Bends in Space-Time vs Invariance

[WCOLtd]

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?

 

[Mentz114]

This thread discusses something similar, in case you haven't found it.

https://www.physicsforums.com/showthread.php?t=248015

 

[Entropia]

According to Einstein's theory of general relativity, the curvature of space-time is caused by the presence of massive objects. This means that the path of the light beam will be affected by the curvature of space-time as it travels towards the mirror. However, the speed of light (c) is considered to be a constant in all frames of reference, meaning that it will travel at the same speed regardless of the curvature of space-time.

In other words, the light beam will still travel at the speed of light (c) along the geodesic path towards the mirror, even though the path may be curved due to the presence of the massive body. This is because the speed of light is not affected by the curvature of space-time, but rather it is the path that is affected.

Therefore, the observer's observations for the time it takes for the light beam to reach their eyes will be the same as if they were located at the distance (r) in flat space-time. This is because the light beam will still travel at the same speed, and the observer will perceive the same amount of time passing, regardless of the curvature of space-time.