The Spherically Symmetric Vacuum in Covariant $F(T) = T + \frac{\alpha}{2}T^{2} + \mathcal{O}(T^{\gamma})$ Gravity Theory

Understand

Recently, a fully covariant version of the theory of $F(T)$ torsion gravity has been introduced (arXiv:1510.08432v2 [gr-qc]).

• In covariant $F(T)$ gravity the Schwarzschild solution is not a vacuum solution for $F(T)\neq T$ and therefore determining the spherically symmetric vacuum is an important open problem.
• Within the covariant framework we perturbatively solve the spherically symmetric vacuum gravitational equations around the Schwarzschild solution for the scenario with $F(T)=T + (\alpha/2)\, T^{2}$, representing the dominant terms in theories governed by Lagrangians analytic in the torsion scalar.
• From this we compute the perihelion shift correction to solar system planetary orbits as well as perturbative gravitational effects near neutron stars.