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This paper deals with the thermodynamics of gravitational radiation arising from the Bondi-Sachs space-time. The equation of state found allows us to conclude that the dependence of the energy density on the temperature is a quadratic power of the latter. Such a conclusion is possible once the consequences of the first law of thermodynamics are analyzed. Then, in analogy to electromagnetic radiation, the same approach used by Planck to obtain the quantum of energy of the gravitational radiation is proposed. An energy for the graviton proportional to the cubic frequency is found. The graviton is here understood as the quantum of gravitational energy. [ABSTRACT FROM AUTHOR]

The concept and definitions of the energy–momentum and angular momentum of the gravitational field in the teleparallel equivalent of general relativity (TEGR) are reviewed. The importance of these definitions is justified by three major reasons. First, the TEGR is a well established and widely accepted formulation of the gravitational field, whose basic field strength is the torsion tensor of the Weitzenböck connection. Second, in the phase space of the TEGR there exists an algebra of the Poincaré group. Not only the definitions of the gravitational energy–momentum and 4‐angular momentum satisfy this algebra, but also the first class constraints related to these definitions satisfy the algebra. And third, numerous applications of these definitions lead to physically consistent results. These definitions follow from a well established Hamiltonian formulation, and rely on the idea of localization of the gravitational energy. In this review, the concept of localizability of the gravitational energy is revisited, in light of results obtained in recent years. The behavior of free particles is studied in the space–time of plane fronted gravitational waves (pp‐waves). Free particles are here understood as particles that are not subject to external forces other than the gravitational acceleration due to pp‐waves. Since these particles acquire or loose kinetic energy locally, the transfer of energy from or to the gravitational field must also be localized. This theoretical result is considered an important and definite argument in favor of the localization of the gravitational energy–momentum, and by extension, of the gravitational 4‐angular momentum. [ABSTRACT FROM AUTHOR]

In recent years, f(Q)$f(\mathbb {Q})$ gravity has enjoyed considerable attention in the literature and important results have been obtained. However, the question of how many physical degrees of freedom the theory propagates—and how this number may depend on the form of the function f—has not been answered satisfactorily. In this article it is shown that a Hamiltonian analysis based on the Dirac‐Bergmann algorithm—one of the standard methods to address this type of question—fails. The source of the failure is isolated and it is shown that other commonly considered teleparallel theories of gravity are affected by the same problem. Furthermore, it is pointed out that the number of degrees of freedom obtained in Phys. Rev. D 106 no. 4, (2022) by K. Hu, T. Katsuragawa, and T. Qui (namely eight), based on the Dirac‐Bergmann algorithm, is wrong. Using a different approach, it is shown that the upper bound on the degrees of freedom is seven. Finally, a more promising strategy for settling this important question is proposed. [ABSTRACT FROM AUTHOR]

In this work, the influence of the boundary term B is analyzed in a string-like thick brane scenario in the gravity context f (T , B) . For that, three models of f (T , B) are proposed, i. e., f 1 (T , B) = T + k B n , f 2 (T , B) = T + k (- T + B) n and f 3 (T , B) = T + k 1 T 2 + k 2 B 2 , where n, k and k 1 , 2 are parameters that control the deviation from the usual teleparallelism. The first relevant result obtained was the appearance of a super-located tower in the core for energy density. Furthermore, the greater the influence of the boundary term, the new maximums and minimums appear in the energy density. All this indicates the emergence of capable structures from split to the brane. The second relevant result was obtained by analyzing the gravitational perturbations, where the effective potential presents the supersymmetric form of quantum mechanics, leading to well-localized massless modes. [ABSTRACT FROM AUTHOR]

