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Journal articles on the topic 'Teleparallelismo'

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Author: Grafiati

Published: 10 March 2023

Last updated: 11 March 2023

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1

D’Ambrosio, Fabio, Lavinia Heisenberg, and Simon Kuhn. "Revisiting cosmologies in teleparallelism." Classical and Quantum Gravity 39, no. 2 (December 23, 2021): 025013. http://dx.doi.org/10.1088/1361-6382/ac3f99.

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Abstract We discuss the most general field equations for cosmological spacetimes for theories of gravity based on non-linear extensions of the non-metricity scalar and the torsion scalar. Our approach is based on a systematic symmetry-reduction of the metric-affine geometry which underlies these theories. While for the simplest conceivable case the connection disappears from the field equations and one obtains the Friedmann equations of general relativity, we show that in f ( Q ) cosmology the connection generically modifies the metric field equations and that some of the connection components become dynamical. We show that f ( Q ) cosmology contains the exact general relativity solutions and also exact solutions which go beyond. In f ( T ) cosmology, however, the connection is completely fixed and not dynamical.

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2

FIORINI, FRANCO, and RAFAEL FERRARO. "A TYPE OF BORN-INFELD REGULAR GRAVITY AND ITS COSMOLOGICAL CONSEQUENCES." International Journal of Modern Physics A 24, no. 08n09 (April 10, 2009): 1686–89. http://dx.doi.org/10.1142/s0217751x09045236.

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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.

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3

Maluf, J. W., and A. Goya. "Space–time defects and teleparallelism." Classical and Quantum Gravity 18, no. 23 (November 22, 2001): 5143–54. http://dx.doi.org/10.1088/0264-9381/18/23/310.

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4

VON BORZESZKOWSKI, HORST-HEINO. "TELEPARALLELIZED AND AFFINE THEORIES OF GRAVITY: NEW PERSPECTIVES FOR MACHIAN AND QUANTUM GRAVITY." International Journal of Modern Physics A 17, no. 29 (November 20, 2002): 4153–60. http://dx.doi.org/10.1142/s0217751x02013174.

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We compare metric theories to theories with teleparallelism and affine theories of gravity in order to discuss perspectives in the canonical quantization of gravity opened by a realization of Mach's principle.

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5

Korunur, M., M. Saltı, and O. Aydogdu. "An axially symmetric scalar field and teleparallelism." European Physical Journal C 50, no. 1 (February 6, 2007): 101–7. http://dx.doi.org/10.1140/epjc/s10052-006-0195-1.

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6

Nishino, Hitoshi, and Subhash Rajpoot. "Teleparallelism for a massive spin-2 field." Classical and Quantum Gravity 28, no. 12 (May 26, 2011): 125019. http://dx.doi.org/10.1088/0264-9381/28/12/125019.

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7

Lawrence, Tom. "Tangent space symmetries in general relativity and teleparallelism." International Journal of Geometric Methods in Modern Physics 18, supp01 (April 26, 2021): 2140008. http://dx.doi.org/10.1142/s0219887821400089.

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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.

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8

Bamba, Kazuharu, Jaume de Haro, and Sergei D. Odintsov. "Future singularities and teleparallelism in loop quantum cosmology." Journal of Cosmology and Astroparticle Physics 2013, no. 02 (February 5, 2013): 008. http://dx.doi.org/10.1088/1475-7516/2013/02/008.

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9

Delphenich, DH. "The use of the teleparallelism connection in continuum mechanics." Mathematics and Mechanics of Solids 21, no. 10 (August 6, 2016): 1260–75. http://dx.doi.org/10.1177/1081286514563819.

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10

NASHED, GAMAL G. L. "ENERGY OF SPHERICALLY SYMMETRIC SPACE–TIMES ON REGULARIZING TELEPARALLELISM." International Journal of Modern Physics A 25, no. 14 (June 10, 2010): 2883–95. http://dx.doi.org/10.1142/s0217751x10049037.

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We calculate the total energy of an exact spherically symmetric solutions, i.e. Schwarzschild and Reissner–Nordström, using the gravitational energy–momentum 3-form within the tetrad formulation of general relativity. We explain how the effect of the inertial makes the total energy unphysical. Therefore, we use the covariant teleparallel approach which makes the energy always physical one. We also show that the inertial has no effect on the calculation of momentum.

