It is shown that cosmological equations for homogeneous isotropic models deduced in the framework of the Poincaré gauge theory of gravity by certain restrictions on indefinite parameters of gravitational Lagrangian take at asymptotics the same form as cosmological equations of general relativity theory for $ΛCDM$-model. Terms related to dark matter and dark energy in cosmological equations of standard theory for $ΛCDM$-model are connected in considered theory with the change of gravitational interaction provoked by spacetime torsion.
In the present work, it is shown that the problem of the accelerating expansion of the Universe can be directly solved by applying Einstein geometrization philosophy in a wider geometry. The geometric structure used to fulfil the aim of the work is a version of Absolute Parallelism geometry in which curvature and torsion are simultaneously non vanishing objects. It is shown that, while the energy corresponding to the curvature of space- time gives rise to an attractive force, the energy corresponding to the torsion indicates the presence of a repulsive force. A fine tuning parameter can be adj…
The simplest gauge gravitation theory in Riemann-Cartan space-time leading to the solution of the problem of cosmological singularity and dark energy problem is investigated with purpose to solve the dark matter problem. It is shown that the interaction of the vacuum torsion field with proper angular moments of gravitating objects can lead to appearance at astrophysical scale (galaxies, galactic clusters) additional force of gravitational attraction, which in the frame of standard theory is connected with dark matter.
Cosmological solutions for homogeneous isotropic models in the framework of the Poincaré gauge theory of gravity based on gravitational Lagrangian adopted in the paper by Kun-Feng Shie, James M. Nester and Hwei-Jang Yo (Phys. Rev. D \textbf{78}, 023522 (2008)) are discussed. Cosmological solutions for accelerating Universe obtained in referred paper are compared with corresponding solutions of standard $ΛCDM$-model and also with cosmological solution obtained by authors of this Comment.
Several exact cosmological solutions of a metric-affine theory of gravity with two torsion functions are presented. These solutions give a essentially different explanation from the one in most of previous works to the cause of the accelerating cosmological expansion and the origin of the torsion of the spacetime. These solutions can be divided into two classes. The solutions in the first class define the critical points of a dynamical system representing an asymptotically stable de Sitter spacetime. The solutions in the second class have exact analytic expressions which have never been found …
The "dark energy" problem is investigated in the framework of the Poincare gauge theory of gravity in 4-dimensional Riemann-Cartan space-time. By using general expression for gravitational Lagrangian homogeneous isotropic cosmological models with pseudoscalar torsion function are built and investigated. It is shown that by certain restrictions on indefinite parameters of gravitational Lagrangian the cosmological equations at asymptotics contain effective cosmological constant and can lead to observable acceleration of cosmological expansion. This effect has geometrical nature and is connected …
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 consider a model belonging to the class of gravities with dynamical torsion. The model is free of ghosts and gradient instabilities about Minkowski and torsionless Einstein backgrounds. We find that at zero cosmological constant, the model admits a self-accelerating solution with non-Riemannian connection. Small value of the effective cosmological constant is obtained at the expense of the hierarchy between the dimensionless couplings.
Homogeneous isotropic models built in the framework of the Poincaré gauge theory of gravity (PGTG) based on general expression of gravitational Lagrangian without cosmological constant are analyzed. It is shown that the physical spacetime in the vacuum in the frame of PGTG can have the structure of flat de Sitter spacetime with torsion. Some physical consequences of obtained conclusion are discussed.
In the framework of the spacetime with torsion, we obtain the flavor evolution equation of the mass neutrino oscillation in vacuum. A comparison with the result of general relativity case, it shows that the flavor evolutionary equations in Riemann spacetime and Weitzenböck spacetimes are equivalent in the spherical symmetric Schwarzschild spacetime, but turns out to be different in the case of the axial symmetry.
