To really get gravity, we need to look at gravity in its most extreme forms. A powerful enough gravitational field should send out waves powerful enough to be observed here on Earth. But gravity in those kind of concentrations is hard to come by. Gravitational waves, like sound waves, lose strength over increasing distances.
For the required extremes, we look toward events like galaxy collisions and systems of orbiting neutron stars. For the gnarliest distortions of space-time, however, there are black holes, cosmic entities that rip through space-time itself.
It's an event so extreme that coming up with good solvable equations for it is a deep challenge, yet a group of physicists at Cornell University recently claimed to have devised calculations for describing the gravitational lensing effects of a black hole binary system for the first time: black holes ripping each other apart.
The problem with calculating a black hole is that its guts always contain a singularity. This is a point where gravity and its effects become infinite, and infinity is not an easy quantity to deal with mathematically. How can we hope to bridge the dynamic range between infinite space-time curvature and the ever so slight waves that might actually reach Earth? We can at least start with some cool images.
The Cornell researchers aren't offering some new full-on answer so much as a new visualization (the first, they argue) of how light would behave around a binary black hole system. What would a nearby observer actually see as a pair of black holes orbit, spiral inward, and finally merge? As expected, the result is awesome.
"This is in contrast to most [binary black hole] visualizations, in which the positions or horizons of the two black holes are simply shown as a function of time in some coordinate system," the physicists write. "We instead compute the paths of light rays that enter the observer's eye or camera to find what would actually be seen."
To simulate the impossible, which would be charting the courses of an uncountable number of photons traveling around a black hole binary, the Cornell group overlaid a colored grid pattern against a horizon line populated by the two colliding black holes. Then, rather than imagine individual photons traveling at the observer from the system, the simulation imagines the photons traveling toward the horizon, a sort of mirror image or reversal of real life.
"A naıve approach would be to trace all possible light rays emanating from the light source to determine which rays reach the camera and from what directions they arrive, but this is computationally infeasible," the Cornell team explains. "A more efficient approach is to reverse the problem by tracing light rays away from the camera and backwards in time."
In computer graphics, this is called ray casting. Basically, imagine a stream of photons pouring out of your eye or camera toward some scene. Each photon eventually hits something and is partially absorbed and partially reflected according to some given properties about the material and the environment. This collision is assigned some corresponding value (a color, in this case).
The point is that by firing simulated photons from the eye or lens toward the scene, we're not wasting any computations on photons that wouldn't even make it back to the lens or would be otherwise obscured.
In addition to generating a bunch of awesome images, the Cornell team did reach at least one deep conclusion: binary systems look an awful lot like just single black holes. "On large scales the lensing from inspiraling binaries resembles that of single black holes," they write, "but on small scales the resulting images show complex and in some cases self-similar structure across different angular scales."