Find the mass of a black hole from just its radius?

In summary, when trying to find the mass of a black hole with only knowledge of its radius, the Schwartzschild radius formula ##r_s=\frac{2Gm}{c^2}## can be rearranged to isolate the mass and find the answer. Other suggested equations, such as ##2GR/c^2## and ##R^2c^2/2G##, are not correct. A helpful calculator can also be used for this calculation.
  • #1
Lamdbaenergy
35
1
I know the original schwarzschild formula for finding the radius of the black hole, but what equation can be used to find its mass if you ONLY know its radius?
 
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  • #2
Can't you use the same formula? Only instead of using mass to find the Schwartzschild radius, use the Schwartzschild radius to find the mass.
 
  • #3
Bandersnatch said:
Can't you use the same formula? Only instead of using mass to find the Schwartzschild radius, use the Schwartzschild radius to find the mass.

Nope, got nowhere near the right mass. I tried for a solar mass black hole, too. Any other suggestions?
 
  • #4
Can you show what you did exactly?
 
  • #5
Bandersnatch said:
Can you show what you did exactly?

2GR/c^2, then I tried R^2c^2/2G
 
  • #6
Neither of those is correct. Start with the Schwartzschild radius formula ##r_s=\frac{2Gm}{c^2}## and isolate the mass on one side.
 
  • #7

1. How can you determine the mass of a black hole from just its radius?

The mass of a black hole can be calculated using the Schwarzschild radius and the speed of light. The formula is M = rS(c^2)/2G, where M is the mass, rS is the Schwarzschild radius, c is the speed of light, and G is the gravitational constant.

2. What is the Schwarzschild radius?

The Schwarzschild radius is a measure of the size of the event horizon of a black hole. It is the distance from the center of the black hole at which the escape velocity exceeds the speed of light. It is calculated using the formula rS = 2GM/c^2, where G is the gravitational constant, M is the mass of the black hole, and c is the speed of light.

3. Can the mass of a black hole be directly measured?

No, the mass of a black hole cannot be directly measured. This is because the intense gravitational pull of a black hole prevents any light or matter from escaping, making it impossible to observe or measure its mass directly. Instead, scientists use indirect methods, such as measuring its effect on surrounding matter or using gravitational lensing, to estimate the mass of a black hole.

4. How accurate are the calculations for determining the mass of a black hole from its radius?

The calculations for determining the mass of a black hole from its radius are based on the theory of general relativity and have been extensively tested and confirmed through observations. However, there may be some uncertainties and limitations in the measurements and calculations, especially for extremely massive or rapidly spinning black holes.

5. Can the mass of a black hole change over time?

Yes, the mass of a black hole can change over time. A black hole can grow in mass by consuming surrounding matter, such as stars or gas, through its strong gravitational pull. It can also lose mass through a process called Hawking radiation, where it emits particles and energy due to quantum effects near the event horizon.

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