The Geometric Extension of Green's Functions and its Application in Global Wave Equations

Abstract

In this research we considered the geometrical interpretation of the wave equation. We have constricted the geometrical set up for the problem such as fiber bundle and it's coresection . We have also utilized Lorentzian geometry to formulate our problem, where we have described our boundary conditions on Cauchy hyper-surface. This has led to a parallel construction of Green's Function appropriate to a global description of wave equation on differential manifold. The formulation of the solution yields the local solution on space time as known before.