We discuss the f(R)-theories of gravity with torsion in the framework of jet-bundles. Such an approach is particularly useful since the components of the torsion and curvature tensors can be chosen as fiber jet-coordinates on the bundles and then the symmetries and the conservation laws of the theory can be easily achieved. Field equations of f(R)-gravity are studied in empty space and in presence of various forms of matter as Dirac fields, Yang--Mills fields and spin perfect fluid. Such fields enlarge the jet-bundles framework and characterize the dynamics. Finally we give some cosmological applications and discuss the relations between f(R)-gravity and scalar-tensor theories.
One of the most appealing results of metric-affine gauge theory of gravity is a close parallel between the Riemann curvature two-form and the Cartan torsion two-form: While the former is the field strength of the Lorentz-group connection one-form, the latter can be understood as the field strength of the coframe one-form. This parallel, unfortunately, is not fully established until one adopts Trautman's idea of introducing an affine-vector-valued zero-from, the meaning of which has not been satisfactorily clarified. This paper aims to derive this parallel from first principles without any ad h…
While one can in principle augment gravity theory with torsion, it is generally thought that any such torsion affects would be too small to be of consequence. Here we show that this cannot in general be the case. We show that the limit of vanishing torsion is not necessarily a continuous one, with the theory obtained in the limit not necessarily coinciding with the theory in which torsion had never been present at all. However, for a standard torsion tensor that is antisymmetric in two of its indices we have found two cases in which the vanishing torsion limit is in fact continuous, namely Ein…
Torsion gravitational effects in the quantum interference of charged particles are investigated. The influence of axial torsion in the Schiff-Banhill effect (SB) inside a metallic shell is given. The effect of torsion on the surface of the earth on (SB) experiment is estimated. Torsion gravity effects on the Sagnac phase-shift of neutron interferometry are also computed.
We investigate a linearized tensor-tensor theory of gravity with torsion and a perturbed torsion wave solution is discovered in background Minkowski spacetime with zero torsion. Furthermore, gauge transformations of any perturbed tensor field are derived in general background non-Riemannian geometries. By calculating autoparallel deviations, both longitudinal and transverse polarizations of the torsion wave are discovered.
It is found that conformally coupled induced gravity with gradient torsion gives a dilaton gravity in Riemann geometry. In the Einstein frame of the dilaton gravity the conformal symmetry is hidden and a non-vanishing cosmological constant is not plausible due to the constraint of the conformal coupling.
We study models of axi-dilaton gravity in space-time geometries with torsion. We discuss conformal re-scaling rules in both Riemannian and non-Riemannian formulations. We give static, spherically symmetric solutions and examine their singularity structure.
We will consider the torsional completion of gravity for a background filled with Dirac matter fields, studying the weak-gravitational non-relativistic approximation, in view of an assessment about their effective phenomenology: we discuss how the torsionally-induced non-linear interactions among fermion fields in this limit are compatible with all experiments, and remarks on the role of torsion to suggest new physics are given.
Cosmic strings inside Schwarzschild black holes in teleparallel gravity are considered.Torsion flux inside the black hole is compute like a torsion vortex on a superfluid.Since some components of torsion are singular on Schwarzschild horizon and others remain finite we compute a torsion invariant to decide whether the torsion is singular and where torsion singularities located.It is found out that as in the curvature case of Einstein's black hole the event horizon is not a mere coordinate singularity for torsion although a true torsion singularity is found at the center of the teleparallel bla…
Curvature and torsion of linear transports along paths in, respectively, vector bundles and the tangent bundle to a differentiable manifold are defined and certain their properties are derived.
Dirac equation is written in a non-Riemannian spacetime with torsion and non-metricity by lifting the connection from the tangent bundle to the spinor bundle over spacetime. Foldy-Wouthuysen transformation of the Dirac equation in a Schwarzschild background spacetime is considered and it is shown that both the torsion and non-metricity couples to the momentum and spin of a massive, spinning particle. However, the effects are small to be observationally significant.
In this paper, we consider the torsional completion of gravitation for an underlying background filled with Dirac fields, applying it to the problem of neutrino oscillations: we discuss the effects of the induced torsional interactions as corrections to the neutrino oscillation mechanism.
