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Redshifted gravitational mass of a static thin shell

A thin spherical shell of proper surface mass density

ρ

held at Schwarzschild radius

r_{st}

around mass

M

contributes, to first order in its mass,

Δ M_{\infty} = 4 π r_{st}^{2} ρ 1 - \frac{2 M}{r _{st}}

to the exterior Schwarzschild mass parameter.

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