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…
Given a spacetime with nonvanishing torsion, we discuss the equation for the evolution of the separation vector between infinitesimally close curves in a congruence. We show that the presence of a torsion field leads, in general, to tangent and orthogonal effects on the congruence; in particular, the presence of a completely generic torsion field contributes to a relative acceleration between test particles. We derive, for the first time in the literature, the Raychaudhuri equation for a congruence of timelike and null curves in a spacetime with the most generic torsion field.
Chern-Simons electrodynamics in 2+1-spacetimes with torsion is investigated. We start from the usual Chern-Simons (CS) electrodynamics Lagrangian and Cartan torsion is introduced in the covariant derivative and by a direct coupling of torsion vector to the CS field. Variation of the Lagrangian with respect to torsion shows that Chern-Simons field is proportional to the product of the square of the scalar field and torsion. The electric field is proportional to torsion vector and the magnetic flux is computed in terms of the time-component of the two dimensional torsion. Contrary to early massi…
We extend the geometrical ideas of the spacetime deformations to study the physical foundation of the post-Riemannian geometry. To this aim, we construct the theory of 'two-step spacetime deformation' as a guiding principle. We address the theory of teleparallel gravity and construct a consistent Einstein-Cartan (EC) theory with the 'dynamical torsion'. We show that the equations of the standard EC theory, in which the equation defining torsion is the algebraic type and, in fact, no propagation of torsion is allowed, can be equivalently replaced by the set of 'modified EC equations' in which t…
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.
Spacetimes with everywhere vanishing curvature tensor, but with torsion different from zero only on world sheets that represent closed loops in ordinary space are presented, also defects along open curves with end points at infinity are studied. The case of defects along timelike loops is also considered and the geodesics in these spaces are briefly discussed.
We consider the model of modified gravity with dynamical torsion. This model was previously found to have promising stability properties about various backgrounds. Here we study the stability of linear perturbations about the self-accelerating solution. We apply the $(3 + 1)$-decomposition and consider the scalar sector of perturbations. We find that the number of degrees of freedom is equal to 2, which is the same as in Minkowski background. However, there is at least one instability in the scalar sector, if the value of background torsion is large enough. This does not rule out the possibili…
In the context of the teleparallel equivalent of general relativity, we obtain the tetrad and the torsion fields of the stationary axisymmetric Kerr spacetime. It is shown that, in the slow rotation and weak field approximations, the axial-vector torsion plays the role of the gravitomagnetic component of the gravitational field, and is thus the responsible for the Lense-Thirring effect.
The Einstein-Cartan-Kibble-Sciama ({\sf ECKS}) theory of gravity naturally extends Einstein\rq{}s general relativity ({\sf GR}) to include intrinsic angular momentum (spin) of matter. The main feature of this theory consists of an algebraic relation between spacetime torsion and spin of matter which indeed deprives the torsion of its dynamical content. The Lagrangian of {\sf ECKS} gravity is proportional to the Ricci curvature scalar constructed out of a general affine connection so that owing to the influence of matter energy-momentum and spin, curvature and torsion are produced and interact …
The motion of test particles along circular orbits in the vacuum $C$ metric is studied in the Frenet-Serret formalism. Special orbits and corresponding intrinsically defined geometrically relevant properties are selectively studied.
Analytical wormhole solutions in $U_4$ theory are presented. It is discussed whether the extremely short range repulsive forces, related to the spin angular momentum of matter, could be the ``carrier'' of the exoticity that threads the wormhole throat.
