Varieties of Parametric Classes of Exact Solutions in General Relativity Representing Static Fluid Balls

We have presented a method of obtaining parametric classes of spherically symmetric analytic solutions of the general relativistic field equations in canonical coordinates. A number of previously known classes of solutions have been rediscovered which describe perfect fluid balls with infinite central pressure and infinite central density though their ratio is positively finite and less than one. From the solution of one of the newly discovered classes, we have constructed a causal model in which outmarch of pressure and density is positive and monotonically decreasing, and pressure-density ratio is positive and less than one throughout within the balls. Corresponding to this model, we have maximized the Neutron star mass 2.40Θ with the linear dimensions of 28.43 kms and surface red shift of 0.4142.