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In any physical theory, it is important to understand when solutions to the fundamental field equation exist, and answering this question has been the central theme of York's scientific work, culminating in the achievement, with Yvonne Choquet-Bruhat, of formulating the Einstein field equation as a well-posed system in the sense of the theory of partial differential equations.
In general relativity, Regge calculus is a formalism for producing simplicial approximations of spacetimes that are solutions to the Einstein field equation.
Ronald Kantowski is a theoretical cosmologist, well known in the field of general relativity as the author, together with Rainer K. Sachs, of the Kantowski-Sachs dust solutions to the Einstein field equation.
With sufficiently clever assumptions of this sort, it is often possible to reduce the Einstein field equation to a much simpler system of equations, even a single partial differential equation (as happens in the case of stationary axisymmetric vacuum solutions, which are characterized by the Ernst equation) or a system of ordinary differential equations (as happens in the case of the Schwarzschild vacuum).