Study on anisotropic stars in the framework of Rastall gravity
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ORIGINAL ARTICLE
Study on anisotropic stars in the framework of Rastall gravity Piyali Bhar1
· Francisco Tello-Ortiz2 · Ángel Rincón3
· Y. Gomez-Leyton4
Received: 23 June 2020 / Accepted: 20 August 2020 © Springer Nature B.V. 2020
Abstract We investigate the existence of high dense compact objects in the light of Rastall gravity theory. The material content is driven by an imperfect fluid distribution and the inner geometry is described by the Tolman–Kuchowicz space–time. The validity of the obtained model is checked by studying the main salient features such as energy– density, radial and tangential pressures and anisotropy factor. Since Einstein gravity theory shares the same vacuum solution with Rastall gravity theory, the interior geometry is joining in a smoothly way with the exterior Schwarzschild’s solution. The equilibrium of the model under different gradients is analyzed by using the modified hydrostatic equilibrium equation, containing the so–called Rastall gradient. The compact structure has a positive anisotropy factor which enhances the balance and stability mechanisms. To check the potentially stable behavior, we employ Abreu’s and adiabatic index criterion. It was found that the model is completely stable. The incidence of the Rastall’s parameter γ on all the physical quantities that characterize the model is described by the help of graphical analysis. Concerning the γ spectrum we have considered 0.3142 ≤ γ ≤ 0.3157. All the results are compared with the general relativity case. Keywords General relativity · Exact solution · Compact stars · Equation of state · Anisotropy
B P. Bhar
[email protected]
1
Department of Mathematics, Government General Degree College, Singur, West Bengal 712409, India
2
Departamento de Física, Facultad de ciencias básicas, Universidad de Antofagasta, Casilla 170, Antofagasta, Chile
3
Instituto de Física, Pontificia Universidad Católica de Valparaíso, Avenida Brasil 2950, Casilla 4059, Valparaíso, Chile
4
Departamento de Física, Universidad Católica del Norte, Av. Angamos 0610, Antofagasta, Chile
1 Introduction General Relativity Einstein (1916) is, up to now, the most successful theory for explaining the gravitational interaction. This is because its predictions for solar system experiments are consistent with the observational data. Indeed, at cosmological scales, General Relativity is still valid (assuming the extra unknown components like dark matter (DM) and dark energy (DE)). In cases where we desire to bypass the concepts of DE and DM, it is necessary to go beyond classical Einstein Gravity. Many alternative theories have been proposed, some of them are: (i) scalartensor theories (Brans–Dicke Brans and Dicke (1961), Torres et al. (1998), Sharif and Manzoor (2014), Balakrishna and Shinkai (1998), Zhang et al. (2017), (ii) f (R) theories De Felice and Tsujikawa (2010), Sotiriou and Faraoni (2010), Clifton et al. (2012), Capozziello and De Laurentis (2011) and (iii) others Clifton et al. (2012), Moffat (2006), Moffat and Toth (2009). These theories
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