A Simple Equation to Calculate the Gaussian Curvature of Space-Time According to the Schwarzschild Model

The Flamm paraboloid is a space-time solution to the problem posed by Schwarzschild concerning finding a solution other than the trivial one to Einstein’s equations in an empty space. For this reason, it also represents the space that exists in the surrounding of a gravitational point mass. The solution of J. Droste that we study here, the Flamm paraboloid, leads to calculating values of the Gaussian curvature of its space-time that require a complicated process of obtaining. We have found a simple equation that allows calculating these values in a simple way. This equation obtained here through algebraic calculation is exact in the space-time represented by the Flamm paraboloid.

Keywords: Schwarzschild Model, Gauss Curvature of Space-time, J. Droste Solution.