<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by Rudolf</i>
<br />Tom, a few responses back you mentioned that Einstein wrote a paper why he thinks black holes are impossible. Can the contents be found somewhere (on the Internet) or do you know which points he made to explain his objections?<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">The paper is [A. Einstein, "Annals of Mathematics", vol. 40, #4, pp. 922-936 (October 1939], written late in his career while he was at Princeton), and shows Einstein's respect for physical principles over mathematical reasoning. The following excerpts give the broad flavor of the paper ("r = m/2" refers to the event horizon):
"If one considers Schwarzschild's solution of the static gravitational field of spherical symmetry ..., [g_44] vanishes for r = m/2. This means that a clock kept at this place would go at rate zero. Further it is easy to show that both light rays and material particles take an infinitely long time (measured in 'coordinate time') in order to reach the point r = m/2 when originating from a point r > m/2. In this sense the sphere r = m/2 constitutes a place where the field is singular.
"There arises the question whether it is possible to build up a field containing such singularities with the help of actual gravitating masses, or whether such regions with vanishing g_44 do not exist in cases which have physical reality. ... [brief discussion of uncompressible liquids omitted]
"One is thus led to ask whether matter cannot be introduced in such a way that questionable assumptions are excluded from the very beginning. In fact this can be done by choosing, as the field-producing mass, a great number of small gravitating particles which move freely under the influence of the field produced by all of them together. This is a system resembling a spherical star cluster. ... The result of the following consideration will be that it is impossible to make g_44 zero anywhere, and that the total gravitating mass which may be produced by distributing particles within a given radius, always remains below a certain bound. [core of analysis omitted; skipping to conclusions]
"The essential result of this investigation is a clear understanding as to why the 'Schwarzschild singularities' do not exist in physical reality. ... The 'Schwarzschild singularity' does not appear for the reason that matter cannot be concentrated arbitrarily. And this is due to the fact that otherwise the constituting particles would reach the velocity of light.
"This investigation arose out of discussions [with Robertson and Bargmann] on the mathematical and physical significance of the Schwarzschild singularity. The problem quite naturally leads to the question, answered by this paper in the negative, as to whether physical models are capable of exhibiting such a singularity." [End of Einstein quote]
-|Tom|-
Topic Author
