Stable and self-consistent compact star models in teleparallel gravity
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Regular Article - Theoretical Physics
Stable and self-consistent compact star models in teleparallel gravity G. G. L. Nashed1,2,a , S. Capozziello3,4,5,b 1
Centre for Theoretical Physics, The British University in Egypt, P.O. Box 43, El Sherouk City, Cairo 11837, Egypt Egyptian Relativity Group (ERG), Cairo University, Giza 12613, Egypt 3 Dipartimento di Fisica “E. Pancini“, Universitá di Napoli “Federico II”, Complesso Universitario di Monte Sant’ Angelo, Edificio G, Via Cinthia, 80126 Naples, Italy 4 Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Napoli, Complesso Universitario di Monte Sant’Angelo, Edificio G, Via Cinthia, 80126 Naples, Italy 5 Laboratory for Theoretical Cosmology, Tomsk State University of Control Systems and Radioelectronics (TUSUR), 634050 Tomsk, Russia
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Received: 25 August 2020 / Accepted: 12 October 2020 © The Author(s) 2020
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 PSR J 1614-2230, with estimated mass M = 1.97 ± 0.04 M , and radius R = 9.69 ± 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.
1 Introduction Soon after the formulation of general relativity (GR), several theories were constructed in view of fixing as many issues as possible related to the gravitational field. Among these theories, there is the one formulated by H. Weyl which tried to unify gravitation and electromagnetism in 1918 [1]. Einstein a e-mail:
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himself, in 1928 [2], adopted the same philosophy by Weyl adopting the Weitzenböck geometry. In this formulation, one has to introduce tetrad fields to describe dynamics, unlike GR whose dynamical variable is the metric. The tetrad field has 16 components which made Einstein think that the extra 6 components, with respect to the metric, could describe the components of the electromagnetic field. Nevertheless, it was shown that these extra 6 components are linked to the local Lorentz invariance of the theory [3,4]. Despite the failure of the Weyl and Einstein attempts, the n
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