On Kottler's path: Origin and evolution of the premetric program in gravity and in electrodynamics

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

doi:10.1142/s0218271816400162

Cited by 38 publications

(58 citation statements)

References 177 publications

(275 reference statements)

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“…From a physical viewpoint it represents self-interaction and is related to the non-linear nature of the gravitational interaction in general relativity 3 . In principle, one can consider the total energy-momentum Σ (total) µ that includes both the gravitational and matter contributions, and rewrite the field equations (25) as…”

Section: A1···mentioning

confidence: 99%

Teleparallel theories of gravity as analogue of nonlinear electrodynamics

et al. 2018

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The teleparallel formulation of gravity theories reveals close structural analogies to electrodynamics, which are more hidden in their usual formulation in terms of the curvature of spacetime. We show how every locally Lorentz invariant teleparallel theory of gravity with second order field equations can be understood as built from a gravitational field strength and excitation tensor which are related to each other by a constitutive relation, analogous to the premetric construction of theories of electrodynamics. We demonstrate how the previously studied models of f (T) and f (Tax, Tten, Tvec) gravity as well as teleparallel dark energy can be formulated in this language. The advantage of this approach to gravity is that the field equations for different models all take the same compact form and general results can be obtained. An important new such result we find is a constraint which relates the field equations of the tetrad and the spin connection.

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Section: A1···mentioning

confidence: 99%

Teleparallel theories of gravity as analogue of nonlinear electrodynamics

et al. 2018

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“…The premetric formalism was studied intensively in the book [4]. For an account of the recent developments in this area, see our review [5].…”

Section: Introductionmentioning

confidence: 99%

“…Although Kottler's premetric program works well in Newtonian gravity [1] and even in a flat gravitomagnetism model [5], it seems to be completely unacceptable in general relativity (GR). This is due to the well-known fact that Einstein's theory is essentially based on a pseudo-Riemann geometry with the metric tensor as its primary variable.…”

Section: Introductionmentioning

confidence: 99%

Premetric equivalent of general relativity: Teleparallelism

Itin¹,

Hehl

Obukhov³

2017

Phys. Rev. D

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In general relativity (GR), the metric tensor of spacetime is essential since it represents the gravitational potential. In other gauge theories (such as electromagnetism), the so-called premetric approach succeeds in separating the purely topological field equation from the metric-dependent constitutive law. We show here that GR allows for a premetric formulation, too. For this purpose, we apply the teleparallel approach of gravity, which represents GR as a gauge theory based on the translation group. We formulate the metric-free topological field equation and a general linear constitutive law between the basic field variables. The requirement of local Lorentz invariance turns the model into a full equivalent of GR. Our approach opens a way for a natural extension of GR to diverse geometrical structures of spacetime.Comment: Some corrections made in accordance with criticisms of the referee, references added; this version supersedes the printed version (it contains some slips due to the editorial policy

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“…Lately we followed in [18] the program of Kottler of 1922 to remove the metric tensor of spacetime, the gravitational potential within general relativity theory (GR), from the fundamental laws of classical electromagnetism and gravity as far as possible. In particular, we applied this to the theory of gravity [31] in that we started from a translational gauge theory of gravity, also known as teleparallel theory of gravity (TG) 1 .…”

Section: Introductionmentioning

confidence: 99%

Premetric teleparallel theory of gravity and its local and linear constitutive law

et al. 2018

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We continue to investigate the premetric teleparallel theory of gravity (TG) with the coframe (tetrad) as gravitational potential. We start from the field equations and a local and linear constitutive law. We create a Tonti diagram of TG in order to disclose the structure of TG. Subsequently we irreducibly decompose the 6th order constitutive tensor under the linear group. Moreover, we construct the most general constitutive tensors from the metric and the totally antisymmetric Levi-Civita symbol, and we demonstrate that they encompass nontrivial axion and skewon type pieces. Using these tools, we derive for TG in the geometric-optics approximation propagating massless spin 0, 1, and 2 waves, including the special case of Einstein's general relativity.

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On Kottler's path: Origin and evolution of the premetric program in gravity and in electrodynamics

Cited by 38 publications

References 177 publications

Teleparallel theories of gravity as analogue of nonlinear electrodynamics

Teleparallel theories of gravity as analogue of nonlinear electrodynamics

Premetric equivalent of general relativity: Teleparallelism

Premetric teleparallel theory of gravity and its local and linear constitutive law

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