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The main goal of this paper is to investigate one of the important
astrophysical systems, namely Thick accretion disks, in the background of the
spherically symmetric solution in Born-Infeld teleparallel gravity to examine
observable predictions of the theory in the vicinity of black holes. Thus, the
properties of the non-self-gravitating equilibrium surfaces characterising the
Thick accretion disks model are studied. In addition, we find an observational
bound on the parameter of the model as $\lambda\gtrsim 140$. We show this
analytical accretion disk model for different values of $\lambda$ and compare
the result with the corresponding Schwarzschild solution in the general theory
of relativity.

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