Energy Requirements for Compressing Matter into a Black Hole

In summary, the amount of energy needed to compress a coffee mug into a black hole would be enough to overcome neutron degeneracy pressure and would require a certain amount of work. This amount of energy would also be needed to compress a smaller object, such as an atom, into a black hole. However, the problem of fermions in a box makes it difficult to compute the exact energy needed due to the small size of the box and non-Euclidean geometry. Assuming adiabatic compression, the energy required would be roughly equal to G/c^2 multiplied by the Schwarzschild radius.
  • #1
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How much energy would it be necessary for me to compress my coffee mug into a black hole? Would i need less energy for an object with a fraction of the size of my coffee mug? How much energy would i need to collapse a single atom into a black hole, or is that not possible, and is a lot of matter a requirement?
 
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With no math ability, this is just a rough guess. A coffee cup would have to be compressed to somewhere around the size of an electron to become a black hole. I don't think that you could find a set of pliers small enough.
 
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How much energy would it be necessary for me to compress my coffee mug into a black hole? Would i need less energy for an object with a fraction of the size of my coffee mug? How much energy would i need to collapse a single atom into a black hole, or is that not possible, and is a lot of matter a requirement?

A simpler way to think about it would be to think in terms of the force required, which would be enough force to overcome neutron degeneracy pressure. To apply that force from all directions, through a distance that would essentially compress the mug to a point would require a certain amount of work, a la
[tex]
W = \int \vec{F} \cdot d\vec{r}
[/tex]
That is roughly the amount of energy needed(I say roughly because I somewhat simplified the problem).
 
  • #4
I tried to take a stab at this, but I'm not sure how to solve the problem of a relativistic particle in a box.

For all of the different realms (white dwars star matter, neutron degenerate matter), the key problem in computing the energy is that of fermions in a box.

The box here is going to be very small, G/c^2 is 7.42471382 × 10-28 m / kg
and the Schwarzschild radius is r=2(G/c^2) M.

I suppose that this isn't quite right due to the non-euclidean geometry inside the "box", but it would be a first stab.

It wasn't specified, but I would assume that we'd assume that the compression was adiabatic.
 

1. What happens when a coffee mug falls into a black hole?

When a coffee mug falls into a black hole, it will be stretched and distorted by the intense gravitational pull. As it gets closer to the event horizon (the point of no return), it will experience tidal forces that will tear it apart into smaller pieces. These pieces will continue to be pulled towards the singularity (the center of the black hole) and eventually be crushed into a single point of infinite density.

2. Will the coffee mug ever reach the singularity?

No, the coffee mug (or any object) will never actually reach the singularity. As it gets closer and closer to the singularity, time will slow down and eventually come to a complete stop. This is known as gravitational time dilation. From the perspective of an outside observer, it will appear as though the coffee mug is frozen in time at the event horizon.

3. Can we see the coffee mug falling into the black hole?

No, we would not be able to see the coffee mug falling into the black hole. The intense gravitational pull of the black hole would bend light in such a way that it would appear as though the coffee mug is frozen at the event horizon. This phenomenon is known as gravitational lensing.

4. What happens to the coffee inside the mug as it falls into the black hole?

The coffee inside the mug would experience the same fate as the mug. It would be stretched and distorted by the gravitational forces and eventually be crushed into the singularity. However, due to the difference in density between the coffee and the mug, the coffee would likely be torn apart and spread out before reaching the singularity.

5. Can a black hole be created by a coffee mug?

No, a black hole cannot be created by a coffee mug. In order for a black hole to form, a massive amount of matter needs to be compressed into a small enough space to overcome its own gravitational pull. A coffee mug does not have nearly enough mass to create a black hole.

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