Is There a Mysterious Black Hole Constant?

[/caption]If you found yourself in the unfortunate situation of orbiting a black hole, you may be in for a rather dizzying and unpredictable ride. If the black hole is spinning, it will flatten out under centrifugal forces, much like the Earth bulges slightly at the equator, but the black hole’s bulge will be radically greater. As the shape of the black hole changes, so does its gravitational profile.

As you are not orbiting a spherical black hole, you can no longer expect to have a boring, predictable orbit; your orbit will become wild and chaotic, seemingly random. However, it would appear that there is an underlying constant to the mayhem, and what’s more, it seems this constant has also been observed in a more pedestrian system: a three-body Newtonian system. So what’s the link? Physicists aren’t quite sure…

When a massive star exhausts its fuel, it may collapse in on itself to create a black hole (after some exciting supernova action). The angular momentum of the original star is expected to be preserved, producing a rapidly spinning black hole. If the black hole “has no hair” (i.e. it has no electrical charge), the gravitational field solely depends on its mass and spin. If there is deformation due to the spin, the gravitational field changes, sending any orbiting body (like a neutron star) on a crazy roller-coaster ride.

In a new paper by Clifford Will of Washington University in St. Louis, the excited physicist describes the scenario. “The orbits go wild — they gyrate and spin, they’re incredibly complex. It’s fantastic,” Will says.

However, physicist Brandon Carter discovered a mathematical constant back in 1968, showing these apparently chaotic orbits are predictable, and that it even applies to orbits around extremely warped space-time. “Black holes have this extra constant that restores the regularity of the orbits,” comments Saul Teukolsky of Cornell University. “It’s a mystery. Every other situation where we have these extra constants, we have symmetry. But there’s no symmetry for an orbiting black hole — that’s why it is regarded as a miracle.”

Quite simply, physicists have no idea why the Carter constant could arise from the General Relativity description of a spinning black hole. Now, to make the problem even more perplexing, Will carried out a classical (Newtonian) 2-body simulation with a third body orbiting. Again, the same constant appeared. It would appear that there is something special about the predictability of an orbit around this black hole configuration.

Teukolsky, who worked on similar problems for his Ph.D. in 1970, remains baffled by these results. However, Will continues to investigate the problem, by including a term for black hole frame dragging. In this situation, the spinning black hole will drag space-time around it, “creases” (or ripples) in space time being pulled with the direction of spin. In this case, the Carter constant disappears, only to return when higher order terms are added to the equations.

This all means one of two things. Either it is simply an artefact in the mathematics, a curiosity that will eventually be rooted out of the equations. However, there is a tantalising possibility that we are seeing a characteristic of exotic rotating black holes, where the configuration of the surrounding fabric of space-time can allow a predictable orbit to come out of the apparent chaos…

Source: Science News

Here’s an article about black body radiation.