Charged anisotropic compact stellar solutions in torsion-trace gravity via modified chaplygin gas model

Abstract

In present work, we use an extended f(T) gravity namely $f(T,\mathcal {T})$ gravity, representing the coupling of torsion scalar T and the trace of energy-momentum tensor $\mathcal {T}$. In this framework, we find the exact interior anisotropic solutions of compact stars considering Krori–Barua space-time under metric potentials, $a(r)=Br^{2}+Cr^{3},~ b(r)=Ar^{3}$ (A,  B,  C are the unknown parameters), and applying a well-known model $f(T,\mathcal {T})=\alpha _{1}T^{n}(r)+\beta \mathcal {T}(r)+\phi ,~n>1$. To close the system of equations, we utilize an equation of state for modified Chaplygin gas model. By the well-known matching conditions of exterior and interior space-time, we evaluate the unknown model parameters. For four different strange stars, $PSR-J$1614-2230, $SAX-J$1808.4-3658, 4U 1820-30 and $Vela-X$-12 (last two are added in “Appendix”), we made complete physical analysis by plotting trajectories for energy conditions, square speed of sound, mass function, compactness factor and surface redshift. It is observed that our results satisfy all the necessary and sufficient physical conditions, hence physically viable.

Appendix: Graphical analysis of \(Vela-X\)-12 and 4U1820-30

In this Appendix, we present the graphical analysis of the specific strange stars namely, $Vela-X$-12 and 4U1820-30. Our results are consistent and stable for all physical parameters as shown in Figs. 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41 and 42.

Fig. 22

$\rho$ versus r for different stars by varying $\beta$ and n

Fig. 23

$p_{r}$ versus r for different stars by varying $\beta$ and n

Fig. 24

$p_{t}$ versus r for different stars by varying $\beta$ and n

Fig. 25

$\frac{d\rho }{dr}$ versus r for different stars by varying $\beta$ and n

Fig. 26

$\frac{dp_{r}}{dr}$ versus r for different stars by varying $\beta$ and n

Fig. 27

$\frac{d^{2}\rho }{dr^{2}}$ versus r for different stars by varying $\beta$ and n

Fig. 28

$\frac{d^{2}p_{r}}{dr^{2}}$ versus r for different stars by varying $\beta$ and n

Fig. 29

Anisotropic parameter versus r for different stars by varying $\beta$ and n

Fig. 30

$E^{2}$ versus r for different stars by varying $\beta$ and n

Fig. 31

$\rho +\frac{E^{2}}{8\pi }$ versus r for different stars by varying $\beta$ and n

Fig. 32

$\rho +p_{r}$ versus r for different stars by varying $\beta$ and n

Fig. 33

$\rho +3p_{r}$ versus r for different stars by varying $\beta$ and n

Fig. 34

$\rho +p_{t}+\frac{E^{2}}{4\pi }$ versus r for different stars by varying $\beta$ and n

Fig. 35

$\rho +p_{r}+2p_{t}+\frac{E^{2}}{4\pi }$ versus r for different stars by varying $\beta$ and n

Fig. 36

$v^{2}_{sr}$ versus r for different stars by varying $\beta$ and n

Fig. 37

$v^{2}_{st}$ versus r for different stars by varying $\beta$ and n

Fig. 38

$v^{2}_{st}-v^{2}_{sr}$ versus r for different stars by varying $\beta$ and n

Fig. 39

$|v^{2}_{st}-v^{2}_{sr}|$ versus r for different stars by varying $\beta$ and n

Fig. 40

m(r) versus r for different stars by varying $\beta$ and n

Fig. 41

u(r) versus r for different stars by varying $\beta$ and n

Fig. 42

$z_{s}$ versus r for different stars by varying $\beta$ and n