Merging Black Holes Pt. 2: Ripples in Spacetime

The above Youtube video shows a merging event generating gravitational waves. Now, this video shows two merging white dwarfs, but two merging black holes will do the same thing - only on a much larger scale. It seems crazy to think that this sort of event happens in the universe, but is currently invisible to us. However, in the coming years, that should change.

Gravitational waves are a hot topic in modern astrophysics. They are analogous to most waves, such as water waves or electromagnetic waves (light), except that they are ripples on the background curvature of spacetime itself.

So, what's the big deal with gravitational waves, aside from the fact that they're a cool physics buzzword?

Well, the most exciting prospect of gravitational waves is their potential in the study of different astrophysical phenomena. For most of astronomy, electromagnetic radiation has been the sole source of probing the universe (or, photons for short... it's amazing what we can learn from light rays). Electromagnetic radiation comes from the superposition of (mostly) randomly oriented photons being emitted or absorbed from electrons, atoms, or molecules. Gravitational waves, on the other hand, are generated most strongly from large bulk motions of mass. And, even more incredibly, gravitational waves are not dampened by intervening matter. As a result, the detection of gravitational waves should open an entirely new area of astrophysics previously unseen.  Perhaps, like the advent of infrared and radio astronomy, gravitational wave astronomy will usher in a new era of unprecedented scientific discovery and advancement.

Interferometers like the Laser Interferometer Space Antenna (LISA) and the Laser Interferometer Gravitational-Wave Observatory (LIGO) are currently the most promising ways to detect gravitational waves. Simply put, like most interferometers, a laser is shot at a beamsplitter, which splits the laser beam into two directions (usually perpendicular to each other). These beams hit mirrors, and are then reflected back to a detector, where they are recombined. *Note: I have simplified the process quite dramatically - I have never been very good with instrumentation, so I'm not going to try to go into any specifics.*

(Is it bad that I can't ever say laser without thinking of Dr. Evil's "laser")?

Very simple interferometer design, except for gravitational wave detectors, the movable mirror would not be moved by anything other than gravitational waves. The screen has a great example of what fringe patterns look like.

Since gravitational waves are ripples in the fabric of spacetime itself, a gravitational wave passing through a point in space causes the gravitational field to increase or decrease in magnitude. As a result, if a gravitational wave hits one of the mirrors, the oscillation in gravitational strength should shift the mirror back and forth. This causes the path length for one of the mirrors to deviate from the original value, so that when the beams are later recombined at the detector, the observed fringe patterns should change in accordance with the mirror oscillations. These fringe patterns can then be used to deduce the strength of the passing gravitational wave.

Gravitational wave schematic. The top portion shows the three phases of coalescence: the quasi-circular inspiral phase, the plunge and merger, and the ringdown. The bottom portion shows the amplitude of the emitted gravitational waves that correspond to the above merger process. (Image credit: Baumgarte and Shapiro 2011).

Black hole mergers, incidentally, are especially interesting in the study of gravitational waves. This is because gravitational waves are theorized to carry away most of the angular momentum and energy from these systems, which causes the merging black holes to coalesce. The above figure (that I scanned, sorry for the poor quality, ha ha!) shows a schematic of the phases of a black hole merger, and how those phases relate to gravitational wave strength. The top portion shows a cartoon of the merger, including the early quasi-circular inspiral phase, the plunge and merger phase, and the final ringdown stage. The bottom part shows the wave amplitude (or, strength) versus time. For two black holes approaching each other in the early inspiral phase, the emission of gravitational radiation causes the orbits to circularize and decay. Gravitational waves at this point will be at relatively low levels. But during the late inspiral phase, when the binary is in tight, circular orbits, and during the actual merger, gravitational waves should be at their strongest. This is where LIGO and LISA will be able to detect gravitational waves.

Unfortunately, even though the very early and late stages of coalescence has been simulated fairly easily, the actual late inspiral and merging phases are not as simple. For that part of the merger, post-Newtonian and perturbation methods break down. Therefore, providing templates for the signatures of merging black holes requires advancements in numerical relativity, which will push computational techniques to their limits. 

For more info, please see:
Abramovici, A. et. al 1992, Science, Vol. 256, pp. 325-333
Baumgarte, T. W. & Shapiro, S. L. 2011, Physics Today, Vol. 64 No. 10, pp. 32-3
Berti, E., Cardoso, V. & Will, C. M. 2006, Phys. Rev., 73, 6