A surprising feature of our present four dimensional universe is that its evolution appears to be governed solely by spacetime curvature without any noticeable effect of spacetime torsion. In the present paper, we give a possible explanation of this enigma through ``cosmological evolution'' of spacetime torsion in the backdrop of a higher dimensional braneworld scenario. Our results reveal that the torsion field may had a significant value at early phase of our universe, but gradually decreased with the expansion of the universe. This leads to a negligible footprint of torsion in our present v…
We compute the corrections to the orbital Lense-Thirring effect (or frame-dragging) in the presence of spacetime torsion. We derive the equations of motion of a test body in the gravitational field of a rotating axisymmetric massive body, using the parametrized framework of Mao, Tegmark, Guth and Cabi. We calculate the secular variations of the longitudes of the node and of the pericenter. We also show how the LAser GEOdynamics Satellites (LAGEOS) can be used to constrain torsion parameters. We report the experimental constraints obtained using both the nodes and perigee measurements of the or…
Investigations of the dynamic modes of the Poincare gauge theory of gravity found only two good propagating torsion modes; they are effectively a scalar and a pseudoscalar. Cosmology affords a natural situation where one might see observational effects of these modes. Here we consider only the ``scalar torsion'' mode. This mode has certain distinctive and interesting qualities. In particular this type of torsion does not interact directly with any known matter and it allows a critical non-zero value for the affine scalar curvature. Via numerical evolution of the coupled nonlinear equations we …
We have investigated the motion of timelike particles along geodesic in the background of accelerating and rotating black hole spacetime. We confirmed that the chaos exists in the geodesic motion of the particles by Poincaré sections, the power spectrum, the fast Lyapunov exponent indicator and the bifurcation diagram. Moreover, we probe the effects of the acceleration and rotation parameters on the chaotic behavior of a timelike geodesic particle in the black hole spacetime. Our results show that the acceleration brings richer physics for the geodesic motion of particles.
We derive the static spherically symmetric vacuum solution for a spacetime with non-vanishing torsion by solving the field equations analytically. The effects of torsion appear as a single parameter in the line element. For the positive values of this parameter, the resulting line element is found to be of the Reissner-Nordstrom type. This parameter is related to the spin of matter and acts as a torsion 'charge' much like the electric charge in conventional Reissner-Nordstrom geometry. We also analyze the existence and stability of the orbits for both massless and massive particles in this set…
Isotropic cosmology built in the Riemann-Cartan spacetime is investigated. Properties of homogeneous isotropic cosmological models filled with usual gravitating matter and scalar fields are studied in the beginning of cosmological expansion near the limiting energy density. It is shown that cosmological models are regular not only with respect to the Hubble parameter and the energy density but also with respect to the torsion and curvature tensors.
We have studied the torsion cosmology model in Kaluza-Klein theory. We considered two simple models in which the torsion vectors are $A_μ=(α,0,0,0)$ and $A_μ=a(t)^2(0,β,β,β)$, respectively. For the first model, the accelerating expansion of the Universe can be not explained without dark energy which is similar to that in the standard cosmology. But for the second model, we find that without dark energy the effect of torsion can give rise to the accelerating expansion of the universe and the alleviation of the well-known age problem of the three old objects for appropriated value of the model p…
We revisit the Riemann-Cartan geometry in the context of recent higher-dimensional theories of spacetime. After introducing the concept of torsion in a modern geometrical language we present some results that represent extensions of Riemannian theorems. We consider the theory of local embeddings and submanifolds in the context of Riemann-Cartan geometries and show how a Riemannian spacetime may be locally and isometrically embedded in a bulk with torsion. As an application of this result, we discuss the problem of classical confinement and the stability of motion of particles and photons in th…
It is assumed that the two-component spinor formalisms for curved spacetimes that are endowed with torsionful affine connexions can supply a local description of dark energy in terms of classical massive spin-one uncharged fields. The relevant wave functions are related to torsional affine potentials which bear invariance under the action of the generalized Weyl gauge group. Such potentials are thus taken to carry an observable character and emerge from contracted spin affinities whose patterns are chosen in a suitable way. New covariant calculational techniques are then developed towards deri…
We develop some ideas discussed by E. Schucking [arXiv:0803.4128] concerning the geometry of the gravitational field. First, we address the concept according to which the gravitational acceleration is a manifestation of the spacetime torsion, not of the curvature tensor. It is possible to show that there are situations in which the geodesic acceleration of a particle may acquire arbitrary values, whereas the curvature tensor approaches zero. We conclude that the spacetime curvature does not affect the geodesic acceleration. Then we consider the the Pound-Rebka experiment, which relates the tim…
Homogeneous isotropic cosmological models built in the framework of the Poincaré gauge theory of gravity based on general expression of gravitational Lagrangian with indefinite parameters are analyzed. Special points of cosmological solutions for flat cosmological models at asymptotics and conditions of their stability in dependence of indefinite parameters are found. Procedure of numerical integration of the system of gravitational equations at asymptotics is considered. Numerical solution for accelerating Universe without dark energy is obtained.
