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Visualizing Warped Spacetime

What on Earth — or off it — could inspire a physicist with the credentials of Caltech’s Kip Thorne to say “I’ve never before coauthored a paper where essentially everything is new. But that’s the case here.” Yet if Thorne couldn’t say that about some of his earlier work with wormholes (!), he feels safe in saying it about the new tools for visualizing warped space and time that are discussed in a paper he and his colleagues have just published. Imagine space and time undulating in hitherto unfathomable patterns as objects like black holes run into each other.

How do we visualize such effects in a credible way? The new tools help us do just that. They are the result of powerful computer simulations that bring to visual life the complex equations of black hole mergers and other extreme events, and they should help us with problems like this one: Manuela Campanelli (University of Texas in Brownsville) and team used simulations a few years ago to show that colliding black holes produce a direct burst of gravitational waves. The result is that the black hole itself seems to recoil, with a force strong enough that the newly merged object can be thrown entirely out of its own galaxy. When this work was done in 2007, nobody could explain how a directional burst of gravitational waves could be produced.

Thorne’s team can now produce an explanation by working with spacetime analogues to the electric and magnetic field lines that describe those two forces. A tendex line describes the stretching force that warped spacetime exerts, while a vortex line describes the twisting of space. Run enough tendex lines together and you create a region — a tendex — of strong stretching. Merge a bundle of vortex lines and the result is a whirling region of space — a vortex.

Image: Two doughnut-shaped vortexes ejected by a pulsating black hole. Also shown at the center are two red and two blue vortex lines attached to the hole, which will be ejected as a third doughnut-shaped vortex in the next pulsation. Credit: The Caltech/Cornell SXS Collaboration.

Let me quote the Caltech news release on the result:

Using these tools, [the researchers] have discovered that black-hole collisions can produce vortex lines that form a doughnut-shaped pattern, flying away from the merged black hole like smoke rings. The researchers also found that these bundles of vortex lines—called vortexes—can spiral out of the black hole like water from a rotating sprinkler.

The computer tools now show how these distortions of spacetime are produced, and can explain things as complex as the black hole collisions and ejection discussed by Campanelli. So what does account for that gravitational kick experienced by the merged black hole at galactic center? The unidirectional force comes from gravitational waves from spiraling vortexes added together with waves from spiraling tendexes, while on the other side, the vortex and tendex waves are canceled out. The newly merged black hole experiences a recoil. The new conceptual tools are useful not just for a black hole scenario, but a wide range of possibilities:

“Though we’ve developed these tools for black-hole collisions, they can be applied wherever space-time is warped,” says Dr. Geoffrey Lovelace, a member of the team from Cornell. “For instance, I expect that people will apply vortex and tendex lines to cosmology, to black holes ripping stars apart, and to the singularities that live inside black holes. They’ll become standard tools throughout general relativity.”

Various black hole merger situations suggest themselves, including two spinning black holes colliding head on or spiraling toward each other before the merger. Each of these scenarios can be explained through the use of tendexes and vortices, but it’s also important to note that in either case, outward-moving vortexes and tendexes become gravitational waves. Usefully, that’s just the kind of waves that the Laser Interferometer Gravitational Wave Observatory (LIGO) has been created to detect. LIGO, which began its search in 2002, looks for gravitational wave emissions from collisions of neutron stars or black holes as well as supernovae. Tendexes and vortexes may help researchers predict the waveforms LIGO is looking for.

The paper is Owen et al., “Frame-dragging vortexes and tidal tendexes attached to colliding black holes: Visualizing the curvature of spacetime,” Physical Review Letters 106, 151101 (2011). Abstract / Preprint.

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Comments on this entry are closed.

  • Mike Lockmoore April 13, 2011, 14:29

    “The newly merged black hole experiences a recoil. ” Did the authors suggest possible applications for _propulsion_? A “unidirectional force” would come in handy for a spaceship. Just saying. :-)

  • Matt April 13, 2011, 15:12

    So.. I’m curious if this could this be related to the anomalous red-shift quasar thing studied by Chip Arp. Is that way off? What effect would a vortex have on passing light? (Sorry for the wild speculation, I was watching a pop-science docu-drama last night about Chip Arp)

  • Christopher Bennett April 13, 2011, 16:55

    Shouldn’t the plurals be “vortices” and “tendices,” to be strict about it?

    I’m curious about the applications of these mathematical tools to wormholes, Alcubierre warps, and the like. Maybe there’s a way to figure out how to combine vortex and tendex lines in the right configurations to produce expansions and compressions of spacetime, maybe get some kind of local antigravity effect by cancelling waves, things like that.

