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Kostik
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- TL;DR Summary
- 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?
$$\tau=t + 4m\sqrt{\frac{r}{2m}} + 2m\log{\frac{\sqrt{r/2m}-1}{\sqrt{r/2m}+1}}$$
$$\rho=t + \frac{2r}{3}\sqrt{\frac{r}{2m}} + 4m\sqrt{\frac{r}{2m}} + 2m\log{\frac{\sqrt{r/2m}-1}{\sqrt{r/2m}+1}}$$
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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