Modeling of compact stars in de Rham–Gabadadze–Tolley like massive gravity

We proposed a new mathematical model of compact structure and analyzed the stability in the de Rham Gabadadze Tolley (dRGT) theory of gravity. The formulation of field equations within the framework of the modified theory is presented by considering the anisotropic matter distribution within the spherically symmetric geometry. We employed the Krori and Barua (KB) metric, denoted as $\varphi \left(r\right)=\frac{1}{2}B{r}^2+d$ and $\lambda \left(r\right)=\frac{1}{2}A{r}^2$, where $A$, $B$, and $C$ represent the unknown constants to generate the solution of field equations. In this investigation, we considered five different known compact stars: Vela X-12 with mass 1.77$M\left(M_{⨀}\right)$ and radius 9.99 km, 4U 1608-52 with mass 1.74$M\left(M_{⨀}\right)$ and radius 9.3 km, PSR J1903+327 with mass 1.667$M\left(M_{⨀}\right)$ and radius 9.438 km, Cen X-3 with mass 1.49$M\left(M_{⨀}\right)$ and radius 9.51 km, and 4U 1820-30 with mass 1.58$M\left(M_{⨀}\right)$ and radius 9.1 km, respectively to observe the physical properties of the presented model. We have checked our model for physical validity and stability by exploring the graphical behavior of some important properties such as energy density, pressure (P_r, P_t), energy conditions, stability via Herrera cracking concept and the adiabatic index, mass function, compactness, and surface redshift on various compact stars considered in this study. Significantly, we analyzed the demeanor of different forces influenced on the system and observed that our model remain in the hydrostatic equilibrium under the impact of these forces. All the obtained results show that our proposed model is realistic and stable.