The Schwarzschild Metric: Obtaining Equation M=Gm/c^2 & Newton Law at Infinity

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SUMMARY

The discussion centers on the derivation of the equation M=Gm/c², where M represents the mass of a black hole in units where both G (gravitational constant) and c (speed of light) are set to one. Participants clarify that this equation serves as a conversion factor from mass to length, with the Schwarzschild radius being twice the equivalent length derived from Gm/c². The conversation also touches on the concept of Newton's law at infinity, linking it to the behavior of gravitational forces in the context of black holes.

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  • Understanding of general relativity concepts
  • Familiarity with the Schwarzschild metric
  • Knowledge of gravitational constant (G) and speed of light (c)
  • Basic principles of mass-energy equivalence
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TimeRip496
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How do you obtain this equation M=Gm/c^2. What does M stand for? Is is Newton law at infinity? Again what is this Newton law at infinity?
 
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TimeRip496 said:
How do you obtain this equation M=Gm/c^2. What does M stand for?

M is just the mass of the black hole using units in which G and c are both equal to one.

We don't have to make this substitution but if we don't we'll be schlepping factors of G and c around everywhere in our equations, and they're complicated enough already.
 
Nugatory said:
M is just the mass of the black hole using units in which G and c are both equal to one.

We don't have to make this substitution but if we don't we'll be schlepping factors of G and c around everywhere in our equations, and they're complicated enough already.
Do you mind telling me a source for such derivation? Cause all the Internet gives is just the derivation of the schwarzschild radius.
 
TimeRip496 said:
Do you mind telling me a source for such derivation?

It's just a conversion factor from mass units to length units; ##Gm / c^2## converts the mass ##m## to an equivalent length. The Schwarzschild radius corresponding to ##m## is just twice that equivalent length.
 

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