Non-rotating or rotating Metric

[Philosophaie]

Is the Milky Way Galaxy non-rotating or rotating?

Which metric is best suited: Schwarzschild or the Kerr Metric, respectively?

 

[Dale]

The galaxy is rotating, but it is not spherically symmetric so neither Kerr nor Schwarzschild is good.

 

[PAllen]

It is also matter dominated (matter is spread throughout, rather than vacuum plus center you can treat as 'black box'). Thus, a rotating, asymmetric dust solution would be required. This requires numerical relativity. Of course, it is adequate, in practice, to use Newtonian gravity with PPN corrections in the galactic center to model galaxy evolution.

 

[Mentz114]

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

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.

 

[PAllen]

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

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]

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.

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]

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 ?

No, but the following website links to a whole series of papers describing their methods:

www.black-holes.org

see specifically:

http://www.black-holes.org/numrel1.html
http://www.black-holes.org/numrel2.html // 3,4 etc.
http://www.black-holes.org/SpEC.html
http://www.black-holes.org/researchers3.html
http://www.black-holes.org/researchers1.html

 

[Mentz114]

No, but the following website links to a whole series of papers describing their methods:

www.black-holes.org
..
..
..

I've had a quick look and it does look interesting. Thank you.