physics - Eddington coordinates

In general relativity, the Eddington coordinates are given by

$ds^2=\left(1-\frac{2\alpha}{r}\right)\,dt^2-\frac{4\alpha}{r}\,dt\,dr-\left(1+\frac{2\alpha}{r}\right)\,dr^2-r^2\,d\Omega^2$

where

$d\Omega^2\equiv d\theta^2+\sin^2\theta\,d\phi^2$ .

The advantage of this coordinate system is that it explicitly shows that the coordinate singularity in the Schwarzschild coordinates is precisely that!

Eddington coordinates