On the teleparallel frame problem

Abstract

The role played by the congruence in the prediction of the gravitational energy in the teleparallel equivalent of general relativity is discussed. It is shown that some congruences yield unphysical predictions. It is also shown that the energy–momentum tensor density predicted by the proper reference frame of an arbitrary accelerated observer vanishes along the observer’s worldline, regardless of its acceleration. The latter result is discussed and arguments both against and in favor of the use of this type of frame to describe the gravitational energy are presented; arguments against the belief that the principle of equivalence is incompatible with the localization of the gravitational energy are also presented. A gauge condition is applied to the teleparallel frame and its consistence is discussed: using three different tetrads for the pp-wave spacetimes, it is shown that the most consistent prediction comes from the tetrad that satisfies this gauge. The possibility of having a well-defined concept of absolute vacuum is also discussed.