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.
In the last few years we have seen an increase interest on gravitational waves due to recent and striking experimental results confirming Einstein's general relativity once more. From the field theory point of view, gravity describes the propagation of selfinteracting massless spin-2 particles. They can be identified with metric perturbations about a given background metric. Since the metric is a symmetric tensor, the massless spin-2 particles present in the Einstein-Hilbert (massless Fierz-Pauli) theory are naturally described by a symmetric rank-2 tensor. However, this is not the only possible consistent massless spin-2 theory at linearized level. In particular, if we add a mass term, a new one parameter (a 1 ) family of models L(a 1 ) shows up. They consistently describe massive spin-2 particles about Einstein spaces in terms of a non-symmetric rank-2 tensor. Here we investigate the massless version of L(a 1 ) in a curved background. In the case a 1 = −1/12 we show that the massless spin-2 particles consistently propagate, at linearized level, in maximally symmetric spaces. A similar result is obtained otherwise (a 1 = −1/12) where we have a non-symmetric scalar-tensor massless model. The case of partially massless non-symmetric models is also investigated. * hemily.gomes@gmail.com † dalmazi@feg.unesp.br 1 Throughout this work we use η µν = (−, +, +, +) 2 The case m 2 = R/6 corresponds to the so-caled Higuchi bound [24].
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 behavior 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.
There are many ways to probe alternative theories of gravity, namely, via experimental tests at solar system scale, cosmological data and models, gravitational waves and compact objects. In this paper, we consider a model of gravity with torsion [Formula: see text] applied to compact objects such as neutron stars (NSs) for a couple of realistic equations of state (EOS). To do so, we follow our previous articles, in which we show how to model compact stars in [Formula: see text] gravity by obtaining its corresponding Tolman–Oppenheimer–Volkof equations. In this modeling of NS in [Formula: see text] gravity presented here, we calculate, among other things, the maximum mass allowed for a given realistic EOS, which would also allow us to evaluate which models are in accordance with the observations. The results already known to General Relativity must be reproduced to some extent and, eventually, we can find models that allow higher maximum masses for NSs than Relativity itself, which could explain, for example, the secondary component of the event GW190814, if this star is a massive NS.
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