Charged anisotropic compact stars in Ricci-inverse gravity

Abstract

The main objective of this work is to use the Karmarkar condition to investigate the charged anisotropic characteristics of compact stars in the recently proposed modified Ricci-inverse gravity. For this purpose, we derive the relativistic anisotropic static spherically symmetric solutions with specific Adler model for the $g_{tt}$ metric potential. To determine the exterior geometry, we use the Bardeen model and carry out various physical tests to determine whether the Ricci-inverse gravity model is physically feasible, and to further investigate for energy density, pressure components, mass–radius relations, energy and equilibrium conditions. The success of Ricci-inverse gravity model for charged anisotropic compact stars is also discussed in our study. It is concluded that the existence of charged anisotropic compact stars is possible with our proposed $f(\mathcal {R},\mathcal {A})$ gravity model. However, our chosen $f(\mathcal {R},\mathcal {A})$ gravity model is not supporting massive stars. The exact limitations are not debated in this work; however, the stars with mass $M= 1.2M_{\bigodot }$ and radii ($R=9$, 9.10, 9.20, 9.30) are acceptable for our chosen model.

Appendix

$$\begin{aligned} \psi _{1}= \,& {} -\frac{e^{-\lambda }}{2}\bigg (2\nu ''+\frac{2\nu '}{r}+\nu {'}^{2}-\nu '\lambda '-\frac{2\lambda '}{r}\bigg )+\frac{2}{r^{2}}\bigg (1-e^{-\lambda }+re^{-\lambda }\bigg (-\frac{\nu '}{2}+\frac{\lambda '}{2}\bigg )\bigg ).\\ \psi _{2}=\, & {} \frac{e^{-(\nu +\lambda )}}{2}\bigg (\nu ''+\frac{2\nu '}{r}+\frac{\nu {'}^{2}}{2}-\frac{\nu '\lambda '}{2}\bigg ). \\ \psi _{3}= \,& {} \frac{e^{-2\lambda }}{2}\bigg (-\nu ''-\frac{\nu {'}^{2}}{2}+\frac{\nu '\lambda '}{2}+\frac{2\lambda '}{r}\bigg ). \\ \psi _{4}=\,& {} \frac{1}{r^{4}}\bigg (1-e^{-\lambda }+re^{-\lambda }\bigg (-\frac{\nu '}{2}+\frac{\lambda '}{2}\bigg )\bigg ). \\ \psi _{5}=\, & {} 4re^{\lambda }\bigg [\bigg (\frac{-1}{2r\nu ''+4\nu '+r\nu {'}^{2}-r\nu '\lambda '}\bigg )+\bigg (\frac{1}{-2r\nu ''+4\lambda '-r\nu {'}^{2}+r\nu '\lambda '}\bigg )\bigg ]+\frac{4r^{2}}{2-2e^{-\lambda }+re^{-\lambda }(\lambda '-\nu ')}.\\ \psi _{6}=\, & {} \frac{4re^{\lambda -\nu }}{2r\nu ''+r\nu {'}^{2}+4\nu '-r\nu '\lambda '}. \\ \psi _{7}= & {} \frac{4r}{-2r\nu ''-r\nu {'}^{2}+r\nu '\lambda '+4\lambda '}. \\ \psi _{8}= \,& {} \frac{2}{2-2e^{-\lambda }+re^{-\lambda }(\lambda '-\nu ')}. \\ \psi _{9}=\, & {} \bigg (\frac{4re^{\lambda -\nu }}{2r\nu ''+r\nu {'}^{2}+4\nu '-r\nu '\lambda '}\bigg )\bigg (\frac{-4re^{\lambda }}{2r\nu ''+r\nu {'}^{2}+4\nu '-r\nu '\lambda '}\bigg ).\\ \psi _{10}=\, & {} \bigg (\frac{4r}{-2r\nu ''-r\nu {'}^{2}+r\nu '\lambda '+4\lambda '}\bigg )\bigg (\frac{4re^{\lambda }}{-2r\nu ''-r\nu {'}^{2}+r\nu '\lambda '+4\lambda '}\bigg ). \\ \psi _{11}= \,& {} \bigg (\frac{2}{2-2e^{-\lambda }+re^{-\lambda }(\lambda '-\nu ')}\bigg )\bigg (\frac{2r^{2}}{2-2e^{-\lambda }+re^{-\lambda }(\lambda '-\nu ')}\bigg ). \\ \end{aligned}$$