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Schwarzschild and Birkhoff a la Weyl
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Schwarzschild and Birkhoff a la Weyl
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We provide a simple derivation of the Schwarzschild solution in General Relativity, generalizing an early approach by Weyl, to include Birkhoff's theorem: constancy of the mass; its deeper, Hamiltonian, basis is also given. Our procedure is illustrated by a parallel derivation of the Coulomb field and constancy of electric charge, in electrodynamics.
Forward citations
Cited by 3 Pith papers
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Black Hole Interiors as a Laboratory for Time-Dependent Classical Double Copy
Trapped black hole interiors admit exact time-dependent classical double copy via Kantowski-Sachs patches from static Kerr-Schild data, characterized by p_parallel = -ρ, with finite single-copy fields in regular solut...
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Birkhoff rigidity from a covariant optical seed
Spherical symmetry in stationary vacuum gravity forces the optical seed to equal the inverse areal radius, making Schwarzschild the unique nowhere-vanishing optical-seed Kerr-Schild geometry.
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Birkhoff rigidity from a covariant optical seed
In spherical vacuum gravity, the covariant optical seed collapses to the real monopole R=±r, and its Kerr-Schild reconstruction is uniquely the Schwarzschild family.
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