The role played by the congruence in the prediction of the gravitational energy in the teleparallel equivalent of general relativity is discussed. It is shown that some congruences yield unphysical predictions. It is also shown that the energy–momentum tensor density predicted by the proper reference frame of an arbitrary accelerated observer vanishes along the observer's worldline, regardless of its acceleration. The latter result is discussed and arguments both against and in favor of the use of this type of frame to describe the gravitational energy are presented; arguments against the belief that the principle of equivalence is incompatible with the localization of the gravitational energy are also presented. A gauge condition is applied to the teleparallel frame and its consistence is discussed: using three different tetrads for the pp-wave spacetimes, it is shown that the most consistent prediction comes from the tetrad that satisfies this gauge. The possibility of having a well-defined concept of absolute vacuum is also discussed. [ABSTRACT FROM AUTHOR]

This paper deals with gravitational thermodynamics. The first and second laws of thermodynamics are established in terms of energy density and pressure, which are defined in the scope of Teleparallelism Equivalent to General Relativity (TEGR). Such laws are applied to gravitational waves, in particular the PP-wave. A negative entropy variation for an isothermal process is obtained. [ABSTRACT FROM AUTHOR]

We analyze the conservation laws in the gauge gravity theory which are derived for the general class of gravitational models with the action invariant under the local Poincaré and the diffeomorphism group. The consistent Noether-Lagrange formalism is developed, revealing the important role of the auxiliary Goldstone and Stueckelberg fields, with the help of which we construct the composite gauge fields that have a clear geometrical and physical meaning. [ABSTRACT FROM AUTHOR]

This article deals with the fractional problem of Sturm–Liouville and the Hilbert space associated with the solutions of this differential equation. We apply a quantization procedure to Schwarzschild space–time and obtain a fractional differential equation. The Hilbert space for these solutions is established. We used equations arising from quantization for the FRW and Reissner–Nordstron metrics to build the respective Hilbert spaces. [ABSTRACT FROM AUTHOR]

Recently, presence of gravitational and axial anomalies in Riemann–Cartan (RC) spacetime [Garcia de Andrade, Class. Quantum Gravity 38 (2021)] indicates that topological densities expressed in terms of torsion may be very useful in understanding the physics involved. Pontryagin and Euler density may be presented in terms of torsion in teleparallelism. In this paper, computation of these topological torsional densities in Kerr black holes is given. The geometric quantisation of torsion is also discussed in terms of the teleparallel metric. Actually, the recent work of Del Grosso and Poplawski [arXiv: 2107.06112] showed that the torsion quantization appears when torsion is the generator of momentum quantum mechanical commutator. Moreover, Poplawski et al. showed that use of quantum torsion in quantum electrodynamic (QED) may avoid the divergences in Feynmann integrals, process called, a torsion regularization. Here, we compute the momenta components in terms of teleparallel Kerr black hole torsion generator, like a Casimir tensor. The quantum generator, while not yet related by torsion, is seen to be naturally associated to axial torsion skew-symmetric in the teleparallel geometry. An important fact is that from torsion quantization, torsion chirality appears naturally in the Einstein–Cartan spin-torsion analogy, where now spin-angular momentum of the black hole is connected to torsion. Torsional chiral anomalies are shown to diverge at black hole singularity, and then they cannot be canceled at singularity. [ABSTRACT FROM AUTHOR]

This study reconstructs the 1928–1929 correspondence between Reichenbach and Einstein about the latter’s latest distant parallelism-unified field theory, which attracted considerable public attention at the end of the 1920s. Reichenbach, who had recently become a Professor in Berlin, had the opportunity to discuss the theory with Einstein and therefore sent him a manuscript with some comments for feedback. The document has been preserved among Einstein’s papers. However, the subsequent correspondence took an unpleasant turn after Reichenbach published a popular article on distant parallelism in a newspaper. Einstein directly wrote to the Editorial Board complaining about Reichenbach’s unfair use of off-the-record information. While Reichenbach’s reply demonstrates a sense of personal betrayal at Einstein’s behavior, his published writings of that period point to a sense of intellectual betrayal of their shared philosophical ideals. In his attempts to unify both electricity and gravitation, Einstein had abandoned the physical heuristic that guided him to the relativity theory, to embrace a more speculative, mathematical heuristic that he and Reichenbach had both previously condemned. A decade-long personal and intellectual friendship grew fainter and then never recovered. This study, relying on archival material, aims to revisit the Reichenbach–Einstein relationship in the late 1920s in light of Reichenbach’s neglected contributions to the epistemology of the unified field theory program. Thereby, it hopes to provide a richer account of Reichenbach’s philosophy of space and time. [ABSTRACT FROM AUTHOR]

