# Photon sphere and perihelion shift in weak $f(T)$ gravity

## TL;DR

This paper derives observable predictions such as photon sphere and perihelion shift in weak $f(T)$ gravity, providing a way to test the theory against observations by extending perturbation calculations of Schwarzschild and Minkowski spacetimes.

## Contribution

It introduces first-order teleparallel perturbations of Schwarzschild and Minkowski geometries to improve and extend existing results in weak $f(T)$ gravity.

## Key findings

- Derived photon sphere and perihelion shift in weak $f(T)$ gravity.
- Extended perturbation analysis of Schwarzschild and Minkowski spacetimes.
- Provided potential observational constraints for $f(T)$ gravity.

## Abstract

Among modified theories of gravity, the teleparallel $f(T)$ gravity is an intensively discussed modelin the literature. The best way to investigate its viabilityis to derive observable predictions which yield evidence or constraints for the model, when compared with actual observations. In this paper we derive the photon sphere and the perihelion shift for weak $f(T)$ perturbations of general relativity. We consistently calculate first order teleparallel perturbations of Schwarzschild and Minkowski spacetime geometry, with which we improve and extend existing results in the literature.