Schwarzschild radius of an object is smaller than Planck length

In summary, the conversation discusses the possibility of producing black holes in particle accelerators, based on the calculation of Schwarzschild Radius. It is stated that particles inside the LHC have smaller radii than the plank length, making it impossible for a black hole to form. The concept of relativistic mass and its relevance to general relativity is also mentioned, with the conclusion that it does not affect the calculation of Schwarzschild radius. The conversation ends with the statement that a unified theory that works with both small distances and strong gravitational fields is still being sought after.
  • #1
ColdheartedGod
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I had this idea when some people said that LHC can produce black hole. Based on the calculation of Schwarzschild Radius, any mass than 9.375×10^7 kg have a Schwarzschild radius smaller than the plank length. Particles inside LHC or other particle accelerator have clearly radii smaller than that.
what will happen to the black hole with smaller radius than the smallest measurable length?
On the other hand, mass moving at a high speed will undergo an increase of apparent mass, will that be counted as its actual mass when calculating the Schwarzschild radius in the case of particle accelerator?
 
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  • #2
ColdheartedGod said:
On the other hand, mass moving at a high speed will undergo an increase of apparent mass, will that be counted as its actual mass when calculating the Schwarzschild radius in the case of particle accelerator?

This question gets asked a lot. The simple answer is "no". Relativistic mass has no relevance to GR.
 
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  • #3
ColdheartedGod said:
what will happen to the black hole with smaller radius than the smallest measurable length?
No one knows.

We have a theory (general relativity) which tells us what happens with intense gravitational fields as long as the distances involved aren't too small. We have a theory (quantum mechanics) which tells us what happens at very small distances as long as the gravitational fields aren’t too strong. We’re still looking for a a unified theory that works with both very small distances and very strong gravitational fields.
On the other hand, mass moving at a high speed will undergo an increase of apparent mass, will that be counted as its actual mass when calculating the Schwarzschild radius in the case of particle accelerator?
No.
(This idea that mass increases with speed is very easily misunderstood; in fact it’s one of those things that you have to unlearn if you want to seriously understand relativity. We have many threads and an Insights article if you want to learn more about why).
 
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1. What is the Schwarzschild radius of an object?

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 equals the speed of light.

2. How is the Schwarzschild radius calculated?

The Schwarzschild radius is calculated using the mass of the object and the gravitational constant. The formula is Rs = 2GM/c^2, where Rs is the Schwarzschild radius, G is the gravitational constant, M is the mass of the object, and c is the speed of light.

3. What is the significance of the Schwarzschild radius being smaller than the Planck length?

The Planck length is the smallest possible length in the universe, and the Schwarzschild radius being smaller than this length indicates that the object is incredibly dense and has a strong gravitational pull. It also suggests that the object may be a black hole.

4. Can an object's Schwarzschild radius be smaller than its own size?

No, an object's Schwarzschild radius cannot be smaller than its own size. If the object's mass were compressed to a point where its Schwarzschild radius was smaller than its own size, it would collapse into a singularity, creating a black hole.

5. What are the implications of an object having a Schwarzschild radius smaller than the Planck length?

The implications of an object having a Schwarzschild radius smaller than the Planck length are still being studied and debated by scientists. Some theories suggest that it could lead to the breakdown of our current understanding of physics, while others propose that it could open up new possibilities for understanding the universe.

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