Relativistic anisotropic models for compact star with equation of state p = f(ρ)

We present new anisotropic models for Buchdahl [H. A. Buchdahl, Phys. Rev. 116 (1959) 1027.] type perfect fluid solution. For this purpose, we started with metric potential e(nu) same as Buchdahl [H. A. Buchdahl, Phys. Rev. 116 ( 1959) 1027.] and e(nu) is monotonically increasing function as suggested by Lake [K. Lake, Phys. Rev. D 67 ( 2003) 104015]. After that we determine the new pressure anisotropy factor Delta with the help of both the metric potentials e(lambda) and e(v) and propose new well behaved general solution for anisotropic fluid distribution. The physical quantities like energy density, radial and tangential pressures, velocity of sound and redshift etc. are positive and finite inside the compact star. In this connection, we have studied the stability of the models, which is most vital one and also we determined the equation of state p = f(rho) for the realistic compact star models. It is noted that the mass and radius of our models can represent the structure of realistic astrophysical objects such as Her X-1 and RXJ 1856-37.