Boson stars in $f(T)$ extended theory of gravity

Spherically symmetric configurations of the noninteracting massive complex scalar field, representing nonrotating boson stars, are considered within the framework of the modified torsion based f(T) gravity, with f(T) = T + alpha T-2/2. We find that with sufficiently large negative value of alpha the mass of the boson stars can be made arbitrarily large. This is in contrast to general relativity where an upper bound, M-max similar to M-Planck(2)/m, to the mass of the boson stars built from the noninteracting scalar field exists and where the masses of boson stars in the astrophysical regime can be obtained only with the introduction of the scalar field self-interaction. With sufficiently large negative alpha we also find negative gravitational binding energy for all masses, which can be seen as an indication of the stability of such configurations. In its positive regime, alpha can not be made arbitrarily large as a phase transition in the stress-energy components of the f(T)-fluid develops. This phenomenon has already been reported to occur in polytropic stars constructed within the foTTHORN gravity theory.