- #1

jinbaw

- 65

- 0

A singularity exists at [tex] r=\pm 1 [/tex]. By calculating [tex] R^{abcd}R_{abcd} [/tex] i found out that this singularity is a coordinate singularity.

I found the geodesic equations for radial photons and performed the eddington-finkelstein coordinate transformation.

my metric turns out to be:

[tex] ds^2 = (1-r^2)dudv-r^2 d\theta^2 - r^2 sin^2\theta d\phi^2 [/tex]

where u and v are the constants of integration for the outgoing and incoming radial photons.

I also took a further coordinate transformation where T=(u+v)/2 and X = (u-v)/2

and the metric takes the form:

[tex] ds^2 = (1-r^2)dT^2-(1-r^2)dX^2-r^2 d\theta^2 - r^2 sin^2\theta d\phi^2 [/tex]

However for [tex] r=\pm 1 [/tex] the metric still does not behave properly.

Do you suggest any other coordinate transformation? Thank you.