Abstract
We derive a Tolman–Oppenheimer–Volkoff equation in neutron star systems within the modified f(T, mathcal {T})-gravity class of models using a perturbative approach. In our approach f(T, mathcal {T})-gravity is considered to be a static spherically symmetric space-time. In this instance the metric is built from a more fundamental vierbein which can be used to relate inertial and global coordinates. A linear function f = T(r) + mathcal {T}(r) + chi h(T, mathcal {T}) + mathcal {O}(chi ^{2}) is taken as the Lagrangian density for the gravitational action. Finally we impose the polytropic equation of state of neutron star upon the derived equations in order to derive the mass profile and mass–central density relations of the neutron star in f(T, mathcal {T})-gravity.
Highlights
It has been shown that the universe is accelerating in its expansion [1,2]
Our focus of this paper is on one alternative theory of gravity called f (T )-gravity, which makes use of a “teleparallel” equivalent of GR (TEGR) [10] approach, in which instead of the torsion-less Levi-Civita connection, the Weitzenböck connection is used, with the dynamical objects being four linearly independent vierbeins [11,12]
In this study the TOV equations are derived in a perturbative way for f (T, T )-gravity
Summary
It has been shown that the universe is accelerating in its expansion [1,2]. The concept of the cosmological constant together with the inclusion of dark matter yield the CDM model which explains a whole host of phenomena within the universe [3,4,5]. Lm is the matter Lagrangian density [22,25] In this instance f is an arbitrary function of the torsion scalar T and the trace of the energy-momentum tensor. Because this is a pure form of tetrad [23], the spin connection elements of the tetrad vanish and ensure that the spin connection terms need not be included [23] Inserting this vierbein into the field equations, from Eq (4) we get the resulting torsion scalar,. We shift our focus into deriving the pressure–radius relation of the TOV equations For this purpose, Eq (12) is considered where a similar treatment will be given i.e. we substitute the torsion scalar equation and the energymomentum definition to give. This result is inserted into the continuity equation given by Eq (9) and results in the second TOV equation required, p(r )χ pr
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