Bends in Space-Time vs Invariance

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SUMMARY

This discussion centers on the behavior of light traveling along a geodesic in the presence of a massive body, specifically a neutron star. The key question posed is whether the speed of light (c) varies due to the curvature of space-time or remains constant regardless of the gravitational influence. It is established that light travels at speed c along a geodesic, but the time taken for light to reach an observer may differ when accounting for the curvature of space-time compared to flat space-time scenarios.

PREREQUISITES
  • Understanding of general relativity and geodesics
  • Familiarity with the concept of light speed (c)
  • Knowledge of gravitational effects on light propagation
  • Basic principles of space-time curvature
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  • Research the implications of general relativity on light propagation
  • Study the concept of geodesics in curved space-time
  • Explore the effects of gravitational lensing on light paths
  • Learn about the Schwarzschild solution and its impact on light behavior near massive bodies
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Physicists, astrophysicists, and students of general relativity who are interested in the interaction between light and gravitational fields, as well as anyone exploring the implications of space-time curvature on light travel.

WCOLtd
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Imagine a beam of light being turned on at the surface of a massive body such as a neutron star, the beam of light travels along a geodesic path towards a mirror located at radius r from the planet's surface, when the light beam hits the mirror, the light bounces back to the observer located at the source of the original beam.

My question is does the speed of light (c), when traveling along a geodesic from a massive body to an observer vary according to bends in space-time? (as if light has traveled a greater distance according to the curvature of space-time) or does light travel at the speed of light (c) in a geodesic no matter what the curvature of space-time is?

In the example, would the observer's observations for the time the light beam to reach his eyes be the same as if it were located at the distance (r) in flat space-time?
 
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