Testing Born-Infeld $f(T)$ teleparallel gravity through Sgr A$^\star$ observations

TL;DR

This paper constrains a Born-Infeld $f(T)$ teleparallel gravity model using Sgr A* observations, analyzing black hole shadows and light deflection, and finds that deviations from General Relativity are very small within observational bounds.

Contribution

It provides observational constraints on the Born-Infeld $f(T)$ gravity parameter using S2 star data and models the black hole shadow, showing minimal deviations from GR within current observational limits.

Findings

Parameter $eta$ constrained to $0 o 6 imes 10^{-4}$ within 1$\sigma$

Shadow size and deflection angle are very close to Schwarzschild predictions

Electromagnetic intensity in shadows is smaller than in GR

Abstract

We use observational data from the S2 star orbiting around the Galactic Center to constrain a black hole solution of extended teleparallel gravity models. Subsequently, we construct the shadow images of Sgr A$^{\star}$ black hole. In particular, we constrain the parameter $\alpha=1/\lambda$ which appears in the Born-Infeld $f(T)$ model. In the strong gravity regime we find that the shadow radius increases with the increase of the parameter $\alpha$. Specifically, from the S2 star observations, we find within 1$\sigma$ that the parameter must lie between $0 \leq \alpha/M^2 \leq 6 \times 10^{-4}$. Consequently, we used the best fit parameters to model the shadow images of Sgr A$^{\star}$ black hole and then using the Gauss-Bonnet theorem we analysed the deflection angle for leading order expansions of the parameter $\alpha$. It is found that within the parameter range, these observables are very close to the Schwarzschild case. Furthermore, using the best fit parameters for the Born-Infeld $f(T)$ model we show the angular diameter is consistent with recent observations for the Sgr A$^{\star}$ black hole angular diameter $(51.8 \pm 2.3) \mu$arcsec and difficult to be distinguished from the GR. For the deflection angle of light, in leading order terms, we find that the deflection angle expressed in the ADM mass coincides with the GR, but the ADM mass in the Born-Infeld $f(T)$ gravity increases with the increase of $\alpha$ and the overall deflection angle is expected to me greater in $f(T)$ gravity. As a consequence of this fact, we have shown that the electromagnetic intensity observed in shadow images is smaller compared to GR.