Oppenheimer-Snyder Model of Gravitational Collapse: Implications

[PeterDonis]

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 $\tau$...

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