Can a beam of very focused gravitational wave collapse into a black hole as ordinary matter(particle or radiation) does?
Alternative question: can a black hole grow by absorbing gravitational wave as well as absorbing ordinary matter?
It has been puzzling me that whether gravitational wave is "real matter", since gravitational wave can possess energy and momentum, but it has no well defined stress tensor. That's how I came up with this question. If the answer is negative, that means gravitational wave still cannot be unified with matter, otherwise there may be a potencial theory to explain the energy and momentum of gravitational wave.
I have read the answers to a similar question. But I was concerned that the result of numerical calculation may be unreliable because of the error. I want a more rigorous proof. (I will check the articles later)
