynamic stability and causality. We then determine which values of $\ensuremath{\alpha}$ are realized in a large range of example systems, including $\mathrm{D}p\mathrm{\text{\ensuremath{-}}}\mathrm{D}q$ probe brane constructions and ``bottom-up'' models with gauge and scalar fields.

New symmetries in Fierz-Pauli massive gravity

We expose a new symmetry for linear perturbations around a solution of non-linear Fierz-Pauli massive gravity plus a bare cosmological constant. The cosmological constant is chosen such that the background metric is flat while the Stuckelberg fields have a non-trivial profile. Around this background, at linear order the new symmetry reduces the propagating degrees of freedom to those of General Relativity, namely the massless helicity 2 modes only. We discuss the physical consequences and possible applications of these findings.

Palatini approach to bouncing cosmologies and DSR-like effects

It is shown that a quadratic gravitational Lagrangian in the Palatini formulation is able to capture different aspects of quantum gravity phenomenology in a single framework. In particular, in this theory field excitations propagating with different energy-densities perceive different background metrics, a fundamental characteristic of the DSR and Rainbow Gravity approaches. This theory, however, avoids the so-called soccer ball problem. Also, the resulting isotropic and anisotropic cosmologies are free from the big bang singularity. This singularity avoidance occurs non-perturbatively and shares some similitudes with the effective dynamics of loop quantum cosmology.

GRAVITATIONAL OSCILLATIONS IN MULTIDIMENSIONAL ANISOTROPIC MODEL WITH COSMOLOGICAL CONSTANT AND CONTRIBUTIONS INTO THE ENERGY OF VACUUM

The paper studied classical oscillations of background metric in the multidimensional anisotropic model of Kazner in the de-Sitter stage and obtained dependence of fluctuations on dimension of spacetime with infinite expansion. Stability of the model could be achieved when the number of spacelike dimensions equals to or more than four. We calculated the contributions to the density of "vacuum energy", that are provided by proper oscillations of background metric and compared with contribution of cosmological arising from particles due to expansion. As it turned out, contribution of gravitational oscillation of metric into density of "vacuum energy" should play a significant role in the de-Sitter stage.

Covariantization of nonlinear elasticity

In this paper we make a connection between covariant elasticity based on covariance of energy balance and Lagrangian field theory of elasticity with two background metrics. We use Kuchař’s idea of reparametrization of field theories and make elasticity generally covariant by introducing a "covariance field", which is a time-independent spatial diffeomorphism. We define a modified action for parameterized elasticity and show that the Doyle-Ericksen formula and spatial homogeneity of the Lagrangian density are among its Euler–Lagrange equations.

Visser’s massive graviton bimetric theory revisited

A massive gravity theory was proposed by Visser in the late 1990s. This theory, based on a background metric ${b}_{\ensuremath{\alpha}\ensuremath{\beta}}$ and on an usual dynamical metric ${g}_{\ensuremath{\alpha}\ensuremath{\beta}}$ has the advantage of being free of ghosts as well as discontinuities present in other massive theories proposed in the past. In the present investigation, the equations of Visser's theory are revisited with particular care on the related conservation laws. It will be shown that a multiplicative factor is missing in the graviton tensor originally derived by Visser, which has no incidence on the weak field approach but becomes important in the strong field regime when, for instance, cosmological applications are considered. In this case, contrary to some previous claims found in the literature, we conclude that a nonstatic background metric is required in order to obtain a solution able to mimic the $\ensuremath{\Lambda}\mathrm{CDM}$ cosmology.

Palatini actions and quantum gravity phenomenology

We show that an invariant an universal length scale can be consistently introduced in a generally covariant theory through the gravitational sector using the Palatini approach. The resulting theory is able to capture different aspects of quantum gravity phenomenology in a single framework. In particular, it is found that in this theory field excitations propagating with different energy-densities perceive different background metrics, which is a fundamental characteristic of the DSR and Rainbow Gravity approaches. We illustrate these properties with a particular gravitational model and explicitly show how the soccer ball problem is avoided in this framework. The isotropic and anisotropic cosmologies of this model also avoid the big bang singularity by means of a big bounce.

Generic Local Uniqueness and Stability in Polarization Tomography

The problem of polarization tomography is considered on a Riemannian manifold. This problem comes from the physical problem of recovering the anisotropic part of the dielectric permittivity tensor of a quasi-isotropic medium from polarization measurements made around the boundary, but is more general. In greater than three dimensions local uniqueness and stability are established for generic background metrics, and near generic tensor fields through the study of a related linear inverse problem. The same results are established on a natural subspace of tensor fields in dimension three.

Non-linear preheating after inflation and gravitational wave production

We present the evolution of the full set of Einstein equations during preheating after inflation, for a generic supersymmetric model of hybrid inflation. Preheating of the scalar metric fluctuations does affect the evolution of vector and tensor modes, and in particular they do enhance the induced stochastic background of gravitational waves during preheating.This gives an energy density in general an order of magnitude larger than that obtained by evolving the tensors fluctuations in an homogeneous background metric. This enhancement can improve the expectations for detection by planned gravitational waves observatories.

Massive gravity simplified: a quadratic action

We present a simplified formulation of massive gravity where the Higgs fields have quadratic kinetic term. This new formulation allows us to prove in a very explicit way that all massive gravity theories considered so far inevitably have Boulware-Deser ghost in non-trivial fluctuations of background metric.

