Energy–momentum current for coframe gravity

Abstract

The obstruction for the existence of an energy momentum tensor for the gravitational field is connected with differential-geometric features of the Riemannian manifold. It has not to be valid for alternative geometrical structures. A teleparallel manifold is defined as a parallelizable differentiable 4D-manifold endowed with a class of smooth coframe fields related by global Lorentz, i.e., SO(1, 3) transformations. In this article a general free parametric class of teleparallel models is considered. It includes a 1-parameter subclass of viable models with the Schwarzschild coframe solution.A new form of the coframe field equation is derived from the general teleparallel Lagrangian by introducing the notion of a 3-parameter conjugate field strength F a . The field equation turns out to have a form completely similar to the Maxwell field equation d * F a = T a . By applying the Noether procedure, the source 3-form T a is shown to be connected with the diffeomorphism invariance of the Lagrangian. Thus the source T a of the coframe field is interpreted as the total conserved energy-momentum current. The energy-momentum tensor for coframe is defined. The total energymomentum current of a system of a coframe and a material fields is conserved. Thus a redistribution of the energy-momentum current between a material and a coframe (gravity) fields is possible in principle, unlike as in the standard GR. For special values of parameters, when the GR is reinstated, the energy-momentum tensor gives up the invariant sense, i.e., becomes a pseudo-tensor. Thus even a smallparametric change of GR turns it into a well defined Lagrangian theory.

Conserved currents in gravitational models with quasi-invariant Lagrangians: Application to teleparallel gravity

“…The 2-form F : d# is the translational gauge field strength (which in geometric terms is equal to the anholonomity object of the tetrad). The irreducible decomposition of the field strength reads (see [15][16][17]20] for details) The teleparallel model (4.1) belongs to the class of quasiinvariant theories. In fact, one can verify that under a change of the coframe # 0 x # , the Lagrangian changes by a total derivative:…”

“…As is well known, in addition to the geometric framework of general relativity, gravitation can also be described in terms of a gauge theory. In fact, teleparallel gravity corresponds to a gauge theory for the translation group [15][16][17]. In this theory, instead of curvature, torsion represents the gravitational field.…”

Wormhole Solution and Energy in Teleparallel Theory of Gravity

“…Outside these regions naked singularity does not appear and one obtains a traverse wormhole. The throat of this wormhole g tt (R = 2m) gives the conditions that g tt = −k 1 2 ⇒ (k 1 = 0 is required to ensure the traversability). The properties of this wormhole are discussed by Dadhich et al [34].…”

“…It is considered as an essential part of generalized non-Riemannian theories such as the Poincaré gauge theory [1][2][3][4][5][6][7] or metric-affine gravity [8] as well as a possible physical relevant geometry by itself-teleparallel description of gravity [9,10]. Teleparallel approach is used for positive-gravitational--energy proof [11].…”

Conservation laws for vacuum tetrad gravity

“…Pellegrini and Plebanski [6], Hehl [7], Tupper and Phillips [8], Hayashi and Nakano [9], Hayashi and Shirafuji [10], Nester and Tung [11], Meyer [12]; for considerable subsequent literature cf. Itin [13].…”