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11

de A. Campos, R., P. S. Letelier, and C. G. de Oliveira. "Canonical Quantization Procedure in a Theory with Absolute Teleparallelism." Progress of Theoretical Physics 74, no. 3 (September 1, 1985): 626–29. http://dx.doi.org/10.1143/ptp.74.626.

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12

Lu, Wenjie, Wolung Lee, and Kin-Wang Ng. "Teleparallel Poincaré cosmology and ΛCDM model." International Journal of Modern Physics D 23, no. 06 (May 2014): 1450057. http://dx.doi.org/10.1142/s0218271814500576.

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We apply the teleparallelism condition to the Poincaré gauge theory (PGT) of gravity. The resultant teleparallelized cosmology is completely equivalent to the Friedmann cosmology derived from Einstein's general theory of relativity. The torsion is shown to play the role of the cosmological constant driving the cosmic acceleration. We then extend such theory to include the effect of spin and explore the possibility of accounting for the current accelerating universe by a spinning dark energy.

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13

Ulhoa, S. C., and R. G. G. Amorim. "On Noncommutative Corrections of Gravitational Energy in Teleparallel Gravity." Journal of Gravity 2013 (June 13, 2013): 1–7. http://dx.doi.org/10.1155/2013/217813.

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We use the theory of teleparallelism equivalent to general relativity based on noncommutative spacetime coordinates. In this context, we write the corrections of the Schwarzschild solution. We propose the existence of a Weitzenböck spacetime that matches the corrected metric tensor. As an important result, we find the corrections of the gravitational energy in the realm of teleparallel gravity due to the noncommutativity of spacetime. Then we interpret such corrections as a manifestation of quantum theory in gravitational field.

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14

Mielke, Eckehard W. "Chern–Simons solutions of the chiral teleparallelism constraints of gravity." Nuclear Physics B 622, no. 1-2 (February 2002): 457–71. http://dx.doi.org/10.1016/s0550-3213(01)00597-1.

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15

Mielke, Eckehard W. "Ashtekar's complex variables in general relativity and its teleparallelism equivalent." Annals of Physics 219, no. 1 (October 1992): 78–108. http://dx.doi.org/10.1016/0003-4916(92)90313-b.

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16

Bamba, Kazuharu, Chao-Qiang Geng, and Ling-Wei Luo. "Generation of large-scale magnetic fields from inflation in teleparallelism." Journal of Cosmology and Astroparticle Physics 2012, no. 10 (October 31, 2012): 058. http://dx.doi.org/10.1088/1475-7516/2012/10/058.

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17

Vargas, Jos� G. "Geometrization of the physics with teleparallelism. I. The classical interactions." Foundations of Physics 22, no. 4 (April 1992): 507–26. http://dx.doi.org/10.1007/bf00732920.

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18

Fazlpour, Behnaz, and Ali Banijamali. "Tachyonic Teleparallel Dark Energy in Phase Space." Advances in High Energy Physics 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/279768.

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Recently, nonminimal coupling between a noncanonical scalar field and gravity in the framework of teleparallelism has been proposed. Noncanonical scalar field is tachyon field, and the model is known as tachyonic teleparallel dark energy. Here, we perform a dynamical analysis of the model, find its critical points, and study their stability. We find that all the critical points are dark energy dominated solutions corresponding to an accelerating universe. It is also shown that there exist two critical lines which are stable attractors of the model.

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19

ULHOA, S. C., A. F. SANTOS, and R. G. G. AMORIM. "ON THE ENERGY–MOMENTUM FLUX IN GÖDEL-TYPE MODELS." Modern Physics Letters A 28, no. 10 (March 28, 2013): 1350039. http://dx.doi.org/10.1142/s0217732313500399.

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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.

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20

Ulhoa, S. C., E. P. Spaniol, H. G. V. Gonzalez, and R. G. G. Amorim. "On the quantization of a neutron star." Modern Physics Letters A 35, no. 09 (March 21, 2020): 2050051. http://dx.doi.org/10.1142/s0217732320500510.

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This paper deals with quantum gravitation applied to a simple neutron star model. For the quantization process, we use the Weyl prescription that can be used for functions that are not defined in the phase space. The Weyl quantization is applied to the expression of gravitational energy defined in the context of Teleparallelism Equivalent to General Relativity (TEGR). From this, a quantum equation is obtained whose observable is the classical energy. As a consequence, we obtained discretizations for the mass of the star and its angular momentum.

