Résumé:
This thesis deals with a study of the fundamental theory of gravity on torsional manifolds, but
with vanishing curvature tensors. The theory is called Teleparallel Gravity (TEGR). Their eld
equations are equivalent to the General Relativity (GR). The lack of research in this eld is
mainly due to historical reasons since Einstein developed GR before TEGR. Both theories have
the same equations, and can be regarded as the basic theory of gravitation, but their physical
interpretations are very di¤erent. GR understands gravity as deformation of the space-time
while the TEGR return to the view that gravity is one force mediated by the torsion tensor.
Then even if they are similar on the eld equations, their physical interpretations are very
di¤erent. However, generalized TEGR theories are completely di¤erent from GR and even
from generalizations of GR.
All Teleparallel theories of gravity are based on the scalar torsion T which contains only
rst derivatives of tetrads. On the other hand, GR is based on the Ricci scalar R which
depends on second derivatives of the metric tensor. Therefore, some Teleparallel theories are
mathematically simpler than other modi ed theories coming from GR. In fact modi ed GR
theories need some mechanisms to cancels terms of order higher than 2.
The main topi of this thesis is to study the existence of Neutron stars in TEGR theory non
minimally coupled to a scalar eld with a scalar potential. The results obtained are new and
accurate. Indeed, for particular values of the theory parameters, we have obtained NSs with
masses less than the ones in GR theory, but which remain consistent with the astrophysical
observations.
