• Dharmendra Kumar Singh
• Dr. Ram Kumar Sinha
• Mrs. Anjali Kumari

In this paper we develop the method for finding the best theory and their best proving of Einstein field equation and their application. E-C field equation is the relation for find the pressure and density of fluid surrounding the distribution and applicable the Newtonian force on the wall of cubic geometrical shape as a sphere. In this paper we adopt the theory of Richard. C. Tolman’s technique which is published in January 3, 1939. In this equation we also use the formulae on Newton’s laws of gravitation and law of cooling. In the Einstein C. Field equation we observe some problems. This problem is, if we applied the thermo dynamical pressure on the sphere after then no convert total energy in mechanical energy. Some energy be loss surrounding the sphere. That means the absorption of total heat energy into mechanical energy is not converted in work done. We will try to resolve the E-C equation and also we will be try to find some new idea for saving the maximum energy. In this paper we devote the study of equation of Weisskop’s conclusion and correlate it with E-C field equation for static fluid sphere. Also it is used the theorem of Swartz-Child lemma for exterior solution of physically the study for field in the empty space surrounding a spherically symmetrical body in four solution. This paper has two fold objectives. First objective is giving the method for solving the non linear differential equation of first order and higher order which applying to find the equilibrium for gravitational pressure and second objective is the four method which we can’t treating the directly for correlating the solution of equation in E-C field. we consider Adopting Tolman’s technique , we solve the field equations and also discuses it’s two special cases. We have also calculated pressure and density for the distribution.

Einstein field equation, pressure of fluid, Newton’s equation, Weisskop’s conclusion, Tolman technique.

"E-C field equations for static fluid spheres", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.11, Issue 6, page no.K89-K97, June-2024, Available :http://www.jetir.org/papers/JETIR2406A11.pdf

"E-C field equations for static fluid spheres", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.11, Issue 6, page no. ppK89-K97, June-2024, Available at : http://www.jetir.org/papers/JETIR2406A11.pdf