# Oppenheimer-Snyder Model of Gravitational Collapse: Mathematical Details

• PeterDonis
In summary, the conversation discusses the model of gravitational collapse of a spherically symmetric massive object, which was first published in a 1939 paper by Oppenheimer and Snyder. The follow-up article provides further mathematical details about the model, using a different approach from the original paper. This approach is inspired by the approach described in MTW and Landau & Lifschitz. The conversation also mentions a different approach taken by Weinberg in the vacuum region outside the collapsing matter, where he finds an expression for the interior metric in coordinates similar to standard Schwarzschild coordinates. However, this approach will not be discussed in this conversation.
PeterDonis
Mentor
In a previous article, I described in general terms the model of gravitational collapse of a spherically symmetric massive object, first published by Oppenheimer and Snyder in their classic 1939 paper. In this follow-up article, I will give further mathematical details about the model, using an approach somewhat different from their original paper (and inspired by the approach described in MTW and Landau & Lifschitz).
(Note: Weinberg takes a different approach in the vacuum region outside the collapsing matter. Instead of finding an expression for the exterior vacuum metric in comoving coordinates, he finds an expression for the interior metric in coordinates similar to standard Schwarzschild coordinates. We will not discuss that approach here, but it is instructive to compare the two. The latter approach, which also has similarities to the approach taken in the...

Cientific124, Greg Bernhardt, Dale and 1 other person

## 1. What is the Oppenheimer-Snyder Model of Gravitational Collapse?

The Oppenheimer-Snyder Model of Gravitational Collapse is a mathematical model that describes the gravitational collapse of a massive star into a black hole. It was developed by physicists J. Robert Oppenheimer and Hartland Snyder in 1939.

## 2. How does the Oppenheimer-Snyder Model work?

The model is based on the theory of general relativity and considers a spherically symmetric collapsing star. It takes into account the effects of gravity, pressure, and density on the star's collapse, and predicts the formation of an event horizon and singularity at the center of the black hole.

## 3. What are the key assumptions of the Oppenheimer-Snyder Model?

The model assumes that the star is initially in hydrostatic equilibrium, meaning that the inward force of gravity is balanced by the outward pressure of the star's core. It also assumes that the star's collapse is adiabatic, meaning that no heat is exchanged with its surroundings.

## 4. What are the limitations of the Oppenheimer-Snyder Model?

The model does not take into account the effects of rotation, magnetic fields, or other forms of matter besides dust. It also does not consider the possibility of the star forming a neutron star instead of a black hole.

## 5. How does the Oppenheimer-Snyder Model contribute to our understanding of black holes?

The Oppenheimer-Snyder Model was the first mathematical model to predict the formation of a black hole from the collapse of a massive star. It has helped to further our understanding of the properties and behavior of black holes, and has been used as the basis for more complex models and simulations.

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