Search

We present a static, spherically symmetric, traversable wormhole solution to multimetric gravity which is sustained by only nonexotic matter, i.e., matter which satisfies all energy conditions. The possibility of this solution arises from the fact that under certain conditions the multimetric gravitational field equations reduce to the Einstein equations, but with a negative effective gravitational constant. We show that the Arnowitt-Deser-Misner mass of this wormhole vanishes, so that it appears massless to observers in the asymptotically flat spacetime. We finally speculate on the feasibility of creating and maintaining this type of wormhole by an advanced civilization. [ABSTRACT FROM AUTHOR]

We calculate the parametrized post-Newtonian parameters γ and β for scalar-tensor gravity with a generic coupling function ω and scalar potential V in the Jordan conformal frame in the case of a static spherically symmetric source. Since the potential generally introduces a radial dependence to the effective gravitational constant as well as to γ and β, we discuss the issue of defining these parametrized post-Newtonian parameters and compare our expressions with previous calculations in simpler cases. We confront our results with current observational constraints on the values of γ and β and thus draw restrictions on the form of the functions ω and V around their asymptotic background values. [ABSTRACT FROM AUTHOR]

We briefly review two recently developed extensions of the Lorentzian geometry of spacetime and prove that they are in fact closely related. The first is the concept of observer space, which generalizes the space of Lorentzian observers, i.e., future unit timelike vectors, using Cartan geometry. The second is the concept of Finsler spacetimes, which generalizes the Lorentzian metric of general relativity to an observer-dependent Finsler metric. We show that every Finsler spacetime possesses a well-defined observer space that can naturally be equipped with a Cartan geometry. Conversely, we derive conditions under which a Cartan geometry on observer space gives rise to a Finsler spacetime. We further show that these two constructions complement each other. We finally apply our constructions to two gravity theories, MacDowell-Mansouri gravity on observer space and Finsler gravity, and translate their actions from one geometry to the other. [ABSTRACT FROM AUTHOR]

We discuss the propagation of gravitational waves in a recently discussed class of theories containing N ≥ 2 metric tensors and a corresponding number of standard model copies. Using the formalism of gauge-invariant linear perturbation theory we show that all gravitational waves propagate at the speed of light. We then employ the Newman-Penrose formalism to show that two to six polarizations of gravitational waves may exist, depending on the parameters entering the field equations. This corresponds to E(2) representations N2, N3, III5 and II6. We finally apply our general discussion to a recently presented concrete multimetric gravity model and show that it is of class N2, i.e., it allows only two tensor polarizations, as it is the case for general relativity. Our results provide the theoretical background for tests of multimetric gravity theories using the upcoming gravitational wave experiments. [ABSTRACT FROM AUTHOR]

Symmetric teleparallel gravity theories, in which the gravitational interaction is attributed to the nonmetricity of a flat, symmetric, but not metric-compatible affine connection, have been a topic of growing interest in recent studies. Numerous works study the cosmology of symmetric teleparallel gravity assuming a flat Friedmann-Lemaître-Robertson-Walker metric, while working in the so-called "coincident gauge," further assuming that the connection coefficients vanish. However, little attention has been paid to the fact that both of these assumptions rely on the freedom to choose a particular coordinate system in order to simplify the metric or the connection, and that they may, in general, not be achieved simultaneously. Here we construct the most general symmetric teleparallel geometry obeying the conditions of homogeneity and isotropy, without making any assumptions on the properties of the coordinates, and present our results in both the usual cosmological coordinates and in the coincident gauge. We find that in general these coordinates do not agree, and that assuming both to hold simultaneously allows only for a very restricted class of geometries. For the general case, we derive the energy-momentum-hypermomentum conservation relations and the cosmological dynamics of selected symmetric teleparallel gravity theories. Our results show that the symmetric teleparallel connection in general contributes another scalar quantity into the cosmological dynamics, which decouples only for a specific class of theories from the dynamics of the metric, and only if the simplest geometry is chosen, in which both assumed coordinate systems agree. Most notably, the f(Q) class of theories falls into this class. [ABSTRACT FROM AUTHOR]