In this work the Poincare-Chern Simons and Anti de Sitter Chern Simons gravities are studied. For both a solution that can be casted as a black hole with manifest torsion is found. Those solutions resemble Schwarzschild and Schwarzschild-AdS solutions respectively.
In this article we construct a relativistic extended metric theory of gravity, for which its weak field limit reduces to the non-relativistic MOdified Newtonian Dynamics regime of gravity. The theory is fully covariant and the way to achieve this is to introduce torsion in the description of gravity as well as with the addition of a particular function of the matter lagrangian into the gravitational action.
We consider the most general torsional completion of gravitation together with electrodynamics for the Dirac spinorial material fields, and we show that consistency arguments constrain torsion to be completely antisymmetric and the dynamics to be parity-invariant and described by actions that are either least-order derivative or renormalizable.
In this article we will take into account the most complete back-ground with torsion and curvature, providing the most exhaustive coupling for the Dirac field: we will discuss the integrability of the interaction of the matter field and the reduction of the matter field equations.
We extend the scope of the Raychaudhuri-Komar singularity theorem of General Relativity to affine theories of gravity with and without torsion. We first generalize the existing focusing theorems using time-like and null congruences of curves which are hypersurface orthogonal, showing how the presence of torsion affects the formation of focal points in Lorentzian manifolds. Considering the energy conservation on a given affine gravity theory, we prove new singularity theorems for accelerated curves in the cases of Lorentzian manifolds containing perfect fluids or scalar field matter sources.
Junction conditions are discussed within the framework of $f(R)$-gravity with torsion. After deriving general junction conditions, the cases of coupling to a Dirac field and a spin fluid are explicitly dealt with. The main differences with respect to Einstein--Cartan--Sciama--Kibble theory $\left(f(R)=R\right)$ are outlined.
It is shown that all torsion-free vacuum solutions of the model of dS gauge theory of gravity are the vacuum solutions of Einstein field equations with the same positive cosmological constant. Furthermore, for the gravitational theories with more general quadratic gravitational Lagrangian ($F^2+T^2$), the torsion-free vacuum solutions are also the vacuum solutions of Einstein field equations.
We present a unifying approach where weak forces and neutrino oscillations are interpreted under the same standards of torsional hybrid gravity. This gravitational theory mixes metric and metric-affine formalism in presence of torsion and allows to derive an effective scalar field which gives rise to a running coupling for Dirac matter fields. In this picture, two phenomena occurring at different energy scales can be encompassed under the dynamics of such a single scalar field, which represents the further torsional and curvature degrees of freedom.
We study a four-dimensional gauge theory of the Poincaré group with topological action which generalizes some well-known two-dimensional gravity models. We classify the spherically symmetric solutions and discuss the perturbative propagation of excitations around flat spacetime.
We study the system of self-dual Maxwell field coupled to 3D gravity with torsion, with Maxwell field modified by a topological mass term. General structure of the field equations reveals a new, dynamical role of the classical central charges, and gives a simple correspondence between self-dual solutions with torsion and their Riemannian counterparts. We construct two exact self-dual solutions, corresponding to the sectors with massless and massive Maxwell field, and calculate their conserved charges.
We study the energy conditions in the framework of the modi- fied gravity with higher-derivative torsional terms in the action. We discuss the viability of the model by studying the energy conditions in terms of the cosmographical parameters like Hubble, deceleration, jerk, snap and lerk parameters. In particular, We consider two spe- cific models that are proposed in literature and examine the viability bounds imposed by the weak energy condition.
We show that the gravitational field equations derived from an action composed of i) an arbitrary function of the scalar curvature and other scalar fields plus ii) connection-independent kinetic and source terms, are identical whether one chooses nonmetricity to vanish and have non-zero torsion or vice versa.