Recently, a new method to simplify calculations in teleparallel theories has been put forward. In this article, this method is improved and used to analyze the gravitational energy–momentum tensor (density) of the Schwarzschild solution in a frame that is arbitrarily accelerated along the z-direction. It is shown that, for a special type of frame, one cannot make the gravitational energy density vanish along the observer's worldline, regardless of the observer's acceleration. The role played by the frame and its relation to the observers' worldlines are investigated. It is shown that, for the aforementioned special frames, the results for the gravitational energy and angular momenta are consistent with what we would expect. [ABSTRACT FROM AUTHOR]

This paper looks at how changes of coordinates on a pseudo-Riemannian manifold induce homogeneous linear transformations on its tangent spaces. We see that a pseudo-orthonormal frame in a given tangent space is the basis for a set of Riemann normal coordinates. A Lorentz subgroup of the general linear transformations preserves this pseudo-orthonormality. We borrow techniques from the methodology of non-linear realizations to analyze this group-subgroup structure. "Parallel maps" are used to relate tangent space at different points. "Parallelisms" across a finite region of the manifold may be built up from them. These are used to define Weitzenböck connections and Levi-Civita connections. This provides a new formulation of teleparallel gravity, in which the tetrad field is viewed as a field-valued group element relating the coordinate basis to the frame basis used in defining a parallelism. This formulation separates the metric degrees of freedom from those associated with the choice of parallelism. The group element can be combined by matrix multiplication with Lorentz transformations of frame or with other Jacobian matrices. We show how this facilitates a new understanding of inertial forces and local Lorentz transformations. The analysis is also applied to translations of the coordinates. If they are constant across spacetime, this has no effect on the tangent space bases. If the translation parameters become fields, they induce general linear transformations of the coordinate basis; however, the tetrad components can only be expressed in terms of translations on a flat spacetime. [ABSTRACT FROM AUTHOR]

We propose a codimension two warped braneworld model within the teleparallel f (T) gravity. Asymptotically, the bulk geometry converges to an A d S 6 spacetime whose cosmological constant is produced by the torsion parameters. Furthermore, the torsion induces an AdS-dS transition on the exterior region. As the torsion parameters vary, the brane undergoes a phase transition from a thick string-like brane into ring-like structures. The bulk-brane Planck mass ration is modified by the torsion. The analysis of the stress–energy condition reveals a splitting brane process satisfying the weak and strong–energy conditions for some values of the parameters. In addition, we investigate the behavior of the gravitational perturbations in this scenario. It turns out that the gravitational spectrum has a linear behavior for small masses and is independent of the torsion parameters for large masses. In the bulk, the torsion keeps a gapless nonlocalizable and stable tower of massive modes. Inside the brane core, the torsion produces new barriers and potential wells leading to small amplitude massive modes and a massless mode localized around the ring structures. [ABSTRACT FROM AUTHOR]

The issue of encoding physical information into metric structure of physical theories has been discussed recently by the author in the case of black hole teleparallelism. In this paper, one obtains a teleparallel chiral currents from quantum anomalies and topological torsional invariants of Nieh-Yan type. The Pontryagin index is also obtained in the case of rotating Kerr spacetime metric of non-static black holes. Magnetic monopoles which appears in this approach can be eliminated by a torsion constraint. These ideas are applied to Kerr and Kerr–Newmann charged black holes. [ABSTRACT FROM AUTHOR]

A hybrid machinery that is useful for calculations in teleparallel theories when the spacetime is spherically symmetric is developed. Using this machinery, the gravitational energy–momentum tensor density of the Schwarzschild spacetime is evaluated in a frame adapted to observers that accelerate in the radial direction. The energy density, the total energy, and the gravitational energy‐momentum flux are obtained. The regularization procedure and the limit where gravity is absent is discussed. It turns out that the regularized energy and energy–momentum flux are consistent in the whole spacetime. The continuity equation for the gravitational energy–momentum also holds for any point outside the black hole. Finally, the static and freely falling cases are discussed. It is found that a static observer measures a negative gravitational energy density, while a freely falling one measures a vanishing density. [ABSTRACT FROM AUTHOR]

