Post by: jeffreyH on 19/03/2015 01:16:16
http://en.wikipedia.org/wiki/Kerr_metric
Of interest is the first set of equations in the mathematical form section. This is a complicated equation but can be viewed in a simpler manner. We can view the spacetime around the black hole like a set of Russian dolls made up of concentric spheres moving away from the event horizon. This description does not account for the flattened sphere that describes the ergosphere. These distortions of the spacetime can be derived from this initial view.
The Russian doll model can however be used to show how the spacetime rotates at the surface of each successive sphere and why this would result in frame dragging and co-rotation of objects within the ergosphere. This can be thought of as a curl in the gravitational field.
Post by: jeffreyH on 19/03/2015 01:29:41
In the case of the Kerr black hole the poles should be completely outside the influence of the ergosphere. While the gravitational influence is still extreme at the poles, objects are not locked into the ergosphere. Hence the freedom of relativistic jets to escape at the poles.
Post by: jeffreyH on 19/03/2015 01:44:31
Details of normal vectors can be found here:
http://mathworld.wolfram.com/NormalVector.html
This deviation towards the equator describes the type and extent of the ergosphere and why co-rotation occurs.
EDIT: Because of this field profile objects moving past a black hole with relativistic rotation can never be said to be moving perpendicular to the field. This also appears to suggest that the direction of approach determines whether or not an object will be consumed by the black hole.
Post by: jeffreyH on 20/03/2015 20:32:50
Polar coordinates:
http://nrich.maths.org/2755
And spherical coordinates:
http://mathinsight.org/spherical_coordinates
Reviewing the Kerr metric in light of this information then can give clues as to exactly what is going on.
http://en.wikipedia.org/wiki/Kerr_metric#Mathematical_form (http://en.wikipedia.org/wiki/Kerr_metric#Mathematical_form)
Post by: jeffreyH on 21/03/2015 15:17:51
Since the momentum p = Mv and since c is also a velocity Mc is an upper limit on momentum. Therefore J/(Mc) is a proportionality of the angular momentum of the mass to its upper limit.
Post by: jeffreyH on 21/03/2015 15:51:36
is the spin coefficient.
Post by: jeffreyH on 21/03/2015 16:38:21
http://en.wikipedia.org/wiki/Introduction_to_angular_momentum
Post by: jeffreyH on 02/05/2015 14:39:16
and has the speed of light and the proper time in the product. Proper time needs to be understood to see what the metric expresses.http://en.wikipedia.org/wiki/Proper_time (http://en.wikipedia.org/wiki/Proper_time)
Post by: jeffreyH on 02/05/2015 17:34:50
http://en.wikipedia.org/wiki/Coordinate_time (http://en.wikipedia.org/wiki/Coordinate_time)
Post by: Colin2B on 10/05/2015 22:12:22
Post by: jeffreyH on 11/05/2015 18:27:17
Is this only applicable to black hole theory or are there other applications?
This deals with extreme conditions. In what we may term 'normal' spacetime the differences are often very small. You could look at neutron stars in a similar way although without the event horizon. I am in the process of reading Galaxy Formation Second Edition by Professor Malcolm Longair. It isn't only gravity that needs to be considered. His book discusses the COBE and WMAP data and the early history of astrophysics and cosmology. I would need to read the section on relativistic gravity before I can answer your question.
Post by: Colin2B on 11/05/2015 18:58:20
I would need to read the section on relativistic gravity before I can answer your question.Thanks, I ask because noted PmbPhy in another thread talking about eigenvalues which I have used in vibration analysis. As the great man said, it's all connected.
Post by: jeffreyH on 11/05/2015 19:34:38
I would need to read the section on relativistic gravity before I can answer your question.Thanks, I ask because noted PmbPhy in another thread talking about eigenvalues which I have used in vibration analysis. As the great man said, it's all connected.
I'll let you know when I've waded through Galaxy Formation.
Post by: jeffreyH on 12/05/2015 13:48:17
I would need to read the section on relativistic gravity before I can answer your question.Thanks, I ask because noted PmbPhy in another thread talking about eigenvalues which I have used in vibration analysis. As the great man said, it's all connected.
I have something to add here but will need to copy the relevant section from Galaxy Formation.
Post by: jeffreyH on 12/05/2015 19:06:40
"A key step in the development of these models was introduced by Hermann Weyl in 1923 of what is known as Weyl's postulate (Weyl, 1923). To eliminate the arbitrariness in the choice of coordinate frames, Weyl introduced the idea that, in the words of Hermann Bondi (Bondi, 1960):
'The particles of the substratum (representing the nebulae) lie in space-time on a bundle of geodesics diverging from a point in the (finite or infinite) past.'
The most important aspect of this statement is the postulate that the geodesics, which represent the world lines of galaxies, do not intersect, except at a singular point in the finite, or infinite past. Again, it is remarkable that Weyl introduced this postulate before Hubble's discovery of the recession of the nebulae. By the term 'substratum' Bondi meant an imaginary medium which can be thought of as a fluid which defines the overall kinematics of the system of galaxies. A consequence of Weyl's postulate is that there is only one geodesic passing through each point in space-time, except at the origin. Once this postulate is adopted, it becomes possible to assign a notional observer to each world line and these are known as fundamental observers. Each fundamental observer carries a standard clock and time measured on that clock from the singular point is called cosmic time.
One further assumption is needed before we can derive the framework for the standard models. This is the assumption known as the cosmological principle and it can be stated:
'We are not located at any special location in the universe.'"
Colin, this is also a situation in which proper against coordinate time can be applied. However the starting point is the big bang and there are still huge gaps in knowledge about this. What does strike me is that the voids between galaxies should have vastly different coordinate time.
Post by: jeffreyH on 08/11/2015 23:24:46
. Comparing this with the Kerr metric shows just how simplified the Schwarzschild solution is.