Schwarzschild radius calculation

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SUMMARY

The formula for calculating the Schwarzschild radius of a black hole is correctly stated as rs = 2GM / c². This equation applies specifically to a stationary mass, where M represents the system's rest mass. In cases involving arbitrary systems, M should account for the mass measured by considering the orbit of a distant body. The formula remains universally valid under conditions where gravitational effects are minimal, and the system's curvature is small.

PREREQUISITES
  • Understanding of general relativity concepts
  • Familiarity with gravitational physics
  • Knowledge of mass-energy equivalence
  • Basic calculus for manipulating equations
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  • Research the implications of the Schwarzschild radius in astrophysics
  • Study the effects of gravitational fields on time dilation
  • Explore the concept of invariant mass in relativistic systems
  • Learn about the role of energy in gravitational interactions
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Physicists, astrophysicists, and students studying general relativity and black hole physics will benefit from this discussion.

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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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