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21

Garcia de Andrade, L. C. "Chiral asymmetries in near-horizon region of charged black hole and teleparallelism." International Journal of Geometric Methods in Modern Physics 18, no. 05 (February 6, 2021): 2150073. http://dx.doi.org/10.1142/s0219887821500730.

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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.

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22

Mazur, P. O., and L. M. Sokolowski. "Teleparallelism as a universal connection on null hypersurfaces in general relativity." General Relativity and Gravitation 18, no. 8 (August 1986): 781–804. http://dx.doi.org/10.1007/bf00770201.

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23

Trzesowski, Andrzej. "Dislocations and internal length measurement in continuized crystals. II. Closed teleparallelism." International Journal of Theoretical Physics 33, no. 4 (April 1994): 951–66. http://dx.doi.org/10.1007/bf00672826.

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24

Pan, Y. Y., and J. Ren. "Spin-Rotation Coupling in the Teleparallelism Description in High Speed Rotation System." International Journal of Theoretical Physics 50, no. 3 (December 9, 2010): 724–28. http://dx.doi.org/10.1007/s10773-010-0602-0.

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25

Nashed, Gamal G. L. "Energy and momentum of general spherically symmetric frames on the regularizing teleparallelism." Chinese Physics B 21, no. 1 (January 2012): 010401. http://dx.doi.org/10.1088/1674-1056/21/1/010401.

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26

Zhogin, I. L. "Topological quasi-charges in the Einstein theory of teleparallelism and particle combinatorics." Soviet Physics Journal 33, no. 7 (July 1990): 562–65. http://dx.doi.org/10.1007/bf00899102.

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27

Wu, Yi-Peng. "Inflation with teleparallelism: Can torsion generate primordial fluctuations without local Lorentz symmetry?" Physics Letters B 762 (November 2016): 157–61. http://dx.doi.org/10.1016/j.physletb.2016.09.025.

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28

Bamba, Kazuharu. "Thermodynamic properties of modified gravity theories." International Journal of Geometric Methods in Modern Physics 13, no. 06 (June 15, 2016): 1630007. http://dx.doi.org/10.1142/s0219887816300075.

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We review thermodynamic properties of modified gravity theories, such as [Formula: see text] gravity and [Formula: see text] gravity, where [Formula: see text] is the scalar curvature and [Formula: see text] is the torsion scalar in teleparallelism. In particular, we explore the equivalence between the equations of motion for modified gravity theories and the Clausius relation in thermodynamics. In addition, thermodynamics of the cosmological apparent horizon is investigated in [Formula: see text] gravity. We show both equilibrium and nonequilibrium descriptions of thermodynamics. It is demonstrated that the second law of thermodynamics in the universe can be met, when the temperature of the outside of the apparent horizon is equivalent to that of the inside of it.

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29

Biswas, Sujay Kr, and Subenoy Chakraborty. "Interacting dark energy in f(T) cosmology: A dynamical system analysis." International Journal of Modern Physics D 24, no. 07 (May 27, 2015): 1550046. http://dx.doi.org/10.1142/s0218271815500467.

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This paper deals with an interacting dark energy (DE) model in the framework of f(T) cosmology. A cosmologically viable form of f(T) is chosen (T is the torsion scalar in teleparallelism) in the background of flat homogeneous and isotropic Friedmann–Robertson–Walker (FRW) spacetime model of the universe. The matter content of the universe is chosen as dust interacting with minimally coupled scalar field. The evolution equations are reduced to an autonomous system of ordinary differential equations by suitable transformation of variables. The nature of critical points is analyzed by evaluating the eigenvalues of the linearized Jacobi matrix and stable attractors are examined from the point of view of cosmology. Finally, both classical and quantum stability of the model have been discussed.

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30

ALDAYA, V., and E. SÁNCHEZ-SASTRE. "GAUGE THEORIES OF GRAVITY AND MASS GENERATION." International Journal of Geometric Methods in Modern Physics 05, no. 02 (March 2008): 197–232. http://dx.doi.org/10.1142/s0219887808002710.

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The compensating Utiyama's method including space-time symmetries is revisited as well as the gauge gravitational theories associated with translation, Poincaré and Weyl groups. Then we propose an extension of the gauge symmetry, allowing for the incorporation of the gauge group parameters into the theory as dynamical fields by considering the jet-gauge group as fundamental symmetry. As a consequence, a natural mass-generating mechanism for the gauge potentials arises without damaging gauge invariance. We also present, as a simple example, some sort of generalized Stueckelberg model for the Weyl group, thus accounting for massive dilatonic gauge field. Finally, the standard diffeomorphism symmetry of gravitation is extended by resorting to the jet-diffeomorphism group, formalism which helps to fix the Hilbert-Einstein Lagrangian in the teleparallelism version.

