Stability analysis of neutron stars in Palatini f(R, T) gravity

Abstract

In this paper, we have studied the stability of neutron stars in the background of Palatini f(R, T) gravity. In this context, the static spherically symmetric geometry is considered which is assumed to be coupled with an isotropic matter configurations. The evolution of the system is considered with the help of Tolman–Oppenheimer–Volkoff equations and conformal transformations. We found the stable configurations of the spherical stars with some constraints.

Appendix

$$\begin{aligned} W_{\mu \nu }= & {} \frac{D_{\mu \nu }}{F} + 8\pi g_{\mu \nu }\frac{T}{2F} +\Theta _{\mu \nu }\frac{f_T}{F}+g_{\mu \nu }\frac{f}{2F}-g_{\mu \nu } (T+\Theta )\frac{f_T}{2F},\\ D_{\mu \nu }= & {} (g_{\mu \nu }\Box -\nabla _{\mu } \nabla _{\nu })F +\frac{3}{2F} \left[ \nabla _{\mu }F \nabla _{\nu }F -\frac{g_{\mu \nu }}{2} (\nabla F)^2\right] , \\ D_{tt}= & {} (g_{tt}\Box F -\nabla _{t} \nabla _{t} F)+\frac{3}{2F} \left[ \nabla _{t} F \nabla _{t} F-\frac{g_{tt}}{2} (\nabla F)^2 \right] , \\ W_{tt}= & {} -\frac{3}{4BF^{2}} (F')^{2} +4\pi \frac{B}{F} (\rho -3p) -\frac{Bf}{2F} -\frac{1}{2} B \frac{f_T}{F} (3p + 5\rho ), \\ D_{rr}= & {} (g_{rr}\Box F -\nabla _{r} \nabla _{r} F)+\frac{3}{2F} \left[ \nabla _{r} F \nabla _{r} F-\frac{g_{rr}}{2} (\nabla F)^2 \right] , \\ D_{rr}= & {} (F)'' +\frac{3}{2F} (F')^{2} -\frac{3A}{4F} (F')^{2}, \\ W_{rr}= & {} \frac{(F)''}{F} +\frac{3}{2F^{2}} (F')^{2} -\frac{3A}{4F^{2}} (F')^{2} +4\pi \frac{A}{F} (3p-\rho ) +\frac{Af}{2F} +\frac{1}{2} A \frac{f_T}{F}(\rho -p), \\ D_{\theta \theta }= & {} (g_{\theta \theta }\Box F -\nabla _{\theta } \nabla _{\theta } F)+\frac{3}{2F} \left[ \nabla _{\theta } F \nabla _{\theta } F-\frac{g_{\theta \theta }}{2} (\nabla F)^2 \right] ,\\ D_{\theta \theta }= & {} -\frac{3}{4F} r^{2} (F')^{2},\quad D_{tt}=-\frac{3}{4BF} (F')^{2}, \\ W_{\theta \theta }= & {} -\frac{3}{4F^{2}} r^{2} (F')^{2}+ 4\pi \frac{r^{2}}{F} (3p-\rho ) +\frac{r^{2}f}{2F}+\frac{1}{2} r^{2} \frac{f_T}{F}(\rho -p). \end{aligned}$$