Proposal of a New Scalar Gauge in Relativity Field Equation

In this paper we propose a new gauge term in addition to the conventional gauge to acquire complete solution for the linear approximated gravitational equation. The calculation to make general form for the linear gravitational equation uses the well-known N?ether’s theorem saying that gauge symmetry is equal to conservation law. The unsolved coefficients in the equation require another condition which is leading to new gauge term. This proposed new gauge is a tensor product by a scalar quantity with a metric tensor having the trace value of 2. The scalar component in the 5th row and column of Kaluza-Klein’s metric tensor can be found as 2 diagonal components in our proposed 4×4 metric tensor. We also show that only a constant scalar gauge can be allowed in the curved space-time although arbitrary gauge can exist in the linear space-time.