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31

Mielke, Eckehard W. "Anomaly-free solution of the Ashtekar constraints for the teleparallelism equivalent of gravity." Physics Letters A 251, no. 6 (February 1999): 349–53. http://dx.doi.org/10.1016/s0375-9601(98)00937-2.

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32

Sousa, A. A., and J. W. Maluf. "Canonical Formulation of Gravitational Teleparallelism in 2+1 Dimensions in Schwinger's Time Gauge." Progress of Theoretical Physics 104, no. 3 (September 1, 2000): 531–43. http://dx.doi.org/10.1143/ptp.104.531.

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33

Vargas, Jos� G., Douglas G. Torr, and Alvaro Lecompte. "Geometrization of the physics with teleparallelism. II. Towards a fully geometric Dirac equation." Foundations of Physics 22, no. 4 (April 1992): 527–47. http://dx.doi.org/10.1007/bf00732921.

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34

Formiga, J. B. "Equivalence Between an Extension of Teleparallelism to a Weyl Geometry and General Relativity." International Journal of Theoretical Physics 53, no. 6 (January 19, 2014): 1971–77. http://dx.doi.org/10.1007/s10773-014-2003-2.

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35

Hehl, Friedrich W., Yakov Itin, and Yuri N. Obukhov. "On Kottler's path: Origin and evolution of the premetric program in gravity and in electrodynamics." International Journal of Modern Physics D 25, no. 11 (October 2016): 1640016. http://dx.doi.org/10.1142/s0218271816400162.

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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.

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36

BENNETT, D. L., C. R. DAS, L. V. LAPERASHVILI, and H. B. NIELSEN. "THE RELATION BETWEEN THE MODEL OF A CRYSTAL WITH DEFECTS AND PLEBANSKI'S THEORY OF GRAVITY." International Journal of Modern Physics A 28, no. 13 (May 20, 2013): 1350044. http://dx.doi.org/10.1142/s0217751x13500449.

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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 [Formula: see text] 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.

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37

Chattopadhyay, Surajit. "Interacting modified Chaplygin gas in f(T) gravity framework and analysis of its stability against gravitational perturbation." International Journal of Geometric Methods in Modern Physics 14, no. 03 (February 14, 2017): 1750035. http://dx.doi.org/10.1142/s0219887817500359.

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In this work, we investigate the cosmological application of modified Chaplygin gas (MCG) interacting with pressureless dark matter (DM) in the [Formula: see text] modified gravity framework, where [Formula: see text] is the torsion scalar in teleparallelism. The interaction term has been chosen proportional to the MCG density with positive coupling constant. In the Einstein general relativity (GR) framework, the interacting MCG has been found to have equation of state (EoS) parameter behaving like quintessence. However, the [Formula: see text] gravity reconstructed via the interacting MCG has been found to have EoS crossing the phantom boundary of [Formula: see text]. Thus, one can generate a quintom-like EoS from an interacting MCG model in flat universe in the modified gravity cosmology framework. The reconstructed [Formula: see text] model has been found to interpolate between dust and [Formula: see text]CDM. Stability of the reconstructed [Formula: see text] has been investigated and it has been observed that the model is stable against gravitational perturbation. Cosmological evolution of primordial perturbations has also been investigated and the self-interacting potential has been found to increase with cosmic time and the squared speed of sound has been found to be non-negative.

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38

Garcia de Andrade, L. C. "Dynamo seeds from gravitational torsional anomalies and de Sitter magnetized metrics." Canadian Journal of Physics 100, no. 2 (February 2022): 96–101. http://dx.doi.org/10.1139/cjp-2021-0243.

