Solving Tolman–Oppenheimer–Volkoff equations in f(T) gravity: a novel approach

Abstract

Abstract The torsion models have stood out among the proposals for an alternative description of gravity. The simplest of them, the Teleparallel theory, is equivalent to general relativity and there are many studies dealing with its extension to more general functions of the torsion T. The purpose of our study is to consider a family of f(T) models and apply their corresponding Tolman–Oppenheimer–Volkoff equations to compact objects such as neutron stars.Thus, through a numerical analysis, calculate, among other things, the maximum mass allowed by the model for a neutron star, which also allows us to evaluate which models agree with the observations. In the present paper, the first in the series, we show explicitly the set of equations that must be solved, and how to solve it, in order to model compact stars in f(T) gravity without the need to adopt any particular form for the metric functions or consider any perturbative approach, as has been done in some works in the literature. Examples are given of how our approach works, modelling polytropic stars. We also show that some numerical instabilities reported in a previous study by other authors do not appear in our novel approach. This is an important advance, since it is possible to answer an issue not responded in a previous study, because numerical instabilities prevented proceeding with the calculations. Last but not least, we explicitly show the torsion behaviour inside and outside the star. This is an important question, because with this study we can understand the role of torsion in the structure of the star.