Unit Error in Oppenheimer-Snyder 1939 Paper?

In summary, There is an error in equation 37 of the 1939 Oppenheimer-Snyder paper "On Continued Gravitational Contraction". The last term inside the last parentheses should be $$\frac{3r_0^{1/2} \tau}{2R_b^{3/2}}$$ instead of $$\frac{3r_0^{1/2} \tau}{2R_b^2}$$. This can be seen by setting ##R=R_b## and using (27) for ##r## in the expression for ##M(y)## in (32). By doing so, we get the correct term $$ \frac{ R_b}{r_0 } \left( 1
  • #1
RogueBanana
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Is there an error, perhaps typographical, in the famous 1939 Oppenheimer-Snyder paper "On Continued Gravitational Contraction" (Phys Rev v56 Sept 1, 1956 pp 455-459)?

Do the units balance in equation 37? The last term inside the last parantheses

##\frac{3r_0^{1/2} \tau}{2R_b^2}##

where ##r_0##, ##\tau## and ##R_b## all have units of length (or time), isn't unitless, as it should be to be subtracted from 1.
 
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  • #2
First of all, the curly brackets means that the 2nd line of (37) is still under the logarithm. The factor

$$\frac{3r_0^{1/2} \tau}{2R_b^2}$$

should be

$$\frac{3r_0^{1/2} \tau}{2R_b^{3/2}}.$$

This term comes from the ##R_b r/(r_0 R)## term in the expression for ##M(y)## in (32). We are to set ##R=R_b## and use (27) for ##r##, which gives

$$ \frac{ R_b r}{r_0 R_b} = \frac{ 1}{r_0 } \left( R_b^{3/2} - \frac{3}{2} r_0^{1/2}\tau \right)^{2/3} = \frac{ R_b}{r_0 } \left( 1- \frac{3r_0^{1/2}\tau}{2 R_b^{3/2}} \right)^{2/3}.$$
 

Related to Unit Error in Oppenheimer-Snyder 1939 Paper?

1. What is the Oppenheimer-Snyder 1939 Paper?

The Oppenheimer-Snyder 1939 paper, also known as "On Continued Gravitational Contraction", is a scientific paper written by physicists J. Robert Oppenheimer and H. Snyder. It describes their theoretical model for the formation of a black hole from a collapsing star.

2. What is unit error in the Oppenheimer-Snyder 1939 Paper?

The unit error in the Oppenheimer-Snyder 1939 paper refers to a mistake made in the mathematical equations used to describe the collapse of a star into a black hole. The error was discovered by mathematician Roy Kerr in 1963 and corrected in his own paper.

3. How did the unit error affect the results of the Oppenheimer-Snyder 1939 Paper?

The unit error affected the results of the Oppenheimer-Snyder 1939 paper by causing an incorrect prediction for the final state of a collapsing star. The original paper predicted that the star would collapse to a point of infinite density, but the corrected equations showed that the star would instead form a rotating black hole.

4. Why is the Oppenheimer-Snyder 1939 Paper still significant despite the unit error?

Despite the unit error, the Oppenheimer-Snyder 1939 paper is still significant because it was one of the first theoretical models to describe the formation of a black hole. It also served as a foundation for later work and led to further advancements in our understanding of black holes.

5. Has the Oppenheimer-Snyder 1939 Paper been retracted or corrected?

The original Oppenheimer-Snyder 1939 paper has not been retracted, but it has been corrected by Kerr's subsequent paper. The corrected equations are now widely accepted and used in black hole research. However, the original paper is still referenced and studied for its historical significance.

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