Neutron stars have super nuclear density. We derive the EoS for a neutrino-free proto-neutron star (PNS) that is at finite entropy. The core includes antikaon condensates as a constituent. We find EoS for a range of entropies and antikaon optical potentials. In a non-rotating compact star, the mass-radius sequence relation has been well established through Tolman-Oppenheimer-Volkoff equation. We study the change of mass and constituents of a static PNS star for different parameters and thermodynamic conditions. However rotation induces many changes in the star equilibrium and its structural properties evolve. We also study the effect of rapid rotation on the shape of PNS that is at finite-entropy and the core of which contains antikaon condensates and estimate the gravitational wave amplitude roughly.