A non-topological Lorentz gauge model of gravity with torsion based on Gauss-Bonnet type Lagrangian is considered. The Lagrangian differs from the Lovelock term in four-dimensional space-time and has a number of interesting features. We demonstrate that the model admits a propagating torsion unlike the case of the topological Lovelock gravity. Due to additional symmetries of the proposed Gauss-Bonnet type Lagrangian the torsion has a reduced set of dynamical degrees of freedom corresponding to the spin two field, U(1) gauge vector field and spin zero field. A remarkable feature is that the kin…
The gauge approach to gravity based on the local Lorentz group with a general independent affine connection A_{μcd} is developed. We consider SO(1,3) gauge theory with a Lagrangian quadratic in curvature as a simple model of quantum gravity. The torsion is proposed to represent a dynamic degree of freedom of quantum gravity at scales above the Planckian energy. The Einstein-Hilbert theory is induced as an effective theory due to quantum corrections of torsion via generating a stable gravito-magnetic condensate. We conjecture that torsion possesses an intrinsic quantum nature and can be confine…
The torsion is shown to be vitally important in the explanation of the evolution of the universe in a large class of gravitational theories containing quadratic terms of curvature and torsion. The cosmological solutions with homogeneous and isotropic torsion in a model of de Sitter gauge theory of gravity are presented, which may explain the observation data for SN Ia when parameters are suitably chosen and supply a natural transit from decelerating expansion to accelerating expansion without the help of the introduction of other strange fields in the theory.
We study the Hamiltonian structure of the general parity-invariant model of three-dimensional gravity with propagating torsion, with eight parameters in the Lagrangian. In the scalar sector, containing scalar or pseudoscalar modes with respect to maximally symmetric background, the phenomenon of constraint bifurcation is observed and analyzed. The stability of the Hamiltonian structure under linearization is used to identify dynamically acceptable values of parameters.
Torsion detection from totally skew symmetric torsion waves in the context of teleparallel gravity is discussed. A gedanken experiment to detect Cartan's contortion based on a circle of particles not necessarily spinning is proposed. It is shown that by making use of previous value of contortion at the surface of the Earth computed by Nitsch of $10^{-24} s^{-1}$ a relative displacement of $10^{-21}$ is obtained which is of the order of the gravitational wave of $10^{-3}Hz$. Since LISA has been designed to work in the mHz regime this GW detector could be used for an indirect detection of torsio…
We consider the most general renormalizable theory of propagating torsion in Einstein gravity for the Dirac matter distribution and we demonstrate that in this case torsion is a massive axial-vector field whose coupling to the spinor gives rise to conditions in terms of which gravitational singularities are not bound to form; we discuss how our results improve those that are presented in the existing literature, and that no further improvement can be achieved unless one is ready to re-evaluate some considerations on the renormalizability of the theory.
In the model of de Sitter gauge theory of gravity, the empty homogenous and isotropic spacetimes with constant curvature scalar and nonvanishing homogenous and isotropic torsion must have de Sitter metrics. The static de Sitter spacetime with static, O(3)-symmetric, vector torsion is the only spherically symmetric, vacuum solution with the metric of the form $g_{μν}={\rm diag}(A^2(r),-B^2(r),-r^2,-r^2\sin^2þ)$. The expressions of the torsion for different de Sitter spacetimes are presented. They are different from one to another. The properties of different de Sitter spacetimes with torsion ar…
We investigate the propagation of light rays and evolution of optical scalars in gauge theories of gravity where torsion is present. Recently the modified Raychaudhuri equation in the presence of torsion has been derived. We use this result to derive the basic equations of geometric optics for several different interesting solutions of the Poincar{é} gauge theory of gravity. The results show that the focusing effects for neighboring light rays will be different than general relativity. This in turn has practical consequences in the study of gravitational lensing effects and also determining th…
In this paper we consider torsion gravity in the case of the Dirac field, and by going into the rest frame we study what happens when a uniform precession as well as a phase are taken into account for the spinor field; we discuss how partially conserved axial-vector currents and torsion-spin attractive potentials justify negative Takabayashi angle and energy smaller than mass: because in this instance the module goes to zero exponentially fast then we obtain stable and localized matter distributions suitable to be regarded as a description of particles.
The role of torsion in f(R) gravity is considered in the framework of metric-affine formalism. We discuss the field equations in empty space and in presence of perfect fluid matter taking into account the analogy with the Palatini formalism. As a result, the extra curvature and torsion degrees of freedom can be dealt as an effective scalar field of fully geometric origin. From a cosmological point of view, such a geometric description could account for the whole Dark Side of the Universe.
