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Is it theoretically possible to create a superposition of gravitational waves that form a locally static negative curvature, something like the dark energy?

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  • $\begingroup$ Why do you think dark energy causes negative curvature? $\endgroup$
    – G. Smith
    Commented Jun 17, 2019 at 15:31
  • $\begingroup$ @G.Smith Well, I assume that would generate the repulsive gravity. But any way, I'm just curious. $\endgroup$
    – Hulkster
    Commented Jun 17, 2019 at 15:44

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Superposition of gravitational waves if averaged over the regions larger than the typical wavelength would produce an effective stress-energy tensor that would serve as a matter source in the Einstein field equations. But this stress-energy tensor will have the same properties as stress-energy of any other type of incoherent radiation: the pressures would be positive, in the isotropic case the equation of state would be $p=\frac13 \rho$ (in relativistic units). Dark energy (if it exists) would have negative pressures with the equation of state $p=-\rho$ (in the simplest case, other models of dark energy are also considered). So, gravitational waves could not be contributing to the accelerating expansion of the universe, the main observational evidence of dark energy.

On the other hand it is possible to confine a large number of gravitational waves within a small region of space trapping them by their own gravity, thus forming an approximately static object, a geon. Here is a description taken from this paper of one such geon solution, constructed by Brill & Hartle:

Brill and Hartle [1], BH, developed a very useful method for finding approximate solutions to Einstein’s equations that correspond to high frequency gravitational waves propagating in a background geometry, which is created by the average stress-energy of the waves themselves. In their paper they applied this method to the case of a static spherically symmetric background geometry and found that gravitational waves can remain confined in a region for a time much longer than the region’s light-crossing time. This so-called gravitational geon is generated by a large number of high frequency, small amplitude gravitational waves. The time average of the curvature due to these waves creates the background geometry of the geon, and this background geometry traps the waves for a long time in a region of space called the “active” region. The BH solution is important because it serves as an example in which the gravitational field both creates and responds to its own effective stress-energy. It is also an example of a nontrivial (approximate) solution to the vacuum Einstein equations that has no curvature singularities.

As we can see, such geons are not truly static, with enough time gravitational waves would escape and the geon would dissolve.

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  • $\begingroup$ Thanks for answering. $\endgroup$
    – Hulkster
    Commented Jun 18, 2019 at 7:11
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I’m Yess that’s very close to understanding, that regular matter when it’s in its einstate or in collapsed probability wave function form and what we cannot observe as an observer with only 5 senses and three dimensions. The probability wave collapse with a telescope will most likely receive wave clipping in some form due to the small path of collapses waves. I believe if we make the biggest telescope EVER IN SPACE then we could see a lot more of probably what we already see space is infinite not in the way of our comparison and it’s also expanding faster than we can keep up with it so even if there’s something on the other side we will probably never know it may be a secret like what gravity really is. And, maybe we really shouldnt find out and maybe we are a construct of some other being or entities consciousness. Maybe we’re a machine simulation like the matrix it’s almost a reality or could be not everyone wants peace which slows science in science we have no enemies we’re all observers following the rules and trying to understand itself then there’s that thing u don’t want me to say n I’m going to tell u when your feeling down n out you remember every particle in your body that makes you u was created inside a star Soo long ago so tap into the knowledge passed down n give into your curiosity hard love you all! -jt

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