Solving Tolman-Oppenheimer-Volkoff equations in $f(T)$ gravity: a novel approach applied to polytropic equations of state

Abstract

The Teleparallel Theory is an alternative theory of gravity equivalent to General Relativity (GR) and with non-vanishing torsion T . Some extensions of this theory, the so-called f (T ) models, have been subject of many recent works. The purpose of our work in the end is to consider recent results for a specific family of f (T ) models by using their corresponding Tolman-Oppenheimer-Volkof to describe compact objects such as neutron stars. By performing numerical calculations, it is possible to find, among other things, the maximum mass allowed by the model for a neutron star for a given equation of state (EOS), which would also allow us to evaluate which models are in accordance with observations. To begin with, the present work, the second in the series, considers polytropic EOSs since they can offer a simpler and satisfactory description for the compact objects. In addition, with these EOSs, we can already assess how different the f (T ) theories are in relation to GR with respect to the stellar structure. The results already known to GR must be reproduced to some extent and, eventually, we can find models that allow higher maximum masses than Relativity itself, which could explain, for example, the secondary component of the event GW190814. This particular issue will be subject of a forthcoming paper, the third in the series, where realistic EOSs are considered.

Solving Tolman-Oppenheimer-Volkoff equations in f(T) gravity: a novel approach applied to some realistic equations of state

“…In the first paper of the series [15], we show in detail how to obtain the set of differential equations necessary to model compact stars in f (T ) models. In the second paper [14], we restate the main equations and model spherical stars in a particular f (T ) model adopting polytropic EOSs.…”

“…In [14], it was used the polytropic equation of state to describe the structure of a spherically symmetrical object in gravitational equilibrium in a model with torsion, namely, f (T, ξ ) = T + ξ T 2 , where ξ is a free parameter. The TOV equations correspondent to f (T, ξ ) were obtained in [15] using a novel approach without any restriction on the metric functions or perturbative calculations.…”

“…The TOV equations correspondent to f (T, ξ ) were obtained in [15] using a novel approach without any restriction on the metric functions or perturbative calculations. In this work, we will perform the numerical calculations in a analogous way what was done in [14] for this family of alternative models using, this time, realistic EOSs.…”

“…In Section 2 we present the main results obtained in [15] concerning the model f (T, ξ ). In Section 3, we proceed analogously to [14] in the numerical calculations in order to obtain the "Mass × Radius" and "Mass × Central Density" curves, from which one can obtain, for example, the maximum mass allowed for some realistic and representative EOSs. Finally, the main conclusions are presented in Section 4.…”

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“…For example, in the framework of f (R)/ f (R, T) gravities following works were published: [6][7][8][9][10][11]. In turn, for the teleparallel gravity (and their modifications) there is also exist a couple of works, namely [12][13][14][15][16][17] (and references therein).…”