We consider Lorentz invariant scalar-tensor teleparallel gravity theories with a Lagrangian built from the torsion scalar, a scalar field, its kinetic term and a derivative coupling between the torsion and the scalar field. The field equations of the theory are derived and the relation between the spin connection and the antisymmetric part of the tetrad field equations is found explicitly, which is an important consistency result for Lorentz invariant teleparallel theories of gravity. Afterwards we study the behaviour of this class of theories under conformal transformations and find that such…
Torsion and curvature could play a fundamental role in explaining cosmological dynamics. f(R)-gravity with torsion is an approach aimed to encompass in a comprehensive scheme all the Dark Side of the Universe (Dark Energy and Dark Matter). We discuss the field equations in empty space and in presence of perfect fluid matter taking into account the analogy with the metric-affine formalism. The result is that the extra curvature and torsion degrees of freedom can be dealt under the standard of an effective scalar field of fully geometric origin. The initial value problem for such theories is als…
We study the renormalization of theories of gravity with an arbitrary (torsionful and non-metric) connection. The class of actions we consider is of the Palatini type, including the most general terms with up to two derivatives of the metric, but no derivatives of the connection. It contains 19 independent parameters. We calculate the one loop beta functions of these parameters and find their fixed points. The Holst subspace is discussed in some detail and found not to be stable under renormalization. Some possible implications for ultraviolet and infrared gravity are discussed.
The role played by torsion in gravitation is critically reviewed. After a description of the problems and controversies involving the physics of torsion, a comprehensive presentation of the teleparallel equivalent of general relativity is made. According to this theory, curvature and torsion are alternative ways of describing the gravitational field, and consequently related to the same degrees of freedom of gravity. However, more general gravity theories, like for example Einstein-Cartan and gauge theories for the Poincare and the affine groups, consider curvature and torsion as representing …
We couple a conformal scalar field in (2+1) dimensions to Einstein gravity with torsion. The field equations are obtained by a variational principle. We could not solve the Einstein and Cartan equations analytically. These equations are solved numerically with 4th order Runge-Kutta method. From the numerical solution, we make an ansatz for the rotation parameter in the proposed metric, which gives an analytical solution for the scalar field for asymptotic regions.
It is found that the deviation of an effective potential from the quartic form is related to the metric and vector torsion dependencies of the effective potential in the vector torsion coupled conformally induced gravity.
Torsion and nonmetricity are inherent ingredients in modifications of Eintein's gravity that are based on affine spacetime geometries. In the context of pure f(R) gravity we discuss here, in some detail, the relatively unnoticed duality between torsion and nonmetricity. In particular we show that for R2 gravity torsion and nonmetricity are related by projective transformations. Since the latter correspond simply to redefining the affine parameters of autoparallels, we conclude that torsion and nonmetricity are physically equivalent properties of spacetime. As a simple example we show that both…
The trace anomaly induced dynamics of the conformal factor is investigated in four-dimensional quantum gravity with torsion. The constraints for the coupling constants of torsion matter interaction are obtained in the infrared stable fixed point of the effective scalar theory.
We consider the model of modified gravity with dynamical torsion. This model was found to have promising stability properties about various backgrounds. The model admits a self-accelerating solution. We have shown previously that if the parameters are adjusted in such a way that the torsion is much greater than the effective cosmological constant, the self-accelerating solution is unstable: there are exponentially growing modes. Here we study the scalar perturbations in the case when the torsion is of the order of the effective cosmological constant. We find that there are no exponential insta…
We take a Dirac field non-minimally coupled to the gravitational field within the framework of the Poincaré gauge theory of gravity with torsion and curvature. We study the subcase of "weak" gravity, that is, the gravitational Lagrangian depends only linearly on the curvature and quadratically on the torsion. We include all pieces in curvature and torsion that are of odd parity. The second field equation of gravity is derived by varying the Lorentz connection. We solve it with respect to the torsion and decompose the first field equation of gravity and the Dirac equation into Einsteinian piece…
We investigate the role of the torsion field at the quantum level in the affine-metric theory of gravity. One-loop counterterms are calculated in the theory with terms quadratic in the torsion field.
The role of torsion in quantum three-dimensional gravity is investigated by studying the partition function of the Euclidean theory in Riemann-Cartan spacetime. The entropy of the black hole with torsion is found to differ from the standard Bekenstein-Hawking result, but its form is in complete agreement with the first law of black hole thermodynamics.
