A comparative study of embedding class one, conformally flat, vanishing complexity factor and conformally symmetric solutions and their impacts on compact star structure

For the first time, we have presented in detail the comparative studies of embedding class one (CO), conformally flat (CF), vanishing complexity factor (COM), and conformally symmetric (CS) solutions, which are the easiest way of exploring new solutions of the field equations. All these solutions simplify the two metric potentials problem to one metric potential through specific bridge equations. To compare on the same footing, we have assumed the same $g_{rr}$ metric function and solved the $g_{tt}$ metric functions via the bridge equations. We then compare all the physical quantities like density, pressure, anisotropy, adiabatic index, etc. To check which type of matter is appropriate for these solutions, we have plotted the equation of states (EoSs) and found the best-fitted functions. We have found that CO solution obeys quadratic EoS, the COM solution best fits with linear EoS, CF solution contains normal and exotic matters, while the CS solution follows a cubic polynomial, and also includes normal, stiff, and exotic matters. In the end, we have plotted the $M-R$ curves and fitted them with observed masses of a few neutron stars to predict their radii.