• degrees of freedom
• new general relativity
• teleparallel gravity
• torsion
• Weitzenbock

Teleparallel theories, introduced a few years after the Einstein’s formulation
of General Relativity(GR), represent an alternative way to describe grav-
ity. We say ”alternative” because, unlike General Relativity, which describes
gravity in terms of the curvature of spacetime, Teleparallel theories, are based
on the assumption that the curvature is equal to zero and instead attribute
gravity to torsion or non-metricity.
Despite these significant differences, an important fact emerges from the
study of teleparallel theories: there are special models which are equiva-
lent to General Relativity, in the sense that they reproduce the same re-
sults as Einstein’s theory, even though they are described by torsion or non-
metricity rather than curvature. This happens because both torsion and
non-metricity contain the necessary kinematical degrees of freedom , e.g, a
spin 2 propagating tensor, among others.
In my thesis work I consider a particular Teleparallel theory that describes
gravity in terms of torsion degrees of freedom instead of metric’s , known as
the New General Relativity(NGR).
After showing that under certain conditions this theory coincides with
Teleparallel Equivalent General Relativity(TEGR), which reproduces the
same results as General Relativity, I study NGR in the weak field approxi-
mation with the aim of calculating the gauge invariant degrees of freedom of
this theory and comparing them with those of General Relativity.
To obtain the degrees of freedom of the NGR I consider an approach
based on scalar-vector-tensor decomposition in addition to the Helmoltz de-
composition of the linear pertubations of the spacetime.
From this analysis, the main results of my thesis work are obtained,
namely that New General Relativity has nine degrees of freedom, six of which
do not propagate and three that do propagate. From these results, the im-
portant aspect of my work emerges, namely that New General Relativity has
three more degrees of freedom compared to General Relativity, two of which
do not propagate and one that does propagate.
In particular this new propagating degree of freedom corresponds to a
transverse antisymmetric tensor in three dimension, that could potentially
affects observations.