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

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

2011-06-10

arxiv.org/abs/1106.2040v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

11 pages

Scientific paper

This paper examines the inhomogeneous Einstein equation for a static spherically symmetric metric with a source term corresponding to 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 {\varepsilon}, which can be made arbitrarily close to the Schwarzschild solution as {\varepsilon}{\rightarrow}0 and which in that same limit can be viewed as arising from a point-like source structure.

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