New parametric classes of exact solutions in general relativity and polytropic nature fluid ball with constant sound speed

In this paper we have presented a method of obtaining varieties of new parametric classes of spherically symmetric analytic solutions of the general relativistic field equations in canonical coordinates. A number of previously known classes of solutions has been rediscovered which describe perfect fluid balls with infinite central pressure and infinite central density though their ratio is positively finite and less then one. From the solutions of one of the class we have constructed a causal model of polytrope with constant sound speed Corresponding to the polytrope model we have maximized the Neutron star mass 3.26 M ⊙ with the linear dimensions 32.27 kms with surface red shift 0.7355 and for other class we have constructed a causal model in which outmarch of pressure and density is monotonically decreasing and pressure–density ratio is positive and less than 1 throughout with in the ball. Corresponding to this model we have maximized the Neutron star mass 3.09 M ⊙ with the linear dimensions 30.55 kms with surface red shifts 0.5811.