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

TL;DR

This paper investigates the spherically symmetric vacuum solutions in covariant $F(T)$ gravity with quadratic torsion terms, deriving bounds on deviations from General Relativity using solar system and pulsar observations.

Contribution

It provides the first perturbative solution for vacuum spherically symmetric spacetime in covariant $F(T)$ gravity with quadratic torsion corrections and constrains the coupling constant using observational data.

Findings

Derived the perturbative vacuum solution around Schwarzschild in covariant $F(T)$ gravity.

Set an upper bound on the nonlinear torsion coupling constant $\alpha$ from Mercury's perihelion shift.

Provided an independent constraint on $\alpha$ from binary pulsar data.

Abstract

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. This allows us to set an upper bound on the magnitude of the coupling constant, $\alpha$, which governs deviations from General Relativity. We find the bound on this nonlinear torsion coupling constant by specifically considering the uncertainty in the perihelion shift of Mercury. We also analyze a bound from a similar comparison with the periastron orbit of the binary pulsar PSR J0045-7319 as an independent check for consistency. Setting bounds on the dominant nonlinear coupling is important in determining if other effects in the solar system or greater universe could be attributable to nonlinear torsion.