Colliding Black Holes Twist and Stretch Spacetime


In this striking image, optical light (from the Hubble Space Telescope) and X-ray data (from the Chandra X-ray Observatory) have been combined, highlighting the two supermassive black holes as they stare at each other across the chaos of disturbed stars, dust and hot gas in the center of NGC 6240 (NASA/CXC/MIT/STScI C.Canizares, M.Nowak)

How would you go about visualizing the violent mess in the wake of a black hole collision? As physicists are realizing, with great difficulty.

Understanding how spacetime will respond as two supermassive black holes collide has perplexed astrophysicists for some time. But with the help of some clever theoretical tools, a group of physicists, led by Robert Owen of Cornell University in Ithaca, New York, have found a nifty way of understanding how spacetime reacts under some of the most extreme forces in the cosmos.

In the process of understanding the nature of spacetime, the researchers may have already answered a baffling problem: how colliding supermassive black holes get their kick.

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Warped Spacetime

As a result of Einstein’s general relativity view of the universe, massive objects will cause the warping of spacetime.

The classic visualization of this would be to suspend balls of different masses on a rubber sheet — an analog for the “fabric of spacetime.” The heavier the ball, the greater the distortion (or “warping”) in the rubber sheet. This can be interpreted as the greater the distortion, the deeper the gravitational well in spacetime.


In the case of the Earth, for example, our planet’s mass creates a sloping gravitational “pocket” in spacetime. But for an extreme case, such as a black hole, the pocket’s sides will drop vertically forming a sheer “well” (in our rubber sheet analog, the ball representing the massive black hole will drop through the floor, stretching the rubber sheet til it ripped and crash through the ceiling of the apartment below).

At the point where the black hole’s well goes from “sloping” to “vertical”, anything that falls into this well cannot get out. This limit is known as the “event horizon,” the point at which even light cannot escape.

Now, to complicate matters even further, start spinning the black hole (as the majority of black holes are expected to do). What happens to spacetime then? Not only has it been warped to such an extreme that anything that strays too close is lost to oblivion, but the spinning action causes “creases” in spacetime. The creases will rotate with the black hole, a phenomenon known as “frame dragging.”

So we have extreme warping and frame dragging, how can these characteristics be visualized? How do they interact?

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Tendexes and Vortexes

At points within the warped spacetime, we can imagine a grid of arrows. Each arrow acts like a compass, but instead of pointing at a magnetic object, they are directed by the force of gravity. By linking these arrows, Owen’s team were able to construct a “map” with two different types of lines that represent the warping of spacetime.

One set of lines have been dubbed “tandex lines” and the other, “vortex lines.”

These are two spiral-shaped vortexes (yellow) of whirling space sticking out of a black hole, and the vortex lines (red curves) that form the vortexes (The Caltech/Cornell SXS Collaboration)

Tandex lines represent stretched (or compressed) spacetime — these lines would describe how the tidal forces exerted by a black hole stretch and rip apart any object that strays too close. The vortex lines describe the twisting effect of spacetime. So, as a black hole spins, dragging spacetime with it (frame dragging), the amount of twisting would be represented by vortex lines.

“Anything that falls into a vortex gets spun around and around,” Owen says in a CalTech press release.

This elegant solution to visualizing warped spacetime has already helped the researchers understand the mechanisms behind black hole collisions.

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When Galaxies Collide

The majority of galaxies are thought to have supermassive black holes living in their centers. Should two galaxies collide, a frequent event in cosmological time scales, the central black hole behemoths might merge.

As can be imagined, this scenario will generate a spacetime nightmare. But during black hole mergers, a rather perplexing phenomenon is predicted to occur; the recently merged black hole will often get kicked out of the galaxy and lost to intergalactic space.

And this isn’t just pure theory, such black holes have been detected careening, inexplicably, from their galactic homes.

So how does a supermassive black hole get “kicked”? These monsters are very hard to move, after all.

Owen and his colleagues have an answer. From the CalTech press release:

On one side of the black hole, the gravitational waves from the spiraling vortexes add together with the waves from the spiraling tendexes. On the other side, the vortex and tendex waves cancel each other out. The result is a burst of waves in one direction, causing the merged hole to recoil.
A graphic demonstrating the gravitational waves predicted to be generated after a black hole collision (W. Benger/Max Planck Inst.)

Gravitational Doughnuts

In another fascinating twist, this research also predicts that if two black holes collide head-on, expanding spacetime rings are produced. These rings are composed of vortexes as “doughnut-shaped regions of whirling space” and “tendexes as doughnut-shaped regions of stretching.” Should the black holes spiral inward before colliding, their vortexes and tendexes spiral out of the merged hole, like the ripples and eddies across the surface of a disturbed swimming pool.

These expanding doughnuts go on to generate gravitational waves, a phenomenon being hunted by gravitational wave detectors like the Laser Interferometer Gravitational-Wave Observatory (LIGO).

Naturally, before the tandex and vortex visualization tool can be accepted, other teams of astrophysicists will have to incorporate them into their theoretical models for a broad range of cosmological problems.

However, describing how merged supermassive black holes can be kicked around a galaxy is a very good start.

Source: EurekAlert

Publication: “Frame-Dragging Vortexes and Tidal Tendexes Attached to Colliding Black Holes: Visualizing the Curvature of Spacetime,” Owen et al., Physical Review Letters, 2011. DOI: 10.1103/PhysRevLett.106.151101

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