Non-rotating or rotating Metric

In summary, the Milky Way Galaxy is rotating and is not spherically symmetric, making neither the Schwarzschild nor Kerr Metric suitable for modeling it. Instead, a rotating, asymmetric dust solution using numerical relativity is required. However, for practical purposes, Newtonian gravity with PPN corrections can be used to model galaxy evolution. A recent rotating metric, the boundary value problems for the stationary axisymmetric Einstein equations, has been developed and can be used to model a disk rotating around a black hole. However, it may be more suitable as an ideal model for a black hole with an accretion disk rather than a galaxy due to the lack of perfect symmetry in real systems. Investigations into gravitational wave produced black hole-stellar interactions often use
  • #1
Philosophaie
462
0
Is the Milky Way Galaxy non-rotating or rotating?

Which metric is best suited: Schwarzschild or the Kerr Metric, respectively?
 
Physics news on Phys.org
  • #2
The galaxy is rotating, but it is not spherically symmetric so neither Kerr nor Schwarzschild is good.
 
  • #3
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.
 
  • #4
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.
 
Last edited:
  • #5
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

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.
 
  • #6
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.
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 ?
 
  • #7
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 ?

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
 
  • #8
PAllen said:
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.
 

1. What is the difference between non-rotating and rotating metrics?

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.

2. How are non-rotating and rotating metrics used in physics?

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.

3. What is an example of a non-rotating metric?

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.

4. What is an example of a rotating metric?

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.

5. How do non-rotating and rotating metrics affect the behavior of particles?

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.

Similar threads

  • Special and General Relativity
Replies
5
Views
1K
  • Special and General Relativity
Replies
8
Views
912
  • Special and General Relativity
Replies
19
Views
1K
  • Special and General Relativity
2
Replies
43
Views
2K
  • Special and General Relativity
Replies
1
Views
684
  • Special and General Relativity
Replies
3
Views
700
  • Special and General Relativity
Replies
1
Views
916
  • Special and General Relativity
Replies
6
Views
1K
  • Special and General Relativity
Replies
4
Views
907
  • Special and General Relativity
Replies
8
Views
2K
Back
Top