In this article we calculate the total angular momentum for Kerr space-time for slow rotations in the context of teleparallel gravity. In order to analyze the role of such a quantity, we apply Weyl quantization method to obtain a quantum equation for the z-component of the angular momentum density, and for the squared angular momentum density as well. We present an approximate solution using the Adomian decomposition method (AM), which reveals a discrete characteristic for angular momentum.

The Born–Infeld theory of the gravitational field formulated in Weitzenböck spacetime is studied in detail. The action, constructed quadratically upon the torsion two-form, reduces to Einstein gravity in the low field limit where the Born–Infeld constant λ goes to infinity, and it is described by second order field equations for the vielbein field in D spacetime dimensions. The equations of motion are derived, and a number of properties coming from them are discussed. In particular, we show that under fairly general circumstances, the equations of motion are those of Einstein's General Relativity plus an energy-momentum tensor of purely geometrical character. This tensor is obtained solely from the parallelization defining the spacetime structure, which is encoded in a set of D smooth, everywhere non-null, globally defined 1-forms e a . Spherical symmetry is studied as an example, and we comment on the emergence of the Schwarzschild geometry within this framework. Potential (regular) extensions of it are envisioned. [ABSTRACT FROM AUTHOR]

In 1922, Kottler put forward the program to remove the gravitational potential, the metric of spacetime, from the fundamental equations in physics as far as possible. He successfully applied this idea to Newton's gravitostatics and to Maxwell's electrodynamics, where Kottler recast the field equations in premetric form and specified a metric-dependent constitutive law. We will discuss the basics of the premetric approach and some of its beautiful consequences, like the division of universal constants into two classes. We show that classical electrodynamics can be developed without a metric quite straightforwardly: the Maxwell equations, together with a local and linear response law for electromagnetic media, admit a consistent premetric formulation. Kottler's program succeeds here without provisos. In Kottler's approach to gravity, making the theory relativistic, two premetric quasi-Maxwellian field equations arise, but their field variables, if interpreted in terms of general relativity, do depend on the metric. However, one can hope to bring the Kottler idea to work by using the teleparallelism equivalent of general relativity, where the gravitational potential, the coframe, can be chosen in a premetric way. [ABSTRACT FROM AUTHOR]

In the last dozen years, a wide and variegated mass of observational data revealed that the universe is now expanding at an accelerated rate. In the absence of a well-based theory to interpret the observations, cosmography provides information about the evolution of the universe from measured distances, only assuming that the geometry can be described by the Friedmann-Lemaitre-Robertson-Walker metric. In this paper, we perform a high-redshift analysis which allows us to put constraints on the cosmographic parameters up to the fifth-order, thus inducing indirect constraints on any gravity theory. Here, we are interested in the so-called teleparallel gravity theory, . Actually, we use the analytical expressions of the present day values of and its derivatives as functions of the cosmographic parameters to map the cosmography region of confidences into confidence ranges for and its derivative. Moreover, we show how these can be used to test some teleparallel gravity models without solving the dynamical equations. Our analysis is based on the Union2 Type Ia supernovae (SNIa) data set, a set of 28 measurements of the Hubble parameter, the Hubble diagram constructed from some gamma ray bursts (GRB) luminosity distance indicators and Gaussian priors on the distance from the baryon acoustic oscillations (BAOs) and the Hubble constant . To perform our statistical analysis and to explore the probability distributions of the cosmographic parameters, we use the Markov chain Monte Carlo (MCMC) method. [ABSTRACT FROM AUTHOR]

