Relativity and Cosmology

Nice work! My question: Is there such things as non-rotating black holes? With all the angular momentum of the accretion disc, how much of this gets transferred into the black hole, and does the black hole retain the angular momentum of the original collapsing star?

Hi Cardio07.

My guess is that all black holes have some rotation, although some may be rotating slowly enough to make them approximately non-rotating. The final supernova explosions that creates black holes are not guaranteed to be symmetrical and that may remove some of the angular momentum of the original star.

The orbits around spinning black holes are horrendously complex and I'm taking it one step at a time. My next 'project' may be rotating black holes, but not until I understand the scenario of the non-rotating ones, if ever...

Jorrie

Another factor influencing the spin of the individual binary neutron stars is tidal gravity, which tends to lock the spin to the orbital period over time. Whether this is true for binary black holes, I'm not sure of.

Jorrie

In my quest to understand black holes better, I came across this excellent paper by Jenna Levin et. al: http://arxiv.org/abs/0802.0459 (Jenna is the author of the popular "How the universe got its spots").

They show that there exist analytical solutions to certain complex, but closed orbits around black holes, even rotating ones and even in the strong (near-) field regime. This is very promising and it gives me a tool for checking my own analysis against some reference.

Here are two of the more interesting cases that the paper discusses, plotted from my program, for a static, non-rotating hole (still working on rotating ones):

This 'four leaf clover' orbit repeats itself indefinitely, provided that nothing disturbs it, of course. Each 'leaf' consists of two 'twirls' around the hole plus a 'zoom' to the apastron point and back.

Give the particle just a tiny amount of extra energy and the pattern starts to precess in the direction of the orbit, giving this stunning picture:

Cool! It looks very 3-dimensional, but it's just an optical illusion - the orbit stays on one flat plane...

Jorrie

Hello, everyone,

Jorrie, are you saying that the actual particles orbit is two dimensional at the distance stated from the black hole, or am I confusing the road map for the territory?

/Ari (Orpheuse)

Hi Ari.

All four 'leafs' are traced by the complex path of a single particle orbiting the black hole in one plane only. My x and y coordinates are chosen so that we look perpendicularly onto that plane, i.e., the orbit never veers off into the z-direction.

The fact that you 'see' 3-d in the picture is an optical illusion caused by the patterns. It is as if you look at a colorful map of a perfectly flat surface, where the apparent relief is just an optical illusion.

This planar behaviour of orbits only holds for orbits of an isolated particle around an isolated, non-rotating,^* spherically symmetrical massive object, like a Schwarzschild black hole.

Jorrie

* It is also true for equatorial orbits around a spinning spherically symmetrical massive object.