Premetric equivalent of general relativity: Teleparallelism

Itin, Yakov; Hehl, Friedrich W.; Obukhov, Yuri N.

doi:10.1103/physrevd.95.084020

Cited by 37 publications

(62 citation statements)

References 37 publications

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“…More importantly, although this Cartan version of TEGR cannot be considered as a Poincaré Gauge Theory (PGT) 10 , the whole Poincaré symmetry is required. This point should be compared to the work of [18], which adopts a very different approach, but still reaches the conclusion that TEGR cannot be obtained without the whole Poincaré symmetry.…”

Section: Discussionmentioning

confidence: 97%

Teleparallel gravity equivalent of general relativity as a gauge theory: Translation or Cartan connection?

2019

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In this paper we question the status of TEGR, the Teleparallel Equivalent of General Relativity, as a gauge theory of translations. We observe that TEGR (in its usual translation-gauge view) does not seem to realize the generally admitted requirements for a gauge theory for some symmetry group G: namely it does not present a mathematical structure underlying the theory which relates to a principal G-bundle and the choice of a connection on it (the gauge field). We point out that, while it is usually presented as absent, the gauging of the Lorentz symmetry is actually present in the theory, and that the choice of an Erhesmann connection to describe the gauge field makes the translations difficult to implement (mainly because there is in general no principal translation-bundle). We finally propose to use the Cartan Geometry and the Cartan connection as an alternative approach, naturally arising from the solution of the issues just mentioned, to obtain a more mathematically sound framework for TEGR.

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Section: Discussionmentioning

confidence: 97%

Teleparallel gravity equivalent of general relativity as a gauge theory: Translation or Cartan connection?

2019

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“…In the last equality we introduced the convenient supermetric or constitutive tensor representation of the Lagrangian [8,9,15], where below the metric must be read as a function of the tetrads 1…”

Section: The New General Relativity Lagrangianmentioning

confidence: 99%

Hamiltonian and primary constraints of new general relativity

2019

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We derive the kinematic Hamiltonian for the so-called "new general relativity" class of teleparallel gravity theories, which is the most general class of theories whose Lagrangian is quadratic in the torsion tensor and does not contain parity violating terms. Our approach makes use of an explicit expression for the flat, in general, nonvanishing spin connection, which avoids the use of Lagrange multipliers, while keeping the theory invariant under local Lorentz transformations. We clarify the relation between the dynamics of the spin connection degrees of freedom and the tetrads. The terms constituting the Hamiltonian of the theory can be decomposed into irreducible parts under the rotation group. Using this, we demonstrate that there are nine different classes of theories, which are distinguished by the occurrence or non-occurrence of certain primary constraints. We visualize these different classes and show that the decomposition into irreducible parts allows us to write the Hamiltonian in a common form for all nine classes, which reproduces the specific Hamiltonians of more restricted classes in which particular primary constraints appear. * blixt@ut.ee † manuel.hohmann@ut.ee ‡ christian.pfeifer@ut.ee

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“…It should be pointed out that there have been some promising attempts at formulating a strong-field theory of gravitation that can be expressed in an extended Maxwell form [20]. Furthermore, the basis for those theories is the formulation of Einstein's equations in terms of teleparallelism.…”

Section: The Einstein-maxwell Unification Problemmentioning

confidence: 99%

On the risk of premature unification

Delphenich

2019

J. Phys.: Conf. Ser.

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Although the wish to unify theories into something more fundamental is omnipresent and compelling, nonetheless, in a sense, theories must first be "unifiable." The reasons for the success of the unification of electricity and magnetism into a theory of electromagnetism are contrasted with the reasons for the failure of the Einstein-Maxwell unification of gravitation and electromagnetism and the attempts of quantum gravity to unify Einstein's theory of gravity with quantum field theory. The difference between a unification of two theories, a concatenation of them, and the existence of a formal analogy between them is also discussed.

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Premetric equivalent of general relativity: Teleparallelism

Cited by 37 publications

References 37 publications

Teleparallel gravity equivalent of general relativity as a gauge theory: Translation or Cartan connection?

Teleparallel gravity equivalent of general relativity as a gauge theory: Translation or Cartan connection?

Hamiltonian and primary constraints of new general relativity

On the risk of premature unification

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