Recently, an extension of teleparallelism to a Weyl geometry which allows us to easily establish conformal invariance and 'geometrize' electromagnetism has been presented. In this paper, I extend a result which concerns the existence of the Schwarzschild solution to a particular class of this extension. In addition, I obtain the field equations of some models based on this extension, including the one which is equivalent to Einstein's field equations with a massless scalar field. [ABSTRACT FROM AUTHOR]

We show that plane-fronted gravitational waves induce the breaking of parallelograms in space-time, in the context of the teleparallel equivalent of general relativity. The breaking of parallelograms can be shown by considering a thought experiment that consists of a simple physical configuration, similar to the experimental setup that is expected to lead to the measurement of gravitational waves with the use of laser interferometers. An incident beam of light splits into two beams running along perpendicular arms, endowed with fixed mirrors at the extremes. The reflected light beams are detected at the same point of the splitting. Along each arm, the two light beams define two null vectors: the forward vector and the reflected vector. We show that the sum of these four vectors, the forward and reflected null vectors along the two arms, do form a parallelogram in flat space-time, but not in the presence of plane-fronted gravitational waves. The non-closure of the parallelogram is a manifestation of the torsion of the space-time, and in this context indicates the existence of gravitational waves. [ABSTRACT FROM AUTHOR]

In this paper, we deal with neutron stars, which are described by a perfect fluid model, in the context of the teleparallel equivalent of general relativity. We use numerical computations (based on the RNS code) to find the relation between the angular momentum of the field and the angular momentum of the source. One such relation was established for each stable star resulting from the numerical computation with an equation of state, the central energy density, and the ratio between the polar and equatorial radii as input, the central energy density and the ratio between polar and equatorial radii. We also find a regime in which the relation between gravitational angular momentum and moment of inertia (as well as the angular velocity of the fluid) is linear. We give the spatial distribution of the gravitational energy and show that it depends linearly on the squared angular velocity of the source. [ABSTRACT FROM AUTHOR]

In the present investigation, we show that there exists a close analogy of geometry of space-time in general relativity (GR) with a structure of defects in a crystal. We present the relation between the Kleinert's model of a crystal with defects and Plebanski's theory of gravity. We have considered the translational defects - dislocations and the rotational defects - disclinations - in the three- and four-dimensional crystals. The four-dimensional crystalline defects present the Riemann-Cartan space-time which has an additional geometric property - "torsion" - connected with dislocations. The world crystal is a model for the gravitation which has a new type of gauge symmetry: the Einstein's gravitation has a zero torsion as a special gauge, while a zero connection is another equivalent gauge with nonzero torsion which corresponds to the Einstein's theory of "teleparallelism". Any intermediate choice of the gauge with nonzero connection is also allowed. In the present investigation, we show that in the Plebanski formulation the phase of gravity with torsion is equivalent to the ordinary or topological gravity, and we can exclude a torsion as a separate dynamical variable. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to examine the energy content of the inflationary Universe described by Kantowski-Sachs space-time in quasilocal approach of teleparallel gravity and in the Hamiltonian structure of the teleparallel equivalent of general relativity. The teleparallel versions of field equations are also derived in such a space-time. [ABSTRACT FROM AUTHOR]

In this paper, we work in the context of Teleparallelism Equivalent to General Relativity (TEGR) in order to construct the energy-momentum flux for Gödel-type solutions of Einstein's equations. We use an stationary observer, which is settled by the tetrad choice, to obtain the gravitational pressure for each direction of space in cartesian coordinates. Then, we write down the total pressure for each direction in terms of the pressure of the fluid, thus we are able to identify the role of the gravitational pressure. [ABSTRACT FROM AUTHOR]

We investigate the distribution of gravitational energy in the spacetime of a Schwarzschild black hole immersed in a cosmic magnetic field. This is done in the context of the teleparallel equivalent of general relativity, which is an alternative geometrical formulation of general relativity, where gravity is described by a spacetime endowed with torsion rather than curvature, whose fundamental field variables are tetrad fields. We calculate the energy enclosed by a two-surface of constant radius-in particular, the energy enclosed by the event horizon of the black hole. In this case we find that the magnetic field has the effect of increasing the gravitational energy as compared to the vacuum Schwarzschild case. We also compute the energy (i) in the weak magnetic field limit, (ii) in the limit of vanishing magnetic field, and (iii) in the absence of the black hole. In all cases our results are consistent with what should be expected on physical grounds. [ABSTRACT FROM AUTHOR]

