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.
A simple proof of Birkhoff’s theorem for cosmological constant
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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.