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Whether gravitational waves are real or just a coordinate freedom was argued in the early days of GR. Eventually the conclusion was that they were real. And if they are 'real' then I'm curious if...

Has it ever been shown that in General Relativity, two (or more) colliding gravitational waves can lead to a black hole?

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If you like this question you may also enjoy physics.stackexchange.com/q/3584/2451 –  Qmechanic May 3 '11 at 8:06
    
You may also be interested to know that the same is possible with photons, which is kind of ironic. –  user12345 Feb 8 '13 at 10:51
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2 Answers

It was not showed experimentally - the only experimental evidence of gravitational waves is that some binary pulsars change their orbiting frequency exactly as expected from their losing energy by gravitational waves of the GR-predicted intensity.

However, it is surely established theoretically. The answer is Yes, gravitational waves that carry enough energy and squeeze it to a small enough volume - essentially the volume of the Schwarzschild black hole whose radius $R = 2GM/c^2$ is calculated from the mass $M=E/c^2$ where $E$ is the energy carried by the waves (the numerical coefficient $2$ is not necessarily accurate) - inevitably collapse into a black hole. In fact, a collision of two particles with high enough energies is enough, too. The conjecture due to Thorne that the squeezing of the energy is enough is known as the hoop conjecture.

http://en.wikipedia.org/wiki/Hoop_conjecture

This fact can be numerically calculated by simulating general relativity on a computer. The process in which high-energy collisions of particles - not only gravitons - lead to the birth of black holes is also the dominant or universal scattering effect at huge, trans-Planckian energies (when the energy of a particle is comparable to the lightest black hole or higher).

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Can you give a link to a paper which shows using General Relativity that black holes can form from colliding gravitational waves? What issues were their in defining the energy and momentum of a gravitational wave, and does the formation of a blackhole help to provide an unambiguous energy and momentum to be assigned to the waves now? –  John May 3 '11 at 5:59
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Dear @John, read e.g. the first paragraph of introduction of this paper, arxiv.org/abs/1006.0718 - It refers to Thorne's conjecture and numerical tests by Choptuik and Pretorius; and other related papers. Second point: Total energies and momenta of objects including gravitational waves may be well-defined in GR and measured at infinity, as the ADM energy etc. The only problem is that one cannot canonically attribute the energy to individual regions of space via a density function. –  Luboš Motl May 3 '11 at 7:28
    
A more specific paper that deals with this in extreme detail is http://arxiv.org/abs/0805.3880. The introduction provides a history of the problem. More directly, there is a an entire book dedicated to exact solutions involving colliding plane waves: http://www-staff.lboro.ac.uk/~majbg/jbg/book.html. –  Stingray May 3 '11 at 7:57
    
Worth pointing out is that those black holes created by high energy particles colliding or by gravity waves being "squeezed together in a small enough space" are very small black holes with a microscopic Schwarzschild radius. They will instantly evaporate due to Hawkings Radiation before they get a realistic chance to "consume" anything in their neighborhood. –  IllvilJa May 3 '11 at 8:28
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+1--- good job of stating the obvious. –  Ron Maimon Aug 28 '11 at 20:46
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A couple of links, they could be useful:

On critical collapse of gravitational waves. Evgeny Sorkin. http://arxiv.org/abs/arXiv:1008.3319

Ultra Relativistic Particle Collisions Matthew W. Choptuik, Frans Pretorius http://arxiv.org/abs/arXiv:0908.1780

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