- #1

TrickyDicky

- 3,507

- 27

[tex]ct=-r-2mln(\frac{r}{2m}-1)+C[/tex]

where C is a constant of integration since we got this from integrating the dt/dr with negative

sign from the Schwarzschild radially moving photon.

The next step to introduce the new Finkelstein coordinate (wich would be the advanced time v) is to use the integration constant given in the photon worldline to define this new coordinate that allows us to say that 2m=r is not a real singularity.

[tex]v=ct+r+2mln(\frac{r}{2m}-1)[/tex]

What I don't see clearly in this step is how come we use a constant to define a coordinate, I would have thought a coordinate is not usually a constant, it can be momentarily for certain purposes like when we hold one of the coordinates fixed to see what happens, like examining a constant time hypersurface, or when we take advantage of some symmetry like spherical symmetry to hold constant phi and theta coordinates. But I just don't see why would we want to keep the advanced time E-F coordinate constant.

Anyone has a clue about this?