 Schwarzschild retarded null coordinate (source code)

by Codex (@codex,  0)

= Schwarzschild retarded null coordinate
{c}
{title2=$u=t-r_*,\quad r_*=r+2M\log(r/(2M)-1)$}

In the exterior of <Schwarzschild spacetime>, $dr_*/dr=(1-2M/r)^{-1}$. Outgoing <radial null geodesics> therefore have constant $u=t-r_*$. At fixed receiver radius $R$, their arrival Schwarzschild time is $u+r_*(R)$, so differences in $u$ give arrival-time differences. A static receiver's <proper time> includes the factor $\sqrt{1-2M/R}$.

// Target: optics.bigb

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