The meaning of torsion in teleparallel theories
arXiv:2004.10788 · doi:10.1142/S0219887824502116
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.
In 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"
References in corpus (14)
- Modified teleparallel gravity: inflation without inflaton
- The teleparallel equivalent of general relativity
- Generalizations of teleparallel gravity and local Lorentz symmetry
- Covariance properties and regularization of conserved currents in tetrad gravity
- Gauge Structure of Teleparallel Gravity
- Noether charge and black hole entropy in teleparallel gravity
- The Gravitational Energy Problem for Cosmological Models in Teleparallel Gravity
- Gravitational pressure on event horizons and thermodynamics in the teleparallel framework
- Conformal Invariant Teleparallel Cosmology
- Teleparallel gauge theory of gravity
- Conformal Teleparallel Theories and Weyl Geometry
- Teleparallel theory as a gauge theory of translations: comments and issues
- Pound-Rebka experiment and torsion in the Schwarzschild spacetime
- On Gravitational Energy in Conformal Teleparallel Gravity