In this paper, we propose two new models in f( T) gravity to realize universe acceleration and phantom crossing due to dark torsion in the formalism. The model parameters are constrained and the observational test are discussed. The best fit results favors an accelerating universe with possible phantom crossing in the near past or future followed respectively by matter and radiation dominated era. [ABSTRACT FROM AUTHOR]

Quantized expressions for the gravitational energy and momentum are derived from a linearized theory of teleparallel gravity. The derivation relies on a second-quantization procedure that constructs annihilation and creation operators for the graviton. The resulting gravitational field is a collection of gravitons, each of which has precise energy and momentum. On the basis of the weak-field approximation of Schwarzschild's solution, a new form for the quantization of the mass of a black hole is derived. [ABSTRACT FROM AUTHOR]

The spin-rotation coupling can be described by the torsion axial-vector and teleparallelism of general relativity. In a large scale distance, with a high rotating velocity, the tangent velocity will exceed the velocity of light. To overcome that difficulty, we choose a nonuniform and position-dependent angular velocity, e.g. $\Omega(\rho)=\frac{\Omega}{\sqrt[K]{1+(\Omega\rho/C)^{K}}}$. Based on this choice, we find that the tangent velocity will be less than the speed of light at infinity and never be meaningless. Moreover, the new rotation-spin coupling is derived. And in the case of K=2, it will be consistent with the previous result with the constant angular velocity. [ABSTRACT FROM AUTHOR]

We present a method to calculate the gravitational energy when asymptotic boundary conditions for the space-time are not given. This is the situation for most of the cosmological models. The expression for the gravitational energy is obtained in the context of the teleparallel equivalent of general relativity. We apply our method first to the Schwarzschild-de Sitter solution of Einstein's equation, and then to the Robertson-Walker universe. We show that in the first case our method leads to an average energy density of the vacuum space-time, and in the latter case the energy vanishes in the case of null curvature. [ABSTRACT FROM AUTHOR]

The assumption that matter charges and currents could generate fields, which are called, in analogy with electromagnetism, gravitoeletric and gravitomagnetic fields, dating from the origins of General Relativity (GR). On the other hand, the Teleparallel Equivalent of GR (TEGR), as a gauge theory, seems to be the ideal scenario to define these fields, based on the gauge field strength components. The purpose of the present work is to investigate the nature of the gravitational electric and magnetic fields in the context of the TEGR, where the tetrad formalism on which it is based seems more suited to deal with phenomena related to observers. As its applications, we have studied the gravito-electromagnetic fields for the Schwarzschild solution and for the geometry produced by a spherical rotating shell in slow motion and weak field regime. The expressions obtained, at the linear regime, are very similar to those of electromagnetism. [ABSTRACT FROM AUTHOR]

Born-Infeld deformation strategy to smooth theories having divergent solutions is applied to the teleparallel equivalent of General Relativity. The equivalence between teleparallelism and General Relativity is exploited to obtain a deformed theory of gravity based on second order differential equations, since teleparallel Lagrangian is built just from first derivatives of the vierbein. We show that Born-Infeld teleparallelism cures the initial singularity in a spatially flat FRW universe; moreover, it provides a natural inflationary stage without resorting to an inflaton field. The Born-Infeld parameter λ bounds the dynamics of Hubble parameter H(t) and establishes a maximum attainable spacetime curvature. [ABSTRACT FROM AUTHOR]

We investigate the gravitational radiation produced by a linearly accelerated source in general relativity. The investigation is performed by studying the vacuum C metric, which is interpreted as representing the exterior space–time of an uniformly accelerating spherically symmetric gravitational source, and is carried out in the context of the teleparallel equivalent of general relativity. For an observer sufficiently far from both the (modified) Schwarzschild and Rindler horizons, which is a realistic situation, we obtain a simple expression for the total emitted gravitational radiation. We also briefly discuss on the absolute or relative character of the accelerated motion. [ABSTRACT FROM AUTHOR]

