Question about fast moving objects

[Omicron91]

This may be a very ridiculous question but I thought of something curious in physics class today and came upon a bizarre idea. If an object decreases in size and increases in mass when it reachs towards the speed of light then could an object not eventually drop below it's own schwartschild radius and form a singularirty or do the laws of general/special relativity not apply in this fashion?

[bjmyanks]

. If an object decreases in size and increases in mass QUOTE]

Aren't they one in the same?

[Omicron91]

. If an object decreases in size and increases in mass QUOTE]

Aren't they one in the same?

 

No, due to Lorentz contraction it's length decreases and because of the exceptional amount of energy it's carrying it's mass increases, while, unrelatedly, it moves through time at a different rate.

[bjmyanks]

O man thats crazy. What type of physics are you learning?

[Omicron91]

O man thats crazy. What type of physics are you learning?

 

Grade 12U physics? I mean, I'm pretty sure what I'm saying is accurate and my physics teacher agreed that what I was saying was hypothetically possible but he couldn't verify anything.

[timo]

The only definition of a black hole that I´d know of is that a black hole is a certain spacetime structure. The strucutre of spacetime is absolute. It might look differently depending from your point of view but it is always the same object. So if the object you were talking about does not form a black hole in its frame of rest, the spacetime structure it creates will not be a black hole. This will be true in any coordiante system (frame of reference), then.

 

The sloppy, incomplete but possibly more satisfying answer would be something like: The Scharzschild Radius gets length-contracted, too.

[swansont]

In addition to what Athiest said, the length contraction occurs in the observer frame, not the rest frame. How can the formation of a black hole depend on whether someone is moving?

 

The relevant mass is the rest mass, which is invariant. The changing mass is called relativistic mass, which comes form a (IMO) sloppy application of relativity, because the person wants to use E = mc², but not want to get into the actual equation, which is E² = m²c⁴ + p²c². m in the latter equation is the rest mass. It reduces to the former only when the object is in its rest frame, which precludes the notion of mass being speed-dependent.

[□h=-16πT]

No, the formula for the Schwarzschild radius involves rest mass. Gravitation is frame invariant, if you speed up your field doesn't increase, relativistic mass isn't real.

[gagsrcool]

Hi,

 

I thought schwarzchild radius is the formula for the radius of a blackhole!

What do you mean by the schwarzchild radius of a person???

 

gagsrcool

[Omicron91]

Okay, I understand now, that was essentially what I was asking was whether or not relativisitic mass counted in this question. Thanks!

 

P.S. - Schwartschild radius is for calculating the diameter that something of a certain mass that something would have to be to become a black hole.

[□h=-16πT]

If you want to be accurate about these things, it's for a spherically symmetric static body. For rotating and non-symmetric bodies you have to use different equations. For a rotating, charged, axially symmetric body, there are two "horizons": the ergosphere and an event horizon similar to that of a Schwarzschild black hole.