A New Action-Derived Form of The Black Hole Metric

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Several different but equivalent forms of the spherical black hole (Schwarzschild) are known, as well as several derivations. Here a novel form is derived through the power of the action formalism. The method generalizes to any spherical black hole or brane, and the charged hole case (Reissner-Nordstrom) is worked out in detail.
11 pages, 1 figure. v2: see "Note added" at end of paper for clarifications and added reference. v3: added reference

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