Schwarzschild radius calculation

In summary, the formula for calculating the Schwarzschild radius of a black hole is rs = 2GM / c2, where M is the rest mass of the system. However, for an arbitrary system, M would be the mass measured by considering the orbit of a distant body of known mass. This formula is approximately true for systems with bodies far enough apart where curvature, pressure, and electromagnetic fields are insignificant.
  • #1
verschrankung
11
2
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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  • #2
That's correct.
 
  • #3
Banker said:
That's correct.
Thank you!
 
  • #4
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.
 
  • #5
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.
 

Related to Schwarzschild radius calculation

What is the Schwarzschild radius?

The Schwarzschild radius is a theoretical concept in physics, named after the German astronomer Karl Schwarzschild. It is the radius at which the gravitational pull of a black hole becomes so strong that nothing, including light, can escape from it.

How is the Schwarzschild radius calculated?

The Schwarzschild radius is calculated using the formula Rs = 2GM/c2, where G is the gravitational constant, M is the mass of the black hole, and c is the speed of light. This formula is derived from Einstein's theory of general relativity.

What units are used to measure the Schwarzschild radius?

The Schwarzschild radius is typically measured in units of length, such as meters or kilometers. However, it can also be expressed in terms of the mass of the black hole, using the formula Rs = 2GM/c2, where G and c are constants and M is the mass of the black hole in kilograms.

Can the Schwarzschild radius be calculated for objects other than black holes?

Yes, the Schwarzschild radius can be calculated for any object with a mass. However, it is only significant for objects with extremely large masses, such as black holes. For example, the Schwarzschild radius of the Earth is only about 9 millimeters, whereas the Schwarzschild radius of a black hole with the mass of the Sun is about 3 kilometers.

What is the significance of the Schwarzschild radius?

The Schwarzschild radius is significant because it marks the boundary of a black hole, known as the event horizon. It is the point at which the escape velocity exceeds the speed of light, making it impossible for anything, including light, to escape from the black hole.

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