- #1
archipatelin
- 26
- 0
A metric consistent with interval:
[tex]\mathrm{d}s^2=-\mathrm{d}\tau^2+\frac{4\tau^2}{(1-\rho^2)^2}\left(\mathrm{d}\rho^2+\rho^2\mathrm{d}\theta^2+\rho^2\sin(\theta)^2\mathrm{d}\varphi^2\right)[/tex]
get zero for riemann's tensor, therefor must be isomorphic with minkowski tensor.
But I don't find thus transformation of coordinates from [tex]\tau,\,\rho\rightarrow t,\,r[/tex]
so that after transformation is interval in minkowski form:
[tex]\mathrm{d}s^2=-\mathrm{d}t^2+\fmathrm{d}r^2+r^2\mathrm{d}\theta^2+r^2\sin(\theta)^2\mathrm{d}\varphi^2[/tex].
What's transformation?
[tex]\mathrm{d}s^2=-\mathrm{d}\tau^2+\frac{4\tau^2}{(1-\rho^2)^2}\left(\mathrm{d}\rho^2+\rho^2\mathrm{d}\theta^2+\rho^2\sin(\theta)^2\mathrm{d}\varphi^2\right)[/tex]
get zero for riemann's tensor, therefor must be isomorphic with minkowski tensor.
But I don't find thus transformation of coordinates from [tex]\tau,\,\rho\rightarrow t,\,r[/tex]
so that after transformation is interval in minkowski form:
[tex]\mathrm{d}s^2=-\mathrm{d}t^2+\fmathrm{d}r^2+r^2\mathrm{d}\theta^2+r^2\sin(\theta)^2\mathrm{d}\varphi^2[/tex].
What's transformation?