Field Dependant Metric for Gravitational/EM Fields and a Non-Linear Transformation for Local to Proper Space-Time World

Abstract

In this paper, the introduction of a metric for Gravitational Field is examined based on [4]; this can be extended to EM Fields also by change of the parameters involved (ϵ₁, μ₁) to (ϵ₂, μ₂) We know that E² ‒ c² B² or E² ‒B²
 with is an invariant quantity for the EM Fields which can be extended to gravitational fields, as done in [1]. We discuss the metric for the gravitational case and extended to the EM fields as well. The discussion of anomalous characteristic of Lorentz Transformation (LT) and the introduction of a non-linear transformation connecting Local Space-time coordinates (ct,x) with proper system (cτ, x_τ ) is continued.