Modeling self-bound binary compact object with a slow rotation effect and effect of electric field gradient on the mass-radius limit and moment of inertia

In this paper, we investigate the effects of electric field gradients on the secondary component of GW190814 and other binary compact objects. Using general relativistic equations, we derive a model with three conditions and analyze its metric potentials, electric charge, energy density, stresses, and anisotropy parameter. The metric potentials in our analysis match the Schwarzschild exterior at the stellar surface, exhibiting smooth behavior without any central singularity. The electric charge increases from zero at the core to a maximum at the surface, indicating an outward electric force. The energy density, radial and tangential pressures, and anisotropy all demonstrate well-behaved trends. The model is found stable based on the Harrison-Zeldovich-Novikov criteria, adiabatic index, and causality. Investigating the electric charge influence, we find increased charge leads to decreasing pressures and lower central adiabatic index, suggesting the need to optimize charge for long-term stability. The analysis of mass-radius ratio and moment of inertia-mass demonstrates the model's ability to capture the equation of state (EOS) stiffness. Finally, from the $M-R$ and $I-M$ curves we have shown that the mass obtained for the slowly rotating star is higher than the non-rotating case due to the contribution from rotational energy $\frac{1}{2}I{\Omega }^2$ for all values of $E_0$. It is very surprising to find that the electric field per radial distance i.e. $E/r=\sqrt{E_0}$ is maximum at a particular mass for a chosen radius, specifically for r (km), $M_{NR}\left(M_{\odot }\right)$, and $\sqrt{E_0^{max}}\times {10}^{-4}$ (/km⁴). The electric field per unit radius also influences the EOS significantly with overall form $P_r=a\rho -b{\rho }^2-c$ for all $a,b,c>0$. This means that the EOS contains quark matter, dark energy, and exotic matters.