A Dirac's coordinates ##(\tau, \rho)## for the Schwarzschild metric with ##r \le 2m##

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Do Dirac's coordinates ##(\tau, \rho)## for the Schwarzschild metric have any recognized name?
Dirac in his "GTR" (Chap 19, page 34-35) finds a coordinate system ##(\tau, \rho)## which has no coordinate singularity at ##r=2m##. Explicitly, the transformation looks like (after some algebra):
$$\tau=t + 4m\sqrt{\frac{r}{2m}} + 2m\log{\frac{\sqrt{r/2m}-1}{\sqrt{r/2m}+1}}$$
$$\rho=t + \frac{2r}{3}\sqrt{\frac{r}{2m}} + 4m\sqrt{\frac{r}{2m}} + 2m\log{\frac{\sqrt{r/2m}-1}{\sqrt{r/2m}+1}}$$
The first coordinate ##\tau## is similar to Gullstrand–Painlevé coordinates, except for the first term with an ##r^{3/2}## factor.

Is there a specific name for these coordinates attributable to their original discoverer?
 
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I'm not familiar with it, but I can have a look round later. Your last term in both expressions reduces to zero, though - presumably a typo and probably worth correcting.
 
Ibix said:
I'm not familiar with it, but I can have a look round later. Your last term in both expressions reduces to zero, though - presumably a typo and probably worth correcting.
Thanks - yes, fixed it.
 
Thanks! That looks exactly right.
 
I found a superb analysis of these coordinates in Landau & Lifshitz Vol 2.
 
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