Abstract
In the framework of Teleparallel Gravity, we derive a charged non-vacuum solution for a physically symmetric tetrad field with two unknown functions of radial coordinate. The field equations result in a closed-form adopting particular metric potentials and a suitable anisotropy function combined with the charge. Under these circumstances, it is possible to obtain a set of configurations compatible with observed pulsars. Specifically, boundary conditions for the interior spacetime are applied to the exterior Reissner–Nordström metric to constrain the radial pressure that has to vanish through the boundary. Starting from these considerations, we are able to fix the model parameters. The pulsar textit{PSR J 1614-2230}, with estimated mass M= 1.97 pm 0.04, M_{circledcirc }, and radius R= 9.69 pm 0.2 km is used to test numerically the model. The stability is studied, through the causality conditions and adiabatic index, adopting the Tolman–Oppenheimer–Volkov equation. The mass–radius (M, R) relation is derived. Furthermore, the compatibility of the model with other observed pulsars is also studied. We reasonably conclude that the model can represent realistic compact objects.
Highlights
Himself, in 1928 [2], adopted the same philosophy by Weyl adopting the Weitzenböck geometry
Teleparallel Equivalent of General Relativity (TEGR) and general relativity (GR) are equivalent at the level of field equations at the level of actions, they are different for a total divergence term [8–13]
It is well known that TEGR theory is equivalent to GR up to a total derivative term [127–129]
Summary
Despite the failure of the Weyl and Einstein attempts, the new approaches supplied the notion of gauge theory and the search for a gauge gravity started [5,6]. An application of anisotropic model to stable configurations of neutron stars has been discussed in [49] They showed that anisotropy might have non-negligible effects on the equilibrium mass and on the surface red-shift. The aim of the present paper is to derive a novel charged anisotropic solution in the framework of TEGR and compare it with realistic stellar configurations using physical assumptions on the form of metric potential and the combination of charge and anisotropy. We consider the pulsar PSR J 1614-2230 which estimated mass M = 1.97 ± 0.04M and radius is R = 9.69 ± 0.2 km [102] This peculiar system escapes the standard GR explanation of neutron stars because it is too massive to be stable unless one assumes exotic EoS or alternative gravities.
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