Is the Schwarzschild Metric a Vacuum Solution of the Einstein Equation?

Horace Crater

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arXiv · 1106.2040

Is the Schwarzschild Metric a Vacuum Solution of the Einstein Equation?

Horace Crater

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Abstract

This paper examines the inhomogeneous Einstein equation for a static spherically symmetric metric with a source term corresponding to a perfect fluid with p=-rho. By a careful treatment of the equation near the origin we find an analytic solution for the metric, dependent on a small parameter epsilon, which can be made arbitrarily close to the Schwarzschild solution as ε} tends to zero and which in that same limit can be viewed as arising from a point-like source structure.

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Horace Crater. 2014-04-11. Is the Schwarzschild Metric a Vacuum Solution of the Einstein Equation?. https://arxiv.org/abs/1106.2040

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