In this paper, we use a new asymptotically flat and spherically symmetric solution in the generalized Einstein-Cartan-Kibble-Sciama (ECKS) theory of gravity to study the weak gravitational lensing and its shadow cast. To this end, we first compute the weak deflection angle of generalized ECKS black hole using the Gauss-Bonnet theorem in plasma medium and in vacuum. Next by using the Newman-Janis algorithm without complexification, we derive the rotating generalized ECKS black hole and in the sequel study its shadow. Then, we discuss the effects of the ECKS parameter on the weak deflection angle and shadow of the black hole. In short, the goal of this paper is to give contribution to the ECKS theory and look for evidences to understand how the ECKS parameter effects the gravitational lensing. Hence, we show that the weak deflection of black hole is increased with the increase of the ECKS parameter.
We consider the ESK theory, based on the principle for which the space is filled with matter fields in such a way that Cartan torsion is spin; in the geometry in which Cartan torsion tensor is completely antisymmetric, spin has to be completely antisymmetric: we will show how the complete antisymmetry of spin constraints the form of possible matter field theories as to allow the special case of the simplest one solely, all other most general cases being excluded.
We study cosmological perturbations arising from thermal fluctuations in the big-bounce cosmology in the Einstein-Cartan-Sciama-Kibble theory of gravity. We show that such perturbations cannot have a scale-invariant spectrum if fermionic matter minimally coupled to the torsion tensor is macroscopically averaged as a spin fluid, but have a scale-invariant spectrum if the Dirac form of the spin tensor of the fermionic matter is used.
In this paper, we formulate the Mimetic theory of gravity in first-order formalism for differential forms, i.e., the mimetic version of Einstein-Cartan-Kibble-Sciama (ECKS) gravity. We consider different possibilities on how torsion is affected by conformal transformations and discuss how this translates into the interpolation between two different conformal transformations of the spin connection, parameterized with a zero-form parameter $λ$. We prove that regardless of the type of transformation one chooses, in this setting torsion remains as a non-propagating field. We also discuss the conse…
We firstly present a new asymptotical flat and spherically symmetric solution in the generalized Einstein-Cartan-Kibble-Sciama (ECKS) theory of gravity and then investigate the propagation of photon in this background. This solution possesses three independent parameters which affect sharply photon sphere, deflection angle of light ray and gravitational lensing. Since the condition of existence of horizons is not inconsistent with that of photon sphere, there exists a special case where there is horizon but no photon sphere in this spacetime. Especially, we find that in this special case, the …
The coupling between spin and torsion in the Einstein-Cartan-Sciama-Kibble theory of gravity generates gravitational repulsion at very high densities, which prevents a singularity in a black hole and may create there a new universe. We show that quantum particle production in such a universe near the last bounce, which represents the Big Bang gives the dynamics that solves the horizon, flatness, and homogeneity problems in cosmology. For a particular range of the particle production coefficient, we obtain a nearly constant Hubble parameter that gives an exponential expansion of the universe wi…
Two of the major open questions in particle physics are: (1) Why are the elementary fermionic particles that are so far observed have such low mass-energy compared to the Planck energy scale? And (2), what mechanical energy may be counterbalancing the divergent electrostatic and strong force energies of point-like charged fermions in the vicinity of the Planck scale? In this paper, using a hitherto unrecognized mechanism derived from the non-linear amelioration of Dirac equation known as the Hehl-Datta equation within Einstein-Cartan-Sciama-Kibble (ECSK) extension of general relativity, we pre…
The advent of general relativity settled it once and for all that a theory of spacetime is inextricably linked to the theory of gravity. From the point of view of the gauge principle of Weyl and Yang-Mills-Utiyama, it became manifest around the 1960s (Sciama--Kibble) that gravity is closely related to the Poincare group acting in Minkowski space. The gauging of this external group induces a Riemann-Cartan geometry on spacetime. If one generalizes the gauge group of gravity, one finds still more involved spacetime geometries. If one specializes it to the translation group, one finds a specific …
It is shown, using the Einstein-Cartan-Sciama-Kibble theory of gravity, that gravitational collapse of spin-fluid fermionic matter with a stiff equation of state in a black hole of mass $M$ forms a new universe of mass $\sim M_\ast=M^2 m_n/m_\textrm{Pl}^2$, where $m_n$ is the mass of a neutron. Equaling $M_\ast$ to the mass of the Universe, which is about $10^{26}$ solar masses, gives $M\sim 10^3$ solar masses. Our Universe may thus have originated from the interior of an intermediate-mass black hole.
