- #1

stevebd1

Gold Member

- 749

- 41

I'm currently looking at Kruskal-Szekeres coordinates in relation to a static black hole.

For the exterior region, the coordinates are-

[tex] R=\left(\frac{r}{2GM}-1\right)^{1/2}e^{r/4GM}cosh\left(\frac{t}{4GM}\right)[/tex]

For the interior-

[tex] R=\left(1-\frac{r}{2GM}\right)^{1/2}e^{r/4GM}sinh\left(\frac{t}{4GM}\right)[/tex]

where c = 1 and G, the gravitational constant, is kept explicit.

I've looked extensively on the web but can find very little as to explaining the equations in a bit more depth. I'd appreciate it if someone could shed some light on what e represents and while I'm certain that c^2 appears adjacent to r in the first set of brackets, does it appear anywhere else in the equations? Also, would it be correct to assume that t represents time?

For the exterior region, the coordinates are-

[tex] R=\left(\frac{r}{2GM}-1\right)^{1/2}e^{r/4GM}cosh\left(\frac{t}{4GM}\right)[/tex]

For the interior-

[tex] R=\left(1-\frac{r}{2GM}\right)^{1/2}e^{r/4GM}sinh\left(\frac{t}{4GM}\right)[/tex]

where c = 1 and G, the gravitational constant, is kept explicit.

I've looked extensively on the web but can find very little as to explaining the equations in a bit more depth. I'd appreciate it if someone could shed some light on what e represents and while I'm certain that c^2 appears adjacent to r in the first set of brackets, does it appear anywhere else in the equations? Also, would it be correct to assume that t represents time?

Last edited: