Rastall-Maxwell approach for anisotropic charged strange stars

Abstract

In this work we investigate the Rastall-Maxwell theory around the strange quark matter (SQM). Some solutions are obtained by solving the Modified Tolman-Oppenheimer-Volkoff (TOV) equation in the framework of Rastall gravity. Analysis are performed about the energy condition, the mass-radius relation, the modified TOV equation, the redshift and the stability of the system is checked by exploring the adiabatic index, the compactification factor and the causality condition in order to verify the physical consistency of our model. It comes from our results that for physical values of Rastall parameter, the stellar system is more massive compared to its size. Hence, it emerges from our work that the alternative Rastall theory is a suitable candidate to explain the behavior of massive stellar objects.

APPENDIX

The functions $A_0, A_1,\, A_2,\, A_3$ and  $A_4$ that appears in the relation (44) (45) and (46) are erpanded as:

$$\begin{aligned} A_{0}=\frac{16 \pi \left( 1+r^2 \alpha (3+B )\right) +\left( 1+5 B +4 r^2 (\alpha +3 \alpha B )\right) \gamma }{16 \pi r^2 \left( 4 \pi (3+B )+(1+3 B ) \gamma \right) } \end{aligned}$$

(65)

$$\begin{aligned} A_{1}=-\frac{16 \pi \left( -B +r^2 \alpha (3+B )\right) +\left( -1+3 B +4 r^2 (\alpha +3 \alpha B )\right) \gamma }{16 \pi r^2 \left( 4 \pi (3+B )+(1+3 B ) \gamma \right) }. \end{aligned}$$

(66)

with

$$\begin{aligned} A_2= & {} A_8\, r^2\Big ( \frac{A_{10}}{A_5 A_{11}} -1\Big )+ \alpha ^2(r^2-r^4) \end{aligned}$$

(67)

$$\begin{aligned} A_3= & {} \frac{5r^2\, A^2_7 A_{11}}{A_{11} A_8 A_{13}}+ \alpha ^2(r^2+r^4) \end{aligned}$$

(68)

$$\begin{aligned} A_4= & {} \frac{1}{4 \alpha ^2 A_8\left( \frac{5 A^2_7 A_{13}}{A_{11} A_8 } - \frac{A_5 A_{11}}{A_8 A^2_7} \right) } \end{aligned}$$

(69)

$$\begin{aligned} A_5= & {} \Big (-180 R^2+320 B \pi R^2 r^2-180 R^2 r^4 \alpha ^2+135 R^2 r^7 \alpha ^3\nonumber \\&\quad -320 B \pi R^2 r^2 \gamma +480 \pi R^2 r^2 (-1+\gamma ) c_2+96 \pi r^4 \nonumber \\&\quad \times \Big (4-\gamma +3 (-1+\gamma ) c_1\Big ) \rho _0+640 \pi R^2 r^2 \rho _c-384 \pi r^4 \rho _c\nonumber \\&\quad -160 \pi R^2 r^2 \gamma \rho _c+ 96 \pi r^4 \gamma \rho _c-480 \pi R^2 r^2 c_1 \rho _c +288 \pi r^4 c_1 \rho _c\nonumber \\&\quad +480 \pi R^2 r^2 \gamma c_1 \rho _c-288 \pi r^4 \gamma c_1 \rho _c\Big ) \end{aligned}$$

(70)

$$\begin{aligned} A_7= & {} \Big (640 B \pi R^2-720 R^2 r^2 \alpha ^2+945 R^2 r^5 \alpha ^3-640 B \pi R^2 \gamma \nonumber \\&\quad +960 \pi R^2 (-1+\gamma ) c_2+384 \pi r^2 \Big (4-\gamma +3 (-1+\gamma ) c_1\Big ) \rho _0\nonumber \\&\quad +1280 \pi R^2 \rho _c-1536 \pi r^2 \rho _c-320 \pi R^2 \gamma \rho _c\nonumber \\&\quad +384 \pi r^2 \gamma \rho _c-960 \pi R^2 c_1 \rho _c+1152 \pi r^2 c_1 \rho _c+960 \pi R^2 \gamma c_1 \rho _c \nonumber \\&\quad -1152 \pi r^2 \gamma c_1 \rho _c\Big ) \end{aligned}$$

(71)

$$\begin{aligned} A_8= & {} - A_5,\; A_{11}= A_7^2\; A_{13} = A_5 \end{aligned}$$

(72)