Abstract: A historical account of Einstein''s Fernparallelismus approach toward a unified field theory of gravitation and electromagnetism is given. In this theory, a space–time characterized by a curvature-free connection in conjunction with a metric tensor field, both defined in terms of a dynamical tetrad field, is investigated. The approach was pursued by Einstein in a number of publications that appeared in the period from summer 1928 until spring 1931. In the historical analysis special attention is given to the question of how Einstein tried to find field equations for the tetrads. We claim that it was the failure to find and justify a uniquely determined set of acceptable field equations that eventually led to Einstein''s abandoning this approach. We comment on some historical and systematic similarities between the Fernparallelismus episode and the Entwurf theory, i.e., the precursor theory of general relativity pursued by Einstein in the years 1912–1915. [Copyright &y& Elsevier]

By generalizing the Hodge dual operator to the case of soldered bundles, and working in the context of the teleparallel equivalent of general relativity, an analysis of the duality symmetry in gravitation is performed. Although the basic conclusion is that, at least in the general case, gravitation is not dual symmetric, there is a particular theory in which this symmetry shows up. It is a self dual (or anti-self dual) teleparallel gravity in which, due to the fact that it does not contribute to the interaction of fermions with gravitation, the purely tensor part of torsion is assumed to vanish. The ensuing fermionic gravitational interaction is found to be chiral. Since duality is intimately related to renormalizability, this theory may eventually be more amenable to renormalization than teleparallel gravity or general relativity. [ABSTRACT FROM AUTHOR]

The teleparallel versions of the Einstein and the Landau-Lifshitz energy-momentum complexes of the gravitational field are obtained. By using these complexes, the total energy of the universe, which includes the energy of both the matter and the gravitational fields, is then obtained. It is shown that in the case of a closed universe, the total energy vanishes independently of the pseudotensor used, as well as of the three dimensionless coupling constants of teleparallel gravity. [ABSTRACT FROM AUTHOR]

In the general relativistic description of gravitation, geometry replaces the concept of force. This is possible because of the universal character of free fall, and would break down in its absence. On the other hand, the teleparallel version of general relativity is a gauge theory for the translation group and, as such, describes the gravitational interaction by a force similar to the Lorentz force of electromagnetism, a non-universal interaction. Relying on this analogy it is shown that, although the geometric description of general relativity necessarily requires the existence of the equivalence principle, the teleparallel gauge approach remains a consistent theory for gravitation in its absence. [ABSTRACT FROM AUTHOR]

We consider massive spin 1 fields, in Riemann-Cartan space-times, described by Duffin-Kemmer-Petiau theory. We show that this approach induces a coupling between the spin 1 field and the space-time torsion which breaks the usual equivalence with the Proca theory, but that such equivalence is preserved in the context of the Teleparallel Equivalent of General Relativity. [ABSTRACT FROM AUTHOR]

We present a teleparallel complex gravity as the foundation for the formulation of noncommutative gravity theory. The negative energy ghosts in the conventional formulation with  U(1,3)  local Lorentz connection no longer exists, since the local Lorentz invariance is broken down to  U(1,3)  global Lorentz symmetry. As desired, our teleparallel complex gravity theory also passes the key classical test of perihelion advance of Mercury. Based on this result, we present a Lagrangian for the noncommutative teleparallel gravity theory. [Copyright &y& Elsevier]

Here we study the behaviour of the spin 0 sector of the DKP field in spaces with torsion. First we show that in a Riemann-Cartan manifold the DKP field presents an interaction with torsion when minimal coupling is performed, contrary to the behaviour of the KG field, a result that breaks the usual equivalence between the DKP and the KG fields. Next we analyse the case of the Teleparallel Equivalent of General Relativity (Weitzenböck manifold), showing that in this case there is a perfect agreement between KG and DKP fields. The origins of both results are also discussed. [ABSTRACT FROM AUTHOR]