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

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Discussion Overview

The discussion revolves around the equation M=Gm/c^2, exploring its derivation and its relationship to Newton's law at infinity. Participants inquire about the meaning of M and the implications of this equation in the context of the Schwarzschild metric, touching on theoretical aspects of general relativity and black hole physics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Some participants seek clarification on the meaning of M in the equation M=Gm/c^2 and its connection to Newton's law at infinity.
  • One participant asserts that M represents the mass of the black hole when using units where G and c are both equal to one, suggesting this simplifies the equations involved.
  • Another participant mentions that the equation serves as a conversion factor from mass units to length units, indicating that Gm/c^2 converts mass m to an equivalent length.
  • There is a request for sources or derivations related to the equation, with a specific mention of the derivation of the Schwarzschild radius.

Areas of Agreement / Disagreement

Participants express curiosity about the equation and its implications, but there is no consensus on the derivation or the specific interpretations of M and its relationship to Newton's law at infinity. Multiple viewpoints and questions remain unresolved.

Contextual Notes

Limitations include the lack of detailed derivations for the equation M=Gm/c^2 and the Schwarzschild radius, as well as the dependence on specific unit systems that may not be universally applicable.

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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