Abstract
Zwicky’s observation of the unexpectedly high velocities of the individual galaxies in the cluster of galaxies known as the ComaCluster led to the first appearance of the dark matter hypothesis. Unlike the organized motions in a nearly steady-state of the individual stars in a single spiral galaxy, the galaxies within a cluster are generally observed to move chaotically. Since we are not yet in a position to model such intrinsically time-dependent chaotic systems in General Relativity, we took the first step in the direction of dealing with time-dependence, again with an idealization. In what follows, we will describe our idealized model that brings into play intrinsic time-dependence. As a bonus, we are able to counter some of the criticism that had been levied against our earlier work.
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Notes
- 1.
We remind the reader of the technical language that we use in Relativity: “Stationary” in General Relativity does not necessarily mean “not moving”. It just means that there is no explicit time-dependence in the description of the motion. For example a disk that is perfectly axially symmetric and spinning at a constant rate about its symmetry axis, presents a totally time-independent picture to the observer. The distribution is moving but in terms of its density as a function of position, it is not varying in time. Such was the nature of our idealized model in the previous chapter. “Static” is the special case of “stationary” where the meaning is not only time-independent but also “not moving”.
- 2.
For observers positioned closer and closer to \(r=2m\), it becomes more and more difficult for them to remain at rest relative to the central body. They require greater and greater rocket thrust directed towards the central body to do so. At \(r=2m\), an infinite amount of thrust would be required, underlining the impossibility of doing so. This explains why, on the one hand, the local velocity of the falling particle is seen to be approaching the speed of light as \(r\) approaches \(2m\) yet there is no contradiction with the demand that non-zero rest-mass particles can never attain the speed of light.
- 3.
The Newtonian-based expression depends only upon the value of the amount of mass within the sphere beneath the observation radius and the observation radius itself.
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© 2012 Springer-Verlag Berlin Heidelberg
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Cooperstock, F.I., Tieu, S. (2012). The Motion of Galaxies in Galaxy Clusters. In: Einstein's Relativity. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30385-2_10
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DOI: https://doi.org/10.1007/978-3-642-30385-2_10
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