Gravitational acceleration

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by tvanflandern</i>

If we use Einstein's reasoning and the most likely physical interpretation of his equations, <b>the acceleration for a stationary particle (unlike that for a lightwave) would remain Newtonian: GM/r^2.</b> -|Tom|-
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Hi Uncle Tom,

Do you mean that at distance R &lt;= Rs, no particle can escape from mass M, but light can ?

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by Cindy</i>
<br />Do you mean that at distance R &lt;= Rs, no particle can escape from mass M, but light can?<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">That depends on whom you ask. On this Message Board, the prevailing opinion is that light is a pure wave, not a particle. So it is governed by the law of optical refraction, not by gravitational force. However, the carrying medium for light, called "elysium", is affected by gravity and gets denser near masses. That makes the lightwaves bend, slow down, and get redshifted through the mechanism of refraction.

In this view, nothing special need happen at the critical radius. In the old view where light was a particle, the 18th century astronomer Mitchell was the first to predict a star that could emit no light. Hence, these are properly called "Mitchell stars". Wheeler invention in the 1950s, which he called "black holes", inverts space and time inside the hole and has other weird properties. This is what Einstein said was impossible in his theory, and what has been falsified by recent experiments with the speed of gravity. You can read more about these developments in the Cosmology/Gravity section of the web site this Message Board is maintained on. -|Tom|-

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by tvanflandern</i>
However, Einstein himself wrote a paper in 1939 proving that black holes were impossible in his theory, |Tom|-
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Hi Uncle Tom,

Would you please give me a link for the above statement ?

Thanks,

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by Cindy</i>
<br />Would you please give me a link for the above statement?<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">A. Einstein, "Annals of Mathematics", vol. 40, #4, pp. 922-936 (October 1939, written late in his career while he was at Princeton). This paper shows a respect for physical principles over mathematical reasoning by denying that singularities can occur in reality. He did not use the term "black hole" because that was invented by Wheeler a couple of decades later. Here are some relevant excerpts:

"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 &gt; 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|-

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by tvanflandern</i>
Use the equations of motion for GR. You can find these on p. 1095 of Misner, Thorne and Wheeler's book "Gravitation", among other places. Of course, as for most things in GR, this requires familiarity with advanced mathematics. -|Tom|-
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Hi Uncle Tom,

I don't think that I can derive the formula. However, if it is derived then it will be an approximate formula or an exact one ?

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by Cindy</i>
<br />I don't think that I can derive the formula. However, if it is derived then it will be an approximate formula or an exact one?<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">If you derived it yourself, you could make the approximation as accurate as you pleased, much like the formula for the sine function. However, if you simply take the formula in the reference I gave you, the approximate formula shown is more accurate than any existing observation. -|Tom|-