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Old Jun 17th 2013, 06:54 PM   #1
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Relativity Question?

Can someone explain to me why an acceleration object won't eventual become a black whole? As it gains more and more relativistic mass, shouldn't an object become smaller than its own Schwarzschild radius and make light unescapable? And as a side question, does light have its own gravity? It does have energy and (relativistic)mass(because it has energy).
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Old Jun 18th 2013, 05:26 AM   #2
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Originally Posted by muon321 View Post
Can someone explain to me why an acceleration object won't eventual become a black whole? As it gains more and more relativistic mass, shouldn't an object become smaller than its own Schwarzschild radius and make light unescapable? And as a side question, does light have its own gravity? It does have energy and (relativistic)mass(because it has energy).
There is a subtlety here: A particle has only one mass, the rest mass. All other energy for the (free) particle is given in reference to its momentum via the equation

where m is the rest mass of the particle, and p it's spatial momentum. Note: some authors use m_0 for the rest mass.

Please note that any particle can become a black hole under the right circumstances (very high density) so the question is better phrased in terms of the mass of the particle and its volume. In this case we run into the Fitzgerald contraction:

which means the faster the particle travels the more it gets "squashed into a pancake" in the direction of motion. The particle is "squashed" into a black hole when its volume is less than that of its Schwarzschild's radius. But this has nothing to do with the particle's acceleration.

For your other question anything that has energy has a gravitational field associated with it. But to be notable the particle has to have a Schwarzschild radius that we can actually measure and that isn't likely to happen for any object in the Solar System.

There is one situation that is a notable exception to all of this. So far as we know (with apologies to string theory and others) the elementary particles such as the electron, quarks, etc. have no volume and called "point particles." They have a mass and no volume so this qualifies them to be called "singularities," but for some reason not "black holes."

-Dan
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Last edited by topsquark; Jun 18th 2013 at 05:33 AM.
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