Gravitational Length Contraction

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SUMMARY

The discussion centers on the concept of gravitational length contraction, particularly in relation to the Schwarzschild metric. Participants explore whether gravitational length contraction exists and how it may be derived from the Schwarzschild solution. The conversation highlights the anisotropic nature of light speed in Schwarzschild coordinates and suggests that gravitational length contraction could be defined analogously to time dilation, although its significance appears coordinate-dependent. The lack of formal discussion in textbooks or papers on this topic is noted, indicating a gap in the literature.

PREREQUISITES
  • Understanding of Special Relativity (SR)
  • Familiarity with the Schwarzschild metric
  • Knowledge of time dilation in gravitational fields
  • Basic grasp of coordinate systems in physics
NEXT STEPS
  • Research the implications of the Schwarzschild solution on gravitational phenomena
  • Study the relationship between proper distance and coordinate changes in general relativity
  • Examine existing literature on anisotropic light speed in gravitational fields
  • Explore the concept of spacetime warping in the presence of mass
USEFUL FOR

Physicists, students of general relativity, and anyone interested in the nuances of gravitational effects on spacetime and light propagation.

nigelscott
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I understand the concepts of time dilation and length contraction in SR. I also understand the concept of time dilation in a gravitational field. But what about length contraction in a gravitational field? Is there such a thing and can it be derived from the Schwarzschild metric?
 
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I believe that in the Schwarzschild solution expressed in Schwarzschild coordinates the speed of light is anisotropic and that in order to explain this a "gravitational length contraction" in the radial direction is sometimes thought of.
 
A lot of lay people seem to think that gravitational length contraction should exist for reasons that are unclear, but I don't think I've ever seen a textbook or paper discussing the concept specifically. (It's possible I could have missed a paper on the topic, of course.)

Going from analogy with time dilation, though, I'd guess one could define it as the ratio between proper distance and changes in coordinates.

The value of this ratio will be dependent on the coordinates used of course, just as in the case of time dilation. So I don't see any coordinate-independent significance to the term.
 

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