Gravitational waves (GWs) have opened a new window on fundamental physics in a number of important ways. The next generation of GW detectors may reveal more information about the polarization structure of GWs. Additionally, there is growing interest in theories of gravity beyond general relativity (GR). One such theory which remains viable within the context of recent measurements of the speed of propagation of GWs is the teleparallel analog of Horndeski gravity. In this work, we explore the polarization structure of this newly proposed formulation of Horndeski theory. In curvature-based gravity, Horndeski theory is almost synonymous with extensions to GR since it spans a large portion of these possible extensions. We perform this calculation by taking perturbations about a Minkowski background and consider which mode propagates. The result is that the polarization structure depends on the choice of model parameters in the teleparallel Horndeski Lagrangian with a maximum of seven propagating degrees of freedom. While the curvature-based Horndeski results follows as a particular limit within this setup, we find a much richer structure of both massive and massless cases which produce scalar-vector-tensor propagating degrees of freedom. We also find that the GW polarization that emerges from the teleparallel analog of Horndeski gravity results in analogous massive and massless modes which take on at most four polarizations in the massless sector and two scalar ones in the massive sector. In none of the cases do we find vector polarizations. [ABSTRACT FROM AUTHOR]

A theory of gravity is deduced from the axioms of the premetric program. The starting point is the conservation of energy and momenta, and the equivalence of gravitation and inertia. The latter is what leads to the framework of the so-called purified gravity. The local and linear constitutive relation has 14 components when it is assumed to be metrical, but the compatibility of the constitutive relation with an action principle fixes uniquely the theory of coincident general relativity. The premetric formalism of purified gravity has a direct analogy with massive electromagnetism, the Planck mass corresponding to the Proca mass of the gauge boson. The metric emerges as a Stueckelberg field, and the graviton as a Goldstone boson of the broken symmetry. [ABSTRACT FROM AUTHOR]

In this article we analyze the post-Newtonian approximation of a generalization of the symmetric teleparallel gravity with the help of the parametrized post-Newtonian (PPN) formalism. This class of theories is based on a free function of the five independent quadratic contractions of the nonmetricity tensor. By calculating the PPN metric of these theories, we can restrict the Taylor coefficients of the free function with the help of the PPN parameters and their observational bounds. We find two families of theories whose PPN parameters are identical to those of general relativity, and thus in full agreement with observations. For three further families, we find that only the PPN parameters β and γ deviate, but can be brought arbitrarily close to their general relativity values by an appropriate choice of the Lagrangian, so that also these families contain candidate theories which agree with observations. The remaining theories either possess no well-defined solution of the post-Newtonian field equations, or possess a post-Newtonian limit which exceeds the form assumed in the PPN formalism. [ABSTRACT FROM AUTHOR]

We present an approach to the parametrized post-Newtonian (PPN) formalism which is based on gauge-invariant higher order perturbation theory. This approach divides the components of the metric perturbations into gauge-invariant quantities, which carry information about the physical system under consideration, and pure gauge quantities, which describe the choice of the coordinate system. This separation generally leads to a simplification of the PPN procedure, since only the gauge-invariant quantities appear in the field equations and must be determined by solving them. Another simplification arises from the fact that the gauge-invariant approach supersedes the necessity to first choose a gauge for solving the gravitational field equations and later transforming the obtained solution into the standard PPN gauge, as it is conventionally done in the PPN formalism, whose standard PPN gauge is determined only after the full solution is known. In addition to the usual metric formulation, we also present a tetrad formulation of the gauge-invariant PPN formalism. To illustrate their practical application, we demonstrate the calculation of the PPN parameters of a well-known scalar-tensor class of theories. [ABSTRACT FROM AUTHOR]

