Relativity and Cosmology

    

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

Authors: Fernando Salmon Iza

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 contour 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 by means of an algebraic expansion is exact in the space-time represented by the Flamm paraboloid.

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[v1] 2024-11-18 02:57:27

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