Schwarzschild radius calculation

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Discussion Overview

The discussion revolves around the formula for calculating the Schwarzschild radius of a black hole, specifically examining its correctness and applicability in different contexts. Participants explore theoretical aspects and implications of the formula.

Discussion Character

  • Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant presents the formula for the Schwarzschild radius as rs = 2GM / c² and seeks confirmation of its correctness.
  • Several participants affirm that the formula is correct.
  • Another participant notes that the mass M in the formula refers to a system's rest mass, suggesting that the equation is precise only for stationary masses.
  • A different viewpoint suggests that for an arbitrary system, M should be the mass measured by considering the orbit of a distant body, indicating that the formula holds true universally under certain conditions.
  • This viewpoint further elaborates that for systems where bodies are far apart and curvature is small, the mass considered is approximately the invariant mass of the system, which includes kinetic energy in the center of mass frame.

Areas of Agreement / Disagreement

While there is agreement on the correctness of the formula, there are differing views on the interpretation of the mass M and its implications for different systems, indicating that the discussion remains somewhat contested.

Contextual Notes

Participants highlight limitations regarding the applicability of the formula to stationary masses and the conditions under which it can be considered universally true, including the effects of gravitational interactions and energy considerations.

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Is this the proper formula for calculating the Schwarzschild radius of a black hole?
rs = 2GM / c2
If it is not, or if anyone has one that might work better, could you refer it to me?
 
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That's correct.
 
Banker said:
That's correct.
Thank you!
 
I'd just add that in Physics now days, M is a systems' rest mass while gravitational effects depend on the total energy. So, the equation is precise only for a stationary mass, I believe.
 
For an arbitrary system, the M would be the mass measured by considering the orbit of a distant body of known mass. In this sense, the formula is universally true. For a system of bodies still far enough apart so curvature is small (and pressure and EM fields are insignificant), it is approximately the SR invariant mass of the system - which will include the KE of the bodies in the overall COM frame.
 

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