- #1
- 47,599
- 23,875
In the last article in this series, we finished up with a metric for the Oppenheimer-Snyder collapse:
$$
ds^2 = – d\tau^2 + A^2 \left( \eta \right) \left( \frac{dR^2}{1 – 2M \frac{R_-^2}{R_b^2} \frac{1}{R_+}} + R^2 d\Omega^2 \right)
$$
Now we will look at some of the implications of this metric.
First, let’s review what we already know: ##\tau## is the proper time of our comoving observers, who follow radial timelike geodesics starting from mutual rest for all values of ##R## at ##\tau = 0##. ##R## labels each geodesic with its areal radius ##r## at ##\tau = 0##. ##\eta## is a cycloidal time parameter that ranges from ##0## to ##\pi##; ##\eta = 0## is the starting point of each geodesic at ##\tau = 0##, and ##\eta = \pi## is the point at which each geodesic hits the singularity at ##r = 0##. Inside the collapsing matter, ##\eta## is a function of ##\tau##...