Exploring the Wave of Death in Spacetime

[robousy]

According to:

http://en.wikipedia.org/wiki/Pp-wave_spacetime

"the wave of death is a gravitational plane wave exhibiting a strong nonscalar null curvature singularity, which propagates through an initially flat spacetime, progressively destroying the universe"


I did a spires search for k wave and k death but found nothing.

Has anyone heard of this?

 

[Garth]

No - but it sounds scary!

Garth

 

[Chris Hillman]

Does gtr predict that we might all be about to become pasta?

Not to worry, this is just an amusing name for any plane wave (one of a class of exact solutions in gtr) with a (null nonscalar) curvature singularity which is strong enough to be destructive.

The point is that the nonscalar null curvature singularities occurring in similar plane wave solutions are apparently not "destructive" (according to gtr) because, if you will, the divergence of the curvature components (wrt the frame field of a given observer, often an inertial nonspinning observer, whose frame field is as close as we can come in gtr to a Lorentz frame in the sense of str) happens so quickly that the observer's body doesn't have time to be stretched dangerously before the crisis is over. This point was made in a nice paper by G. F. R. Ellis and B. G. Schmidt, "Classification of Singular Space-Times", Gen. Rel. Grav. 10, 12 (1979): 989-997, using a particularly simple plane wave to illustrate their point. Indeed, in the example I am about to give, the curvature components measured by observers I will specify diverge as one approaches the singularity, but the metric components remain bounded (while nonetheless crushing any inhabitants of the model universe and in fact marginally sphaghettifying them).

Many decades ago, Roger Penrose speculated about "thunderbolts", which are more like axisymmetric pp-waves which propagate a destructive null nonscalar curvature singularity along a specific narrow direction. Some wag, apparently in mockery of certain paranoid "fringe physicists", promptly raised the spectre of presumed vulnerability of Earthlings to any spacelings that might happen along (presumbly far more advanced technogically, somewhat independently of when this hypothetical encounter might happen--- or so goes the "theory"), and suggested that waves of death could be useful deterrent weapons even against arbitrarily advanced adversaries.

This actually comes back to the point I made earlier today in another thread: what constitutes a "prediction of gtr"? One can easily write down perfectly valid exact vacuum solutions (Petrov type N, in fact gravitational plane waves in the sense of Baldwin and Jeffery) which answer to the description of a "wave of death". Here is an example--- anyone who knows how to compute the Einstein tensor of a Lorentzian spacetime can easily verify that this is an exact vacuum solution--- written in a Rosen chart:
$ds^2 = -dt^2 + dz^2 + J_0(\exp(t-z))^2 \, \left( \exp(-2 \, \exp(t-z)) \, dx^2 + \exp(2\, \exp(t-z)) \,dy^2 \right),$
$-\infty < t-z < c, \; \; -\infty < x, \, y < \infty$
for a certain positive real constant c. Here, the frame field
$\vec{e}_0 = \partial_t,\; \; \vec{e}_1 = \partial_z, \; \; \vec{e}_2 = \frac{\exp (\exp(t-z))}{J_0(\exp(t-z))} \, \partial_x, \; \; \vec{e}_3 = \frac{\exp (-\exp(t-z))}{J_0(\exp(t-z))} \, \partial_y$
turns out to define an inertial nonspinning frame field which we can use to compute the physical experience of a certain class of observers. We can verbally summarize the results as follows: initially these observers believe that they are comoving inertial observers in flat spacetime. Bye and bye they begin to notice relative accelerations and tidal stresses on their bodies which increase very suddenly, resulting in sudden and destructive sphaghettification. Since the wave moves at the speed of light, inhabitants of the universe have almost no warning that anything is amiss until they are already being drawn and diced. Even if they had more warning, they cannot escape because the planar wavefronts are infinite planes which sweep up everything in their path; every world line in this model universe ends by striking the curvature singularity.

Does that mean that gtr "predicts" that the universe could end without warning by turning all the stars into pasta? Only in a very naive sense. The tip-off that this alarming solution is intended as an in-joke is that strictly planar wave fronts would be infinite in extent and thus would carry infinite energy! And of course, we might reasonably doubt whether any physical process can create a wave carrying an infinite amount of energy.

In fact, Yurtsever has carefully argued that more realistic models of gravitational waves, which are merely approximately planar wavefronts (as we would expect since every gravitational wave should emerge from some compact region, so that the wavefronts are at best approximately planar, within some box far from the source), develop singularities which are significantly milder than those developed by many strictly plane waves.

Still, this and similar examples have pedalogical value. (Scaring the students is a time honored public school trick--- helps to keep them alert!)

Oh, just one other thing: "thunderbolts" are apparently not subject to the objection I just outlined. One can write down axisymmetric pp-waves featuring similarly destructive null nonscalar curvature singularities which are good approximations to thunderbolts, and which therefore strongly suggest that if one can get a thunderbolt started, it would indeed destroy spacetime itself all along some direction (giving almost no warning to its victims). I should add that Penrose has pointed out that EVERY Lorentzian spacetime is approximately locally isometric to a plane wave in the neighborhod of ANY null geodesic (keyword "Penrose limit"), which is another reason for confidence that if one can create a thunderbolt, it will have the desired effect.

Chris Hillman

P.S. I can't resist adding that some years ago I received a reply to a polite inquiry on a related subject from the author of a well known book on "catastrophe theory". Examination of the bookmark showed, to my surprise, that it had been posted in a place called Pyongyang. True story.

 

[selfAdjoint]

P.S. I can't resist adding that some years ago I received a reply to a polite inquiry on a related subject from the author of a well known book on "catastrophe theory". Examination of the bookmark showed, to my surprise, that it had been posted in a place called Pyongyang. True story.

Now THAT'a scary! Does Bush know? On second thought, let's be careful not to tell him!

 

[Chris Hillman]

Now we know the REAL reason why LIGO was funded

Yes, while I confess that on one level I find the prospect of an arms race seeking to militarize gravitational radiation highly entertaining, since this is probably the most ineffecient proposal for a "death ray" I can imagine, it probably would not be in the best interests of the populations of the nations involved. But heck, when has that ever stopped national leaders who enjoy creating new problems more than they enjoy solving old ones? If we can have star wars, why not gwave wars?

Chris Hillman

 

[pervect]

It's totally off-topic, but in one of Baxter's science fiction series, there is a war going on between civilizations based on dark matter vs civilizations based on normal manner. They fight with gravity-based weapons.

 

[Chris Hillman]

Are we getting OT yet?

Hi, pervect,

I wish to avoid both politics and psychoceramics in this forum, but perhaps I might be permitted the comment that sometimes fantasists can make as much money writing for the Pentagon as for Hollywood. As it were. On one level, this can be highly entertaining for anyone seeking fresh confirmation of the principle that people generally act like idiots. On another, given the billions which are squandered in such fashion, often out of sight of public scrutiny, it can sometimes be a bit depressing, given the fact that serious problems are not addressed due to alleged "lack of resources".

Chris Hillman

 

[Ich]

It's totally off-topic, but in one of Baxter's science fiction series, there is a war going on between civilizations based on dark matter vs civilizations based on normal manner. They fight with gravity-based weapons.

...and lose. Maybe because they could not get sufficient funding for the basic research on those weapons.