Fields and Schwartzchild radius for a black hole

In summary, the Schwartzchild radius represents the distance from a black hole's singularity where the escape velocity equals the speed of light. To create a black hole with a radius of 1.0m for personal research, one would need to determine the necessary mass. The equation V^2 = (2GM)/r can be used, but the attempt to solve for mass using this equation was unsuccessful. The correct equation is V^2 = GMe/Re and solving for mass would require using the formula M = (V^2 * Re)/G.
  • #1
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Homework Statement


The Schwartzchild radius for a black hole is the distance from the singularity of the black hole at which the escape velocity is the speed of light. You wish to create a black hole, with radius of only 1.0m for personal research. How much mass would this required? Would the mass of the earth, 6.0 x 10^24 kg do the job?



Homework Equations


V^2 = GMe/Re

The Attempt at a Solution


I tried using the above equation to find the M, but that was not the right answer...
 
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  • #2
Your formula is incorrect, V2 = (2GM)/r.
 
  • #3
And then I solve for m?
 

Related to Fields and Schwartzchild radius for a black hole

1. What is a field in the context of a black hole?

In the context of a black hole, a field refers to the area surrounding the black hole where its gravitational pull is strong enough to significantly affect the movement of objects and particles. This field is known as the black hole's event horizon.

2. How does the Schwartzchild radius relate to a black hole's size?

The Schwartzchild radius, named after physicist Karl Schwartzchild, is the distance from the center of a black hole where its gravitational pull becomes so strong that not even light can escape. It is directly proportional to the mass of the black hole, meaning the larger the black hole's mass, the larger its Schwartzchild radius.

3. Can the Schwartzchild radius change?

No, the Schwartzchild radius is a constant value determined by the mass of the black hole. It does not change unless the mass of the black hole changes.

4. How is the Schwartzchild radius calculated?

The Schwartzchild radius can be 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. This formula was derived from Einstein's theory of general relativity.

5. What happens at the Schwartzchild radius?

At the Schwartzchild radius, the escape velocity (the speed an object needs to escape the gravitational pull of an object) becomes equal to the speed of light. This means that anything, including light, that crosses the Schwartzchild radius will be unable to escape, making it the point of no return for a black hole.

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