Light bending in $f(T)$ gravity

Understand

In the framework of $f(T)$ gravity, we focus on a weak-field and spherically symmetric solution for the Lagrangian $f(T)=T+\alpha T^{2}$, where $\alpha$ is a small constant which parameterizes the departure from General Relativity.

• In particular, we study the propagation of light and obtain the correction to the general relativistic bending angle.
• Moreover, we discuss the impact of this correction on some gravitational lensing observables, and evaluate the possibility of constraining the theory parameter $\alpha$ by means of observations.
• In particular, on taking into account the astrometric accuracy in the Solar System, we obtain that $|\alpha| \leq 1.85 \times 10^{5}\, \mathrm{m^{2}}$; this bound is looser than those deriving from the analysis of Solar System dynamics, e.g.