On most general exact solution for Vaidya-Tikekar isentropic superdense star

The energy density of Vaidya-Tikekar isentropic superdense star is found to be decreasing away from the center, only if the parameter K is negative. T he most general exact solution for the star is derived for all negative val ues of K in terms of circular and inverse circular functions. Which can fur ther be expressed in terms of algebraic functions for K = 2-(n/delta)(2) < 0 (n being integer and delta = 1,2,3 4). The energy conditions 0 less than or equal to p less than or equal to alpha rho c(2), (alpha = 1 or 1/3) and adiabatic sound speed condition d rho/dp less than or equal to c, when appl ied at the center and at the boundary, restricted the parameters K and alph a such that .18 < -K < 2287 and .004 less than or equal to alpha less than or equal to .86. The maximum mass of the star satisfying the strong energy condition (SEC), (alpha = 1/3) is found to be 3.82 M. at K = -2/3, while th e same for the weak energy condition (WEC), (alpha = 1) is 4.57 M. at K = - >5/2. In each case the surface density is assumed to be 2 x 10(14) gm cm(-3 ). The solutions corresponding to K > 0 (in fact K > 1) are also made meani ngful by considering the hypersurfaces t= constant as 3-hyperboloid by repl acing the parameter R-2 by -R-2 in Vaidya-Tikekar formalism. The solutions for the later case are also expressible in terms of algebraic functions for K = 2-(n/delta)(2) > 1 (n being integer or zero and delta = 1,2,3 4). The cases for which 0 < K < 1 do not possess negative energy density gradient a nd therefore are incapable of representing any physically plausible star mo del. In totality the article provides all the physically plausible exact so lutions for the Buchdahl static perfect fluid spheres.