Schwarzschild radius calculation

AI Thread Summary
The formula for calculating the Schwarzschild radius of a black hole is correctly stated as rs = 2GM / c². However, it is noted that this equation applies specifically to stationary masses, as gravitational effects are influenced by the total energy of a system. For arbitrary systems, the mass (M) should be determined by considering the orbit of a distant body with known mass. In cases where bodies are sufficiently far apart, the formula can be approximated using the special relativity invariant mass, which accounts for the kinetic energy of the system. Overall, the formula is universally applicable under certain conditions.
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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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