Abstract. We solve a class of boundary value problems for the stationary ax-
isymmetric Einstein equations corresponding to a disk of dust rotating uniformly
around a central black hole. The solutions are given explicitly in terms of theta
functions on a family of hyperelliptic Riemann surfaces of genus 4. In the absence
of a disk, they reduce to the Kerr black hole. In the absence of a black hole, they
reduce to the Neugebauer-Meinel disk.
Mentz114 said:There are lots of rotating dust solutions in GR. But as PAllen has said it is good enough to use Newtonian gravity with PPN corrections to model galaxy evolution.
The most recent rotating metric is probably here arXiv:1003.1453v1,
BOUNDARY VALUE PROBLEMS FOR THE STATIONARY AXISYMMETRIC EINSTEIN EQUATIONS: A DISK ROTATING AROUND A BLACK HOLE
JONATAN LENELLS
Yes, it's a shame that so many commonplace physical scenarios are difficult ( or imposible ?) to model with GR. Is there a book on numerical relativity you can recommend ?PAllen said:That's cool, thanks! Maybe better as highly ideal model of a BH with accretion disk rather than a galaxy. Maybe not even that: by definition, an accretion disk is not stationary (BH is growing), and no real system has perfect symmetry. Thus, investigations into GW produced BH-stellar interactions where the start gets eaten (with lots of matter ejected as well), all use numeric relativity.
Mentz114 said:Yes, it's a shame that so many commonplace physical scenarios are difficult ( or imposible ?) to model with GR. Is there a book on numerical relativity you can recommend ?
I've had a quick look and it does look interesting. Thank you.PAllen said:No, but the following website links to a whole series of papers describing their methods:
www.black-holes.org
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Non-rotating metrics refer to a coordinate system in which the space-time is stationary and does not change with time. On the other hand, rotating metrics refer to a coordinate system that is rotating and has a time-dependent space-time structure.
Non-rotating metrics are commonly used in the study of static objects, such as planets and stars, where the space-time is not changing with time. Rotating metrics, on the other hand, are used to describe objects that are in motion, such as black holes or galaxies.
An example of a non-rotating metric is the Schwarzschild metric, which describes the space-time around a non-rotating spherical mass, such as a star or planet.
An example of a rotating metric is the Kerr metric, which describes the space-time around a rotating black hole. This metric takes into account the effects of the black hole's spin on the structure of space-time.
The type of metric used can have a significant impact on the behavior of particles. For example, in a non-rotating metric, particles move along geodesics, which are the shortest paths in curved space-time. In a rotating metric, however, the rotation of space-time can cause particles to experience frame-dragging, which can alter their trajectories.