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Recently gravitational and Nieh–Yan (NY) chiral anomalies have been obtained in Riemann–Cartan space–time (L.C. Garcia de Andrade. Class Quantum Grav. 38(6), 065005 (2021). doi: 10.1088/1361-6382/abd25f ), where electrodynamics is encoded in the metric geometry. In this paper we follow the same pathway by obtaining a class of deformed de Sitter metrics in teleparallelism. The existence of the unmagnetized de Sitter metric (DSMM) without axial anomalies is proved. Unified theories à la Einstein, Eddington, and Schroedinger, called modified de Sitter metrics, present some novel features. First, we show that a pure DSMM in T4 does not induce gravitational anomalies. This is a motivation to study modifications of DSMM. NY torsional anomaly in DSMM teleparallel T4 geometry is shown to vanish in all cases. Gravitational non-trivial anomalies are obtained from these metrics. Torsional anomaly, much used in condensed matter physics, does not vanish. From these deformed DSMM, we show that a dynamo equation with torsional gradient sources is valid from class III of the metrics but is torsionless sourced in class II. We show that in the gravitational anomaly of new deformed de Sitter metric one may cancel the gravitational anomaly, by a proper choice of the metric function. The axial anomaly is obtained for some metric deformation as well. A simple deformation leads to the existence of the NY density in the case of DSMM. This would be class IV of DSMM.

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39

Lucas, Tiago Gribl, Yuri N. Obukhov, and J. G. Pereira. "Regularizing role of teleparallelism." Physical Review D 80, no. 6 (September 30, 2009). http://dx.doi.org/10.1103/physrevd.80.064043.

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40

Wu, Yi-Peng, and Chao-Qiang Geng. "Primordial fluctuations within teleparallelism." Physical Review D 86, no. 10 (November 27, 2012). http://dx.doi.org/10.1103/physrevd.86.104058.

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41

Güdekli, Ertan, Aizhan Myrzakul, and Ratbay Myrzakulov. "Teleparallelism by inhomogeneous dark fluid." Astrophysics and Space Science 359, no. 2 (September 30, 2015). http://dx.doi.org/10.1007/s10509-015-2515-0.

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42

Itin, Yakov, Friedrich W. Hehl, and Yuri N. Obukhov. "Premetric equivalent of general relativity: Teleparallelism." Physical Review D 95, no. 8 (April 12, 2017). http://dx.doi.org/10.1103/physrevd.95.084020.

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43

Ulhoa, S. C., F. L. Carneiro, and J. W. Maluf. "On the thermodynamics of PP-waves." Modern Physics Letters A 37, no. 32 (October 20, 2022). http://dx.doi.org/10.1142/s0217732322502194.

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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.

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44

Mielke, Eckehard W. "Topologically modified teleparallelism, passing through the Nieh-Yan functional." Physical Review D 80, no. 6 (September 23, 2009). http://dx.doi.org/10.1103/physrevd.80.067502.

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45

"Ashtekar's complex variables in general relativity and its teleparallelism equivalent." Annals of Physics 218, no. 2 (September 1992): 385. http://dx.doi.org/10.1016/0003-4916(92)90096-5.

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46

Sahoo, Parbati, Avik De, Tee How Loo, and PRADYUMN KUMAR SAHOO. "Periodic cosmic evolution in f(Q) gravity formalism." Communications in Theoretical Physics, August 30, 2022. http://dx.doi.org/10.1088/1572-9494/ac8d8a.

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Abstract We study the periodic cosmic transit behavior of accelerated universe in the framework of symmetric teleparallelism. The exact solution of field equations is obtained by employing a well known deceleration parameter (DP) called periodic varying deceleration parameter (PVDP), $q=m\cos k t-1$. The viability and physical reliability of the DP are studied by using the observational constraints. The dynamics of periodicity and singularity are addressed in details with respect to time and redshift parameter. Several energy conditions are discussed in this setting.

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47

Formiga, J. B., J. B. Fonseca–Neto, and C. Romero. "An extension of teleparallelism and the geometrization of the electromagnetic field." Physical Review D 87, no. 6 (March 26, 2013). http://dx.doi.org/10.1103/physrevd.87.067702.

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48

Obukhov, Yu N., and J. G. Pereira. "Lessons of spin and torsion: Reply to “Consistent coupling to Dirac fields in teleparallelism”." Physical Review D 69, no. 12 (June 2, 2004). http://dx.doi.org/10.1103/physrevd.69.128502.

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49

Mielke, Eckehard W. "Consistent coupling to Dirac fields in teleparallelism: Comment on “Metric-affine approach to teleparallel gravity”." Physical Review D 69, no. 12 (June 2, 2004). http://dx.doi.org/10.1103/physrevd.69.128501.

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de Andrade, L. C. Garcia. "Gravitational waves LIGO data sourced by spin-1 and spin-0 torsion propagating modes in teleparallelism." European Physical Journal Plus 136, no. 2 (January 28, 2021). http://dx.doi.org/10.1140/epjp/s13360-020-01065-5.

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