A general geometric construction of a generic null hypersurface in presence of torsion in the spacetime (Riemann-Cartan background), generated by a null vector $l^a$, is being developed here. We then explicitly define and structure various corresponding kinematical quantities. The dynamics of the null surface, particularly given by $\hat{G}_{ab}k^al^b$, is also discussed. The later one is constructed under the {\it geodesic constraint} condition. This yields a relation among the rate of change of expansion scalar corresponding to auxiliary null vector $k^a$ and various kinematical entities on …
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…
In the Einstein-Cartan-Sciama-Kibble theory of gravity, the intrinsic spin of fermionic matter generates spacetime torsion and induces gravitational repulsion at extremely high densities. This repulsion prevents the collapsing spin-fluid matter in a black hole from forming a singularity. Instead, the interior of a black hole with a stiff equation of state becomes a new universe, which contracts until a (big) bounce and then expands. We derive the equations describing the dynamics of our Universe, formed in such a scenario, in terms of the conformal time which is a convenient variable for testi…
The Einstein-Cartan-Sciama-Kibble theory of gravity removes the constraint of general relativity that the affine connection be symmetric by regarding its antisymmetric part, the torsion tensor, as a dynamical variable. The minimal coupling between the torsion tensor and Dirac spinors generates a spin-spin interaction which is significant in fermionic matter at extremely high densities. We show that such an interaction averts the unphysical big-bang singularity, replacing it with a cusp-like bounce at a finite minimum scale factor, before which the Universe was contracting. This scenario also e…
The Raychaudhuri equations for the expansion, shear and vorticity are generalized in a spacetime with torsion for timelike as well as null congruences. These equations are purely geometrical like the original Raychaudhuri equations and could be reduced to them when there is no torsion. Using the Einstein-Cartan-Sciama-Kibble field equations the effective stress-energy tensor is derived. We also consider an Oppenheimer-Snyder model for the gravitational collapse of dust. It is shown that the null energy condition (NEC) is violated before the density of the collapsing dust reaches the Planck den…
Locally Rotationally Symmetric Spacetimes in Einstein-Cartan Theory and Their Classification
Institute of Theoretical Physics, Faculty of Mathematics and Physics, Charles University（查理大学数学物理学院理论物理研究所）；DIME Sez. Metodi e Modelli Matematici, Università di Genova（热那亚大学DIME数学方法与模型系）；INFN Sezione di Genova（意大利国家核物理研究所热那亚分部）
We propose a simple scenario which explains why our Universe appears spatially flat, homogeneous and isotropic. We use the Einstein-Cartan-Kibble-Sciama (ECKS) theory of gravity which naturally extends general relativity to include the spin of matter. The torsion of spacetime generates gravitational repulsion in the early Universe filled with quarks and leptons, preventing the cosmological singularity: the Universe expands from a state of minimum but finite radius. We show that the dynamics of the closed Universe immediately after this state naturally solves the flatness and horizon problems i…
During the last five decades, gravity, as one of the fundamental forces of nature, has been formulated as a gauge theory of the Weyl-Cartan-Yang-Mills type. The present text offers commentaries on the articles from the most prominent proponents of the theory. In the early 1960s, the gauge idea was successfully applied to the Poincaré group of spacetime symmetries and to the related conserved energy-momentum and angular momentum currents. The resulting theory, the Poincaré gauge theory, encompasses Einstein's general relativity as well as the teleparallel theory of gravity as subcases. The spac…
Recently, gravitational gauge theories with torsion have been discussed by an increasing number of authors from a classical as well as from a quantum field theoretical point of view. The Einstein-Cartan(-Sciama-Kibble) Lagrangian has been enriched by the parity odd pseudoscalar curvature (Hojman, Mukku, and Sayed) and by torsion square and curvature square pieces, likewise of even and odd parity. (i) We show that the inverse of the so-called Barbero-Immirzi parameter multiplying the pseudoscalar curvature, because of the topological Nieh-Yan form, can only be appropriately discussed if torsion…
We use the Papapetrou method of multipole expansion to show that a Dirac field in the Einstein-Cartan-Kibble-Sciama (ECKS) theory of gravity cannot form singular configurations concentrated on one- or two-dimensional surfaces in spacetime. Instead, such a field describes a nonsingular particle whose spatial dimension is at least on the order of its Cartan radius. In particular, torsion modifies Burinskii's model of the Dirac electron as a Kerr-Newman singular ring of the Compton size, by replacing the ring with a toroidal structure with the outer radius of the Compton size and the inner radius…
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 …
If spacetime torsion couples to the intrinsic spin of matter according to the Einstein-Cartan-Sciama-Kibble theory of gravity, then the resulting gravitational repulsion at supranuclear densities prevents the formation of singularities in black holes. Consequently, the interior of every black hole becomes a new universe that expands from a nonsingular bounce. We consider gravitational collapse of fermionic spin-fluid matter with the stiff equation of state in a stellar black hole. Such a collapse increases the mass of the matter, which occurs through the Parker-Zel'dovich-Starobinskii quantum …
Ever since E.Cartan in the 1920s enriched the geometric framework of general relativity (GR) by introducing a {\it torsion} of spacetime, the question arose whether one could find a measurement technique for detecting the presence of a torsion field. Mao et al.(2007) claimed that the rotating quartz balls in the gyroscopes of the Gravity Probe B experiment, falling freely on an orbit around the Earth, should "feel" the torsion. Similarly, March et al.(2011) argue with the precession of the Moon and the Mercury and extend later their considerations to the Lageos satellite.--- A consistent theor…