  • Paul Gilster April 13, 2011, 17:56

    Christopher Bennett writes:

    Shouldn’t the plurals be “vortices” and “tendices,” to be strict about it?

    Agreed, but the paper uses the other formulation. Grates on me as well.

  • Paul Gilster April 13, 2011, 17:57

    Mike Lockmore writes:

    “The newly merged black hole experiences a recoil. ” Did the authors suggest possible applications for _propulsion_? A “unidirectional force” would come in handy for a spaceship. Just saying. :-)

    Hey, I’m always happy to look for propulsion applications. But first we’d have to harness two black holes and then run them together, a daunting prospect!

  • Roger April 13, 2011, 18:52

    The article talks about computer tools that show how distortions of spacetime are produced. I have always thought particles to be knots in spacetime, with magnetic and electric fields being the effects these knots have on the spacetime around them. Knots would also pull spacetime inward, producing gravity. I wonder if these tools could be used to probe the small scale? Probably need to include quantum effects in their models.

  • Chris April 13, 2011, 20:15

    @Paul:

    At the very least, could computer models be used to simulate what using black holes for propulsion would be like? Using black holes isn’t happening any time soon, barring a MAJOR breakthrough, but using computer models … it seems feasible enough to see what it theoretically would be like.

  • Malcolm Ramsay April 14, 2011, 5:55

    Following up on what both Christopher Bennet and Chris said above, now that we have these new tools, could we work them backwards? Could we set up the vortex and tendex structures for desired results (e.g. unidirectional thrust, “warp drive”, etc.) and then derive methods for creating them? Y’never know, we might be lucky…

    Yours,
    not-Chris

  • Malcolm Ramsay April 14, 2011, 9:03

    And now that I think of it, Paul- re. your comment about having “to harness two black holes and then run them together, a daunting prospect!”; what about these micro-holes that the LHC was supposed to be creating? Could they be collided so as to create a similar thrust and, if so, what would be the magnitude of that thrust?

    Imagine a drive like that, a particle accelerator optimised for the generation of colossal numbers of charged micro-holes that are coupled to the ship electromagnetically so that the recoil when they’re collided drives the ship forward without reaction mass being ejected! We could even scoop interstellar material while en-route- a Gravity Ramjet…

  • Paul Gilster April 14, 2011, 9:53

    Malcolm Ramsay writes:

    Imagine a drive like that, a particle accelerator optimised for the generation of colossal numbers of charged micro-holes that are coupled to the ship electromagnetically so that the recoil when they’re collided drives the ship forward without reaction mass being ejected! We could even scoop interstellar material while en-route- a Gravity Ramjet…

    I like this! It would be interesting to model such interactions, and we’re clearly developing the computer tools to do so. Fascinating notion.

  • Mark Presco April 14, 2011, 12:03

    The subject of the LHC creating micro black holes that Malcolm Ramsey brought up concerns me. I read a sci-fi novel that related how the accidental creation of a miniature black hole gobbled up earth as it oscillated through its center. This is just one of many ways hi-tech cultures can destroy themselves.

    As much as I like reading about future propulsion systems on this site, my priority vis-à-vis space, is to establish an off world colony as soon as possible. Stephen Hawking is right, the survival of the human race depends upon this.

    I would go so far as to expand the mission of the ISP to be the first habitat for the first zero-g pioneers.

  • Mark Presco April 14, 2011, 12:17

    Sorry, I meant the ISS. I would also like to expand the mission of the International Space Station to be a space port for a fleet of shuttles designed to operate throughout the solar system.

  • Tom Baty April 14, 2011, 14:06

    Not to mince words, but I find this discussion and this article very interesting. One comment that got my attention was that this is an analogue to magnetic and electrical fields. It makes me wonder if this vortex and tendex concept could be applied to the collision of two electromagnetic fields at a much reduced level. If so you may not need two black holes, just wondering. I am not an expert in this field, just a facinated observer. I could be all wet, if so please tell me LOL !!!!

    Tom

  • Rob Henry April 14, 2011, 18:54

    Given that general relativity has to obey the laws of momentum these gravitons ejected in the opposite direction must be unbelievably powerful, so much so that wouldn’t they behave like particles? Would they have interesting new behaviours that could be more easily detected than by conventional gravitational wave detectors?

  • Eniac April 15, 2011, 8:43

    My guess is that the waves that are ejected are powerful in the same sense a tsunami is. Out at sea, you can barely detect one when floating on it, its power lies in its huge extent.

    As for the reaction-less drive, this is easy. Photons are also massless, and a flashlight constitutes a reaction-less drive. The thing about such drives, though, is that useful ones require enormous power, and gravitational waves would not have any advantages over light in this respect.