Speed of light vertical and horizontal in gravity

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SUMMARY

The speed of light in a gravitational field varies between vertical and horizontal orientations, as predicted by the Schwarzschild solution. The vertical speed of light is defined as c = cof, while the horizontal speed is c = coSQRT(f), where f = 1 - 2GM/rc². This indicates that the vertical speed is consistently less than the horizontal speed due to the nature of f being less than 1. The discussion confirms that the measurable speed of light remains independent of direction when assessed locally, despite the differences in coordinate speed.

PREREQUISITES
  • Understanding of the Schwarzschild solution in general relativity
  • Familiarity with gravitational fields and their effects on light
  • Basic knowledge of coordinate speed versus measurable speed
  • Concept of local versus coordinate measurements in physics
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  • Research the implications of the Schwarzschild solution on light propagation
  • Explore experimental setups to test the predictions of light speed variations in gravity
  • Study the concept of coordinate speed in general relativity
  • Investigate the effects of gravitational fields on other forms of electromagnetic radiation
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Physicists, astrophysicists, and students of general relativity interested in the behavior of light in gravitational fields.

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The speed of light in a gravitational field is predicted to vary between the horizontal and the vertical.
This prediction comes from the Schwarzschild solution.

The vertical speed c = cof
The horizontal speed c = coSQRT(f)

Where f is 1-2GM/rc2
Because f is smaller than 1, the vertical speed of light is less than the horizontal speed.
Presumably the vertical speed can be down or up which means that it is independent of the direction of gravity as long as it is parallel with the gravity.

Has there been an experiment to test for this prediction?

Is this just an issue of coordinate speed?
It is universally agreed that the speed of light measured locally is independent of direction and always give c.
 
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Is this just an issue of coordinate speed?
Yes.
The measurable speed of light is to first order independent of direction even in a gravitational field.
 

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