Curvature and torsion are the two tensors characterizing a general Riemannian spacetime. In Einstein's general theory of gravitation, with torsion postulated to vanish and the affine connection identified to the Christoffel symbol, only the curvature tensor plays the central role. For such a purely metric geometry, two well-known topological invariants, namely the Euler class and the Pontryagin class, are useful in characterizing the topological properties of the spacetime. From a gauge theory point of view, and especially in the presence of spin, torsion naturally comes into play, and the und…
The irrotational vortex geometry carachter of torsion loops is displayed by showing that torsion loops and nonradial flow acoustic metrics are conformally equivalent in $(1+1)$ dimensions while radial flow acoustic spacetime are conformally related in $(2+1)$ dimensional spacetime. The analysis of 2-dimensional space allows us to express the fluid density in terms of the parameters of torsion loop metric. These results lead us to conclude that the acoustic metric of vortex flows is the gravitational analog of torsion loop spacetime. Since no vorticity in the fluids is considered we do not make…
I explain the geometric basis for the recently-discovered nonholonomic mapping principle which permits deriving laws of nature in spacetimes with curvature and torsion from those in flat spacetime, thus replacing and extending Einstein's equivalence principle. As an important consequence, it yields a new action principle for determining the equation of motion of a free spinless point particle in such spacetimes. Surprisingly, this equation contains a torsion force, although the action involves only the metric. This force makes trajectories autoparallel rather than geodesic. Its geometric origi…
We argue that the geodesic hypothesis based on the autoparalllels of the Levi-Civita connection may need refinement in the scalar- tensor theories of gravity. Based on a reformulation of the Brans- Dicke theory in terms of a connection with torsion determined dynamically in terms of the gradient of the Brans-Dicke scalar field, we compute the perihelion shift in the orbit of Mercury on the alternative hypothesis that its worldline is an autoparallel of a connection with torsion. If the Brans-Dicke scalar field couples significantly to matter and test particles move on such worldlines, the curr…
Homogeneous isotropic cosmological models with two torsion functions filled with scalar fields and usual gravitating matter are built and investigated in the framework of the Poincaré gauge theory of gravity. It is shown that by certain restrictions on indefinite parameters of gravitational Lagrangian the cosmological equations at asymptotics contain an effective cosmological constant that can explain observable acceleration of cosmological expansion. The behavior of inflationary cosmological solutions at extremely high energy densities is analyzed, regular bouncing solutions are obtained. The…
We report a search for new gravitational physics phenomena based on Einstein-Cartan theory of General Relativity including spacetime torsion. Starting from the parametrized torsion framework of Mao, Tegmark, Guth and Cabi, we analyze the motion of test bodies in the presence of torsion, and in particular we compute the corrections to the perihelion advance and to the orbital geodetic precession of a satellite. We describe the torsion field by means of three parameters, and we make use of the autoparallel trajectories, which in general may differ from geodesics when torsion is present. We deriv…
A exact de Sitter-like cosmological solution of quadratic gravitation with torsion has been found. In the limit of constant energy and pressure, it becomes a exact de Sitter spacetime. It exists in a wide class of quadratic gravity theories and is the same in vacuum for all the models in this class, no matter how the coefficients of the quadratic terms in the Lagrangian are. It describes an accelerating universe and gives a cosmological constant which is of the order of magnitude of the observed value. In vacuum the universe is a de Sitter spacetime without torsion. When matter presents, howev…
