Torsion constraints driven by TEGR topological defects in null coordinates, GWs and matching conditions

New constraints on Cartan torsion components are obtained from the teleparallel equivalent of General Relativity (TEGR) repulsive gravity with global textures. The interior solution is considered a global texture fulfilling Einstein gravity, whereas the exterior solution is a spherical symmetric vacuum. The torsion components are constrained from the matching condition in Einstein–Cartan gravity given by, where the interior solution is an Einstein gravity global texture and the exterior solution is a flat spacetime in spherical coordinates. We show that one of the components of torsion trace T²₁₂<<10⁻⁴⁴ T 2 12 < < 10 - 44 GeV, which is much more stringent than the estimate of 10⁻³¹ 10 - 31 GeV by Kostelecky et al. (PRL(2008)) for the torsion Lorentz violation and in dual maser. To compute this bound we use the texture correlation length as the inverse of the Hubble constant and the texture tachyonic and small-angle approximations. Another method for placing bounds on torsion is to use teleparallel gravitational waves (GW). These bounds are based on LIGO data.