Holographic (de)confinement transitions in cosmological backgrounds

For type IIB supergravity with a running axio-dilaton, we construct bulk solutions which admit a cosmological background metric of Friedmann-Robertson-Walker type. These solutions include both a dark radiation term in the bulk as well as a four-dimensional (boundary) cosmological constant, while gravity at the boundary remains nondynamical. We holographically calculate the stress-energy tensor, showing that it consists of two contributions: The first one, generated by the dark radiation term, leads to the thermal fluid of $\mathcal{N}=4$ SYM theory, while the second, the conformal anomaly, originates from the boundary cosmological constant. Conservation of the boundary stress-tensor implies that the boundary cosmological constant is time-independent, such that there is no exchange between the two stress-tensor contributions. We then study (de)confinement by evaluating the Wilson loop in these backgrounds. While the dark radiation term favors deconfinement, a negative cosmological constant drives the system into a confined phase. When both contributions are present, we find an oscillating universe with negative cosmological constant which undergoes periodic (de)confinement transitions as the scale of three-space expands and recontracts.

Minimizers of a weighted maximum of the Gauss curvature

On a Riemann surface \({\overline{\Sigma}}\) with smooth boundary, we consider Riemannian metrics conformal to a given background metric. Let κ be a smooth, positive function on \({\overline{\Sigma}}\). If K denotes the Gauss curvature, then the L ∞-norm of K/κ gives rise to a functional on the space of all admissible metrics. We study minimizers subject to an area constraint. Under suitable conditions, we construct a minimizer with the property that |K|/κ is constant. The sign of K can change, but this happens only on the nodal set of the solution of a linear partial differential equation.

New framework for analyzing the effects of small scale inhomogeneities in cosmology

We develop a new, mathematically precise framework for treating the effects of nonlinear phenomena occurring on small scales in general relativity. Our approach is an adaptation of Burnett's formulation of the shortwave approximation, which we generalize to analyze the effects of matter inhomogeneities as well as gravitational radiation. Our framework requires the metric to be close to a background metric, but allows arbitrarily large stress-energy fluctuations on small scales. We prove that, within our framework, if the matter stress-energy tensor satisfies the weak energy condition (i.e., positivity of energy density in all frames), then the only effect that small-scale inhomogeneities can have on the dynamics of the background metric is to provide an effective stress-energy tensor that is traceless and has positive energy density---corresponding to the presence of gravitational radiation. In particular, nonlinear effects produced by small-scale inhomogeneities cannot mimic the effects of dark energy. We also develop perturbation theory off of the background metric. We derive an equation for the long-wavelength part of the leading order deviation of the metric from the background metric, which contains the usual terms occurring in linearized perturbation theory plus additional contributions from the small-scale inhomogeneities. Under various assumptions concerning the absence of gravitational radiation and the nonrelativistic behavior of the matter, we argue that the short-wavelength deviations of the metric from the background metric near a point $x$ should be accurately described by Newtonian gravity, taking into account only the matter lying within a homogeneity length scale of $x$. Finally, we argue that our framework should provide an accurate description of the actual universe.

Application of time transfer function to McVittie spacetime: gravitational time delay and secular increase in astronomical unit

We attempt to calculate the gravitational time delay in a time-dependent gravitational field, especially in McVittie spacetime, which can be considered as the spacetime around a gravitating body such as the Sun, embedded in the FLRW (Friedmann-Lema\^itre-Robertson-Walker) cosmological background metric. To this end, we adopt the time transfer function method proposed by Le Poncin-Lafitte {\it et al.} (Class. Quant. Grav. 21:4463, 2004) and Teyssandier and Le Poncin-Lafitte (Class. Quant. Grav. 25:145020, 2008), which is originally related to Synge's world function $\Omega(x_A, x_B)$ and enables to circumvent the integration of the null geodesic equation. We re-examine the global cosmological effect on light propagation in the solar system. The round-trip time of a light ray/signal is given by the functions of not only the spacial coordinates but also the emission time or reception time of light ray/signal, which characterize the time-dependency of solutions. We also apply the obtained results to the secular increase in the astronomical unit, reported by Krasinsky and Brumberg (Celest. Mech. Dyn. Astron. 90:267, 2004), and we show that the leading order terms of the time-dependent component due to cosmological expansion is 9 orders of magnitude smaller than the observed value of $d{\rm AU}/dt$, i.e., $15 \pm 4$ ~[m/century]. Therefore, it is not possible to explain the secular increase in the astronomical unit in terms of cosmological expansion.

Hawking radiation as tunneling from squashed Kaluza-Klein black hole

We discuss Hawking radiation from a five-dimensional squashed Kaluza-Klein black hole on the basis of the tunneling mechanism. A simple manner, which was recently suggested by Umetsu, is possible to extend the original derivation by Parikh and Wilczek to various black holes. That is, we use the two-dimensional effective metric, which is obtained by the dimensional reduction near the horizon, as the background metric. By using same manner, we derive both the desired result of the Hawking temperature and the effect of the back reaction associated with the radiation in the squashed Kaluza-Klein black hole background.

Viscosity spectral functions of the dilute Fermi gas in kinetic theory

We compute the viscosity spectral function of the dilute Fermi gas for different values of the s-wave scattering length a, including the unitarity limit a→∞. We perform the calculation in kinetic theory by studying the response to a non-trivial background metric. We find the expected structure consisting of a diffusive peak in the transverse shear channel and a sound peak in the longitudinal channel. At zero momentum the width of the diffusive peak is ω0≃(2ε)/(3η) where ε is the energy density and η is the shear viscosity. At finite momentum the spectral function approaches the collisionless limit and the width is of the order of ω0∼k(T/m)1/2.