In this paper we have investigated the gravitational lensing in a spherically symmetric spacetime with torsion in the generalized Einstein-Cartan-Kibble-Sciama (ECKS) theory of gravity by considering higher order terms. The torsion parameters change the spacetime structure which affects the photon sphere, the deflection angle and the strong gravitational lensing. The condition of existence of horizons is not inconsistent with that of the photon sphere. Especially, there exists a novel case in which there is horizon but no photon sphere for the considered spacetime. In this special case, the de…
We continue the exploration of the consistency of a modified-gravity theory that generalizes General Relativity by including a dynamical torsion in addition to the dynamical metric. The six-parameter theory we consider was found to be consistent around arbitrary torsionless Einstein backgrounds, in spite of its containing a (notoriously delicate) massive spin-2 excitation. At zero bare cosmological constant, this theory was found to admit a self-accelerating solution whose exponential expansion is sustained by a non-zero torsion background. The scalar-type perturbations of the latter torsionfu…
We consider an explicit example of a process, where the entropy carried by radiation through an accelerating two-plane is proportional to the decrease in the area of that two-plane even when the two-plane is not a part of any horizon of spacetime. Our results seem to support the view that entropy proportional to area is possessed not only by horizons but by all spacelike two-surfaces of spacetime.
Riemannian effective spacetime description of Hawking radiation in $^{3}He-A$ superfluids is extended to non-Riemannian effective spacetime. An example is given of non-Riemannian effective geometry of the rotational motion of the superfluid vacuum around the vortex where the effective spacetime Cartan torsion can be associated to the Hawking giving rise to a physical interpretation of effective torsion recently introduced in the literature in the form of an acoustic torsion in superfluid $^{4}He$ (PRD-70(2004),064004). Curvature and torsion singularities of this $^{3}He-A$ fermionic superfluid…
The spinning C-metric was discovered by Plebanski and Demianski as a generalization of the standard C-metric which is known to represent uniformly accelerated non-rotating black holes. We first transform the spinning C-metric into Weyl coordinates and analyze some of its properties as Killing vectors and curvature invariants. A transformation is then found which brings the metric into the canonical form of the radiative spacetimes with the boost-rotation symmetry. By analytically continuing the metric across "acceleration horizons", two new regions of the spacetime arise in which both Killing …
Quasi-local energies for constantly accelerating observers in Bañados, Teitelboim, and Zanelli (BTZ), Schwarzschild and Schwarzschild-de Sitter spacetimes are derived. The energies are expressed in terms of acceleration, cosmological constant, and area, quantities measurable by the observers. Based on results from quantum fields in curved spacetime for the redshifted Hawking temperature, entropy and thermodynamic-like laws are briefly explored in the three spacetimes.
A propagating torsion model is derived from the requirement of compatibility between minimal action principle and minimal coupling procedure in Riemann-Cartan spacetimes. In the proposed model, the trace of the torsion tensor is derived from a scalar potential that determines the volume element of the spacetime. The equations of the model are written down for the vacuum and for various types of matter fields. Some of their properties are discussed. In particular, we show that gauge fields can interact minimally with the torsion without the breaking of gauge symmetry.
