Anisotropic strange stars under simplest minimal matter-geometry coupling in the $f$ ($R,\mathcal{T}$) gravity

We study strange stars in the framework of $f(R,\mathcal{T})$ theory of gravity. To provide exact solutions of the field equations it is considered that the gravitational Lagrangian can be expressed as the linear function of the Ricci scalar $R$ and the trace of the stress-energy tensor $\mathcal{T}$, i.e. $f(R,\mathcal{T})=R+2\chi \mathcal{T}$, where $\chi$ is a constant. We also consider that the strange quark matter (SQM) distribution inside the stellar system is governed by the phenomenological MIT bag model equation of state (EOS), given as $p_r=\frac{1}{3}(\rho -4B)$, where $B$ is the bag constant. Further, for a specific value of $B$ and observed values of mass of the strange star candidates we obtain the exact solution of the modified Tolman-Oppenheimer-Volkoff (TOV) equation in the framework of $f(R,\mathcal{T})$ gravity and have studied in detail the dependence of the different physical parameters, like the metric potentials, energy density, radial and tangential pressures and anisotropy etc., due to the chosen different values of $\chi$. Likewise in GR, as have been shown in our previous work [Deb et al., Ann. Phys. (Amsterdam) 387, 239 (2017)] in the present work also we find maximum anisotropy at the surface which seems an inherent property of the strange stars in modified $f(R,\mathcal{T})$ theory of gravity. To check the physical acceptability and stability of the stellar system based on the obtained solutions we have performed different physical tests, viz., the energy conditions, Herrera cracking concept, adiabatic index etc. In this work, we also have explained the effects, those are arising due to the interaction between the matter and the curvature terms in $f(R,\mathcal{T})$ gravity, on the anisotropic compact stellar system. It is interesting to note that as the values of $\chi$ increase the strange stars become more massive and their radius increase gradually so that eventually they gradually turn into less dense compact objects. The present study reveals that the modified $f(R,\mathcal{T})$ gravity is a suitable theory to explain massive stellar systems like recent magnetars, massive pulsars and super-Chandrasekhar stars, which cannot be explained in the framework of GR. However, for $\chi =0$ the standard results of Einsteinian gravity are retrieved.

Figure 1

Variation of (i) $e^{\nu (r)}$ (upper panel) and (ii) $e^{\lambda (r)}$ (lower panel) as a function of the radial coordinate $r/R$ for the strange star $LMCX-4$. Here $B=83\mathrm{MeV}/{\mathrm{fm}}^3$ and $c_1=0.2$.

Figure 2

Variation of (i) ${\rho }_{\mathrm{eff}}$ (upper panel), (ii) $p_{\mathrm{eff}r}$ (middle panel) and (iii) $p_{\mathrm{eff}t}$ (lower panel) as a function of the radial coordinate $r/R$ for the strange star $LMCX-4$.

Figure 3

Variation of anisotropy as a function of the radial coordinate $r/R$ for the strange star $LMCX-4$.

Figure 4

Variation of energy conditions with the radial coordinate $r/R$ for $LMCX-4$ due to different chosen values of $\chi$.

Figure 5

Mass $(M/M_{\odot })$ vs Radius ($R$ in km) curve for the strange stars due to the different values of $\chi$. The solid circles are representing the maximum mass points for the strange stars.

Figure 6

Variation of (i) $M/M_{\odot }$ (left panel) and (ii) $R$ in km (right panel) as a function of the central density $({\rho }_{\mathrm{eff}c}\in \mathrm{MeV}/{\mathrm{fm}}^3)$ due to different values of $\chi$. The solid circles are representing the maximum mass points for the strange stars.

Figure 7

Variation of the different forces with respect to the radial coordinate $r/R$ for $LMCX-4$ due to different chosen values of $\chi$.

Figure 8

Variation of $|v_{st}^2-v_{sr}^2|$ with the radial coordinate $r/R$ for $LMCX-4$.

Figure 9

Variation of i) ${\mathrm{\Gamma }}_r$ (upper panel) and ii) ${\mathrm{\Gamma }}_t$ (lower panel) with the radial coordinate $r/R$ for $LMCX-4$.

Figure 10

Variation of the (i) compactification factor (upper panel) and (ii) redshift (lower panel) as a function of the radial coordinate $r/R$ for the strange star $LMCX-4$.