Professionally researched relativistic orbits

[jgraber]

If CarlB (or anyone else) wants to compare his recent results to the relativistic orbits used to make predictions for black hole inspirals by the people who work on LIGO, LISA, VIRGO, TAMA, GEO etc., they are readily available on the web at Living Reviews in Relativity:
http://relativity.livingreviews.org/Articles/
See particularly sections 9.3-9.5 of Blanchet's review lrr-2006-4,
and section 5 of Sasaki and Tagoshi's lrr-2003-6.
I think a graphical visualization of these orbits would be of interest to a number of people, including me.
Believe it or not, these orbits are still being continually refined.
There is a regular annual meeting of the real pros, called the “Capra” meetings after the first one, which was held at Caltech's Capra ranch. This year it is at the University of Alabama, Huntsville from June 25-29.
Best to all,
Jim Graber

 

[Chris Hillman]

Correction

No. Typical numerical simulation of black hole mergers involves a much more difficult problem--- the two body problem--- than the problem of studying the motion of particles or laser pulses ("photons") in an exact vacuum solution modeling the exterior field of an isolated compact object, of which the Schwarzschild vacuum is the simplest case--- which merely involves studying in detail a particular soluton to the one-body problem. The distinction is simple: in studies of binary mergers one is generally studying objects of comparable mass.

It is true that there are interesting papers studying infall of a stellar mass object such as, well, a star, into a supermassive black hole, in which one wishes to approximate the tidal distortion of the small object, without trying to tackle the two-body problem in all its glory, so there are intermediate cases between these extremes.

Needless to say, no exact solutions are known which model the two body problem (if one eliminates certain solutions which are too artificial to be of interest to astrophysicists trying to model astronomical objects in Nature).

There are interesting and challenging theoretical problems which really do involve test particle motion. See the review paper by Poisson http://relativity.livingreviews.org/Articles/lrr-2004-6/index.html

ZapperZ locked Carl's thread for reasons he stated, but I did say in that thread that visualizations of Schwarzschild or Kerr are indeed of great interest to many because of the unusual importance of these particular solutions. This includes visualizations of test particle or "photon" motion. However, it is important to understand that the geodesic equations of the Kerr vacuum have been well understood for a very long time. In particular, the solution of the geodesic equations for the Kerr-Newman electrovacuum (thus, for the Kerr vacuum and it's subcase, the Schwarzschild vacuum) has been known since about 1975. See Chandrasekhar, Mathematical Theory of Black Holes. The point is that, as I already told Carl several times, it is to these sources that he must turn in order to check his results.

 

[Stingray]

There are interesting and challenging theoretical problems which really do involve test particle motion. See the review paper by Poisson http://relativity.livingreviews.org/Articles/lrr-2004-6/index.html

Just a slight correction, but Poisson's review is not about test bodies. The lowest-order self-interactions are taken into account. So it's in the intermediate category you've mentioned.

The post-Newtonian results referenced by jgraber actually fail in the extreme mass ratio regime. They work great with binaries of comparable mass, however. The method does break down before the objects can collide, but it still works very well. Some people have had a rather remarkable amount of patience in deriving the PN equations.

 

[pervect]

The interested student doesn't have to go nearly so far to find tools to calculate the orbits of test particles in a Schwarzschild metric. For instance, MTW, "Gravitation", chpater 25.

Note the difference here: the papers presented by jgrabbger calculate something considerably more complex than the textbooks do.

Note that you can't use the more complex calculations above to "check" the textbook results, or vica-versa. They calculate different things. The more complex calculations should of course match better to observations of the physical world.

Students interested in the difference between the orbits of actual planets in the solar system and the orbits of test masses should check out, for example, MTW $40.9, "Do the planets and sun move on geodesics" pg 1126 for a general idea of what approximations are being made in the simple textbook treatment.

Since this thread has a lot of potential to degenerate into a discussion that would re-open a locked thread, I think these pointers to the literature for interested students should be sufficient, and I'm going to close it now.