We show that the presence of spacetime torsion, unlike any other non-trivial modifications of the Einstein gravity, does \emph{not} affect black hole entropy. The theory being diffeomorphism invariant leads to a Noether current and hence to a Noether charge, which can be associated to the heat content of the spacetime. Furthermore, the evolution of the spacetime inheriting torsion can be encoded in the difference between suitably defined surface and bulk degrees of freedom. For static spacetimes the surface and bulk degrees of freedom coincides, leading to holographic equipartition. In doing s…
The lecture explains the geometric basis for the recently-discovered nonholonomic mapping principle which specifies certain laws of nature in spacetimes with curvature and torsion from those in flat spacetime, thus replacing and extending Einstein's equivalence principle. An important consequence is a new action principle for determining the equation of motion of a free spinless point particle in such spacetimes. Surprisingly, this equation contains a torsion force, although the action involves only the metric. This force changes geodesic into autoparallel trajectories, which are a direct mani…
We consider a possible (parity conserving) interaction between the electromagnetic field $F$ and a torsion field $T^α$ of spacetime. For generic elementary torsion, gauge invariant coupling terms of lowest order fall into two classes that are both nonminimal and {\it quadratic} in torsion. These two classes are displayed explicitly. The first class of the type $\sim F T^2$ yields (undesirable) modifications of the Maxwell equations. The second class of the type $\sim F^2 T^2$ doesn't touch the Maxwell equations but rather modifies the constitutive tensor of spacetime. Such a modification can b…
We consider possible perturbations of the black hole event horizon induced by matter with spin, extending the derivation of the Hawking-Hartle formula (tidal heating) in the presence of torsion. When specialised to theories with a non-vanishing (pseudo-)traceless component of the (con)torsion tensor, we remarkably find that the tidal heating phenomenon gets modified by additional torsion-dependent terms, in agreement with previous investigations based on Jacobson's spacetime thermodynamics approach. These results lead to relevant phenomenological and theoretical consequences: modifications in …
Torsion in a 5D spacetime is considered. In this case gravitation is defined by the 5D metric and the torsion. It is conjectured that torsion is connected with a spinor field. In this case Dirac's equation becomes the nonlinear Heisenberg equation. It is shown that this equation has a discrete spectrum of solutions with each solution being regular on the whole space and having finite energy. Every solution is concentrated on the Planck region and hence we can say that torsion should play an important role in quantum gravity in the formation of bubbles of spacetime foam. On the basis of the alg…
An exact solution of $(2+1)$-dimensional Einstein gravity with cosmological constant is studied. The corresponding spacetime is interpreted as an accelerating BTZ spacetime. The proper acceleration, horizon structure, temperature and entropy are presented in detail. The metric being studied is very similar to the one studied by Astorino in arXiv:1101.2616, but the range of parameters is different which results in significant changes in the causal structures.
The C-metric is a solution to Einstein's vacuum field equation that describes an accelerating black hole. In this paper we discuss the propagation of light rays and the resulting lensing features in this metric. We first solve the lightlike geodesic equation using elliptic integrals and Jacobi elliptic functions. Then we fix a static observer in the region of outer communication of the C-metric and introduce an orthonormal tetrad to parameterise the directions of the light rays ending at the position of the observer using latitude-longitude coordinates on the observer's celestial sphere. In th…
The approach of metric-affine field theory is to define spacetime as a real oriented 4-manifold equipped with a metric and an affine connection. The 10 independent components of the metric tensor and the 64 connection coefficients are the unknowns of the theory. We write the Yang-Mills action for the affine connection and vary it both with respect to the metric and the connection. We find a family of spacetimes which are stationary points. These spacetimes are waves of torsion in Minkowski space. We then find a special subfamily of spacetimes with zero Ricci curvature; the latter condition is …
The Einstein equations, apart from being the classical field equations of General Relativity, are also the classical field equations of two other theories of gravity. As the experimental tests of General Relativity are done using the Einstein equations, we do not really know, if gravity is the curvature of a torsionless spacetime, or torsion of a curvatureless spacetime, or if it occurs due to the non-metricity of a curvatureless and torsionless spacetime. However, as the classical actions of all these theories differ from each other by boundary terms, and the Casimir effect is a boundary effe…
The world formulation of the full theory of classical Proca fields in generally relativistic spacetimes is concisely reviewed and the entire set of pertinent field equations is transcribed in a straightforward way into the framework of one of the Infeld-van der Waerden formalisms. Some well-known calculational techniques are then utilized for deriving the wave equations that control the propagation of the fields allowed for. It appears that no interaction couplings between such fields and electromagnetic curvatures are carried by the wave equations at issue. What results is, in effect, that th…
