The meaning of torsion in teleparallel theories

Abstract

The ambiguity of the Weitzenböck connection and the meaning of torsion in teleparallel theories are investigated. A new postulate is added to teleparallel theories in order to remove the ambiguity and the inconsistencies in the calculation of the gravitational energy-momentum tensor and the like. In addition to the known restrictions on the spatial triad, it is shown that some restrictions on the congruence used to build the frame must also be imposed. Nevertheless, no restriction is imposed on a particular observer's worldline. The postulate and the restriction presented in this article are used to define what will be called here an ideal frame. This definition is applied to the Schwarzschild and the pp-wave spacetimes in the context of the Teleparallel Equivalent of General Relativity. In both cases, the results are very appealing and consistent; this includes the impossibility of making the gravitational energy density vanish along the accelerated observers' worldlines used here. Two promising interpretations for the Weitzenböck torsion are presented and discussed in detail. The possibility of having a well defined concept of an absolute vacuum in teleparallel theories is also discussed. Finally, some possible solutions to well-known problems of the f(T) theories are proposed.

arXiv commentIn this version I have split the paper in three parts. The first part has already been published in Braz J Phys 51, 1823 (2021) and the second one is currently considered for peer-review in Modern Physics Letters A, under the title "On the teleparallel frame problem"

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Cited by in corpus (1)

• Gravitational energy in pp-wave spacetimes