Stable and self-consistent compact star models in teleparallel gravity

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 $$\textit{PSR J 1614-2230}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>PSR J</mml:mi> <mml:mspace/> <mml:mn>1614</mml:mn> <mml:mo>-</mml:mo> <mml:mn>2230</mml:mn> </mml:mrow> </mml:math> , with estimated mass $$M= 1.97 \pm 0.04\, M_{\circledcirc },$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>M</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1.97</mml:mn> <mml:mo>±</mml:mo> <mml:mn>0.04</mml:mn> <mml:mspace/> <mml:msub> <mml:mi>M</mml:mi> <mml:mo>⊚</mml:mo> </mml:msub> <mml:mo>,</mml:mo> </mml:mrow> </mml:math> and radius $$R= 9.69 \pm 0.2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>R</mml:mi> <mml:mo>=</mml:mo> <mml:mn>9.69</mml:mn> <mml:mo>±</mml:mo> <mml:mn>0.2</mml:mn> </mml:mrow> </mml:math> 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.

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