We propose a new model for the description of a gravitating multiparticle system, viewed as a kinetic gas. The properties of the (colliding or noncolliding) particles are encoded into a so-called one-particle distribution function, which is a density on the space of allowed particle positions and velocities, i.e., on the tangent bundle of the spacetime manifold. We argue that an appropriate theory of gravity, describing the gravitational field generated by a kinetic gas, must also be modeled on the tangent bundle. The most natural mathematical framework for this task is Finsler spacetime geometry. Following this line of argumentation, we construct a coupling between the kinetic gas and a recently proposed Finsler geometric extension of general relativity. Additionally, we explicitly show how the general covariance of the action of the kinetic gas on the tangent bundle leads to a novel formulation of its energy-momentum conservation in terms of its energy-momentum distribution tensor. [ABSTRACT FROM AUTHOR]

We consider a recently proposed class of extended teleparallel theories of gravity, which entail a scalar field which is nonminimally coupled to the torsion of a flat, metric-compatible connection. This class of scalar-torsion theories of gravity is constructed in analogy to and as a direct extension of the well-studied class of scalar-curvature gravity theories, and has various common features, such as the conformal frame freedom. For this class we determine the parametrized post-Newtonian limit, both for a massive and for a massless scalar field. In the massive case, we determine the effective gravitational constant and the post-Newtonian parameter γ, both of which depend on the distance between the gravitating and test masses. In the massless case, we calculate the full set of parameters and find that only γ and β potentially deviate from their general relativity values. In particular, we find that for a minimally coupled scalar field, the theory becomes indistinguishable from general relativity at this level of the post-Newtonian approximation. [ABSTRACT FROM AUTHOR]

In this article we derive the post-Newtonian limit of a class of teleparallel theories of gravity, where the action is a free function L (T,X,Y,ϕ) of the torsion scalar T and scalar quantities X and Y built from the dynamical scalar field ϕ. We restrict the analysis to a massless scalar field in order to use the parametrized post-Newtonian formalism without modifications, such as introducing an effective gravitational constant which depends on the distance between the interacting masses. In particular the results show a class of fully conservative theories of gravity, where the only nonvanishing parameters are γ and β. For a particular choice of the function L (T,X,Y, ϕ) the theory cannot be distinguished from general relativity in its post-Newtonian approximation. [ABSTRACT FROM AUTHOR]

We derive the post-Newtonian limit of a general class of teleparallel gravity theories, whose action is given by a free function of three scalar quantities obtained from the torsion of the teleparallel connection. This class of theories is chosen to be sufficiently generic in order to include the f(T) class of theories as well as new general relativity as subclasses. To derive its post-Newtonian limit, we first impose the Weitzenböck gauge, and then introduce a post-Newtonian approximation of the tetrad field around a Minkowski background solution. Our results show that the class of theories we consider is fully conservative, with only the parameters β and γ potentially deviating from their general relativity values. In particular, we find that the post-Newtonian limit of any f(T) theory is identical to that of general relativity, so that these theories cannot be distinguished by measurements of the post-Newtonian parameters alone. [ABSTRACT FROM AUTHOR]

In the attempts to apply Finsler geometry to construct an extension of general relativity, the question about a suitable generalization of the Einstein equations is still under debate. Since Finsler geometry is based on a scalar function on the tangent bundle, the field equation which determines this function should also be a scalar equation. In the literature two such equations have been suggested: the one by Rutz and the one by one of the authors. Here we employ the method of canonical variational completion to show that Rutz equation can not be obtained from a variation of an action and that its variational completion yields the latter field equations. Moreover, to improve the mathematical rigor in the derivation of the Finsler gravity field equation, we formulate the Finsler gravity action on the positive projective tangent bundle. This has the advantage of allowing us to apply the classical variational principle, by choosing the domains of integration to be compact and independent of the dynamical variable. In particular in the pseudo-Riemannian case, the vacuum field equation becomes equivalent to the vanishing of the Ricci tensor. [ABSTRACT FROM AUTHOR]