An Evolving Spacetime Metric Induced by a ‘Static’ Source

In a series of recent papers we developed formulation general relativity in which spacetime and the dynamics matter evolve with Poincaré invariant parameter τ. this paper, apply formalism to derive metric induced by ‘static’ event evolving uniformly along its t-axis at spatial origin x=0. The is shown vary t τ, as well distance r, taking maximum value for test particle retarded time τ=t−r/c. resulting picture, an localized space produces field similarly localized, where both We first solution wave equation linearized theory, discuss limitations studying geodesic motion it event. By then examining 4+1 formalism, poses initial problem under τ-evolution, clarify these indicate how they may be overcome full nonlinear equations.