Schwarzschild radius of an object is smaller than Planck length

[ColdheartedGod]

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?

 

[PeroK]

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.

 

[Nugatory]

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).

 

[anorlunda]

Here are some earlier PF threads on the same topic. In all of them, the answer is still "no". But the second thread goes into great detail.

https://www.physicsforums.com/threa...-by-particle-accelerators.971819/post-6183495
https://www.physicsforums.com/threads/black-holes-squishing-earth.956706/#post-6066773