https://doi.org/10.1140/epjc/s10052-022-10971-0
Regular Article - Theoretical Physics
Testing Born–Infeld f(T) teleparallel gravity through Sgr 
observations
1
Physics Department, State University of Tetovo, Ilinden Street nn, 1200, Tetovo, North Macedonia
2
Dipartimento di Fisica Ettore Pancini, Complesso Universitario di Monte S. Angelo, Università degli studi di Napoli Federico II, Via Cinthia Edificio 6, 80126, Naples, Italy
3
Scuola Superiore Meridionale, Largo S. Marcellino 10, 80138, Naples, Italy
4
Istituto Nazionale di Fisica Nucleare, Sezione di Napoli, Complesso Universitario di Monte S. Angelo, Via Cintia Edificio 6, 80126, Naples, Italy
5
Department of Physics, Tokyo Institute of Technology, 1-12-1 Ookayama, Meguro-ku, 152-8551, Tokyo, Japan
6
Laboratory of Theoretical Physics, Institute of Physics, University of Tartu, W. Ostwaldi 1, 50411, Tartu, Estonia
7
School of Natural Sciences, National University of Sciences and Technology, 44000, Islamabad, Pakistan
Received:
20
August
2022
Accepted:
28
October
2022
Published online:
12
November
2022
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 
black hole. In particular, we constrain the parameter 
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 
. Specifically, from the S2 star observations, we find within 
that the parameter must lie between 
. Consequently, we used the best fit parameters to model the shadow images of Sgr black hole and then using the Gauss-Bonnet theorem we analysed the deflection angle for leading order expansions of the parameter . 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 that the angular diameter is consistent with recent observations for the Sgr with angular diameter 
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 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.
© The Author(s) 2022
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