Exploring $f(T)$ Gravity via strongly lensed fast radio bursts

TL;DR

This paper investigates gravitational lensing effects in $f(T)$ gravity, comparing them with General Relativity, and suggests that differences in magnification and time delay could help test and constrain modified gravity theories using fast radio burst observations.

Contribution

It provides analytical expressions for lensing effects in $f(T)$ gravity and explores how plasma environments influence observable differences from General Relativity.

Findings

Magnification and time delay differ significantly between $f(T)$ gravity and GR in plasma environments.

Image positions are indistinguishable between the theories in plasma environments.

Current observational facilities can potentially distinguish between $f(T)$ gravity and GR based on these lensing effects.

Abstract

This study aims to investigate the strong gravitational lensing effects in $f(T)$ gravity. We present the theoretical analytic expressions for the lensing effects in $f(T)$ gravity, including deflection angle, magnification, and time delay. On this basis, we also take the plasma lensing effect into consideration. We compare the lensing effects between the General Relativity in a vacuum environment and the $f(T)$ gravity in a plasma environment. From a strongly lensed fast radio burst, the results indicate that in a plasma environment, General Relativity and $f(T)$ gravity can generate indistinguishable image positions, but the magnification and time delay on these positions are significantly different, which can be distinguished by current facilities in principle. Therefore, the discrepancies between observational results and theoretical expectations can serve as clues for a modified gravity theory and provide constraints on $f(T)$ gravity.