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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##...
The Oppenheimer-Snyder Model of Gravitational Collapse is a theoretical model developed by physicists J. Robert Oppenheimer and Hartland Snyder in 1939. It describes the collapse of a massive star under its own gravitational force and the formation of a black hole.
The implications of the Oppenheimer-Snyder Model are significant in understanding the behavior of massive objects in the universe. It shows that a star with a mass greater than a certain threshold, known as the Tolman-Oppenheimer-Volkoff limit, will inevitably collapse into a singularity, creating a black hole.
The Oppenheimer-Snyder Model differs from other models in that it takes into account the effects of general relativity, which describes how gravity affects the curvature of space-time. It also considers the role of pressure and energy in the collapse process.
While the Oppenheimer-Snyder Model has not been directly observed, its predictions have been confirmed by observations of black holes in the universe. Additionally, it has been used to explain other phenomena, such as the formation of neutron stars.
One limitation of the Oppenheimer-Snyder Model is that it assumes a spherically symmetric collapsing object, which may not always be the case in real-world scenarios. It also does not take into account other factors such as rotation or magnetic fields, which may play a role in the collapse process.