We review how the large $c$ expansion of General Relativity leads to an effective theory in the form of Twistless Torsional Newton-Cartan gravity. We show how this is a strong field expansion around the static sector of General Relativity and illustrate this through two examples.
In this paper we present an alternative cosmological extension of the three-dimensional extended Newtonian Chern-Simons gravity by switching on the torsion. The theory is obtained as a non-relativistic limit of an enhancement and $U(1)$-enlargement of the so-called teleparallel algebra and can be seen as the teleparallel analogue of the Newtonian gravity theory. The infinite-dimensional extension of our result is also explored through the Lie algebra expansion method. An infinite-dimensional torsional Galilean gravity model is presented which in the vanishing cosmological constant limit reprod…
Asymptotic symmetry of the Euclidean 3D gravity with torsion is described by two independent Virasoro algebras with different central charges. Elements of this boundary conformal structure are combined with Cardy's formula to calculate the black hole entropy.
We investigate Lovelock gravity in five dimensions in first order formalism. We construct a new class of solutions: BTZ black ring with(out) torsion. We show that our solution with torsion exists in the different sector of the Lovelock gravity compared to Lovelock Chern-Simons and the sector investigated by Canfora et al. We compute conserved charges of the solutions by using Nester's formula, and confirm the results by canonical method. We show that the theory linearized around the background with torsion possesses additional degrees of freedom compared to general relativity.
Basic aspects of the AdS/CFT correspondence are studied in the framework of 3-dimensional gravity with torsion. After choosing a consistent holographic ansatz, we formulate an improved approach to the Noether--Ward identities for the boundary theory. The method is applied first to the topological Mielke--Baekler model, and then to the more interesting (parity-preserving) 3-dimensional gravity with propagating torsion. In both cases, we find the finite holographic energy-momentum and spin currents and obtain the associated (anomalous) Noether--Ward identities.
We propose four simple Lagrangians for gravity models with dynamical torsion which are free from ghosts and tachyons. The torsion propagates two massive or massless particles of spin 1^\pm and 0^\pm besides the massless graviton 2^+ propagated by metric.
We study the nature of asymptotic symmetries in topological 3d gravity with torsion. After introducing the concept of asymptotically anti-de Sitter configuration, we find that the canonical realization of the asymptotic symmetry is characterized by the Virasoro algebra with classical central charge, the value of which is the same as in general relativity: c=3l/2G.
We derive the field equations for topologically massive gravity coupled with the most general quadratic curvature terms using the language of exterior differential forms and a first order constrained variational principle. We find variational field equations both in the presence and absence of torsion. We then show that spaces of constant negative curvature (i.e. the anti de-Sitter space $AdS_3$) and constant torsion provide exact solutions.
We study the general parity-preserving model of three-dimensional gravity with propagating torsion, with a focus on its nonlinear dynamics in the AdS sector. The model is shown to posses the black hole with torsion as a vacuum solution, provided we adopt certain restrictions on its coupling constants. The canonical analysis in the AdS asymptotic region yields the conserved charges of the black hole and the central charges of the asymptotic conformal symmetry.
We show that topological 3D gravity with torsion can be formulated as a Chern-Simons gauge theory, provided a specific parameter, known as the effective cosmological constant, is negative. In that case, the boundary dynamics of the theory corresponding to anti-de Sitter boundary conditions is described by a conformal field theory with two different central charges.
We extract exact charged black-hole solutions with flat transverse sections in the framework of D-dimensional Maxwell-f(T) gravity, and we analyze the singularities and horizons based on both torsion and curvature invariants. Interestingly enough, we find that in some particular solution subclasses there appear more singularities in the curvature scalars than in the torsion ones. This difference disappears in the uncharged case, or in the case where f(T) gravity becomes the usual linear-in-T teleparallel gravity, that is General Relativity. Curvature and torsion invariants behave very differen…
A classical pp-wave is a 4-dimensional Lorentzian spacetime which admits a nonvanishing parallel spinor field; here the connection is assumed to be Levi-Civita. We generalise this definition to metric compatible spacetimes with torsion and describe basic properties of such spacetimes. We use our generalised pp-waves for constructing new explicit vacuum solutions of quadratic metric-affine gravity.
