Gravitational lensing paradoxon

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SUMMARY

The discussion centers on the gravitational lensing phenomenon, specifically the behavior of two light rays diffracted by a star's gravitational field. It is established that these rays can meet at the same point behind the star, leading to the crossing of their world-lines twice. The conversation clarifies that this scenario is analogous to light rays passing through a glass lens, converging at a focal point, and emphasizes the distinction between space-space diagrams and spacetime diagrams in general relativity. The warped nature of light cones in curved spacetime, particularly near massive bodies like black holes, is also highlighted.

PREREQUISITES
  • Understanding of general relativity principles
  • Familiarity with light cone diagrams in spacetime
  • Knowledge of gravitational lensing effects
  • Basic concepts of optics and light behavior
NEXT STEPS
  • Study the mathematical framework of gravitational lensing
  • Explore the properties of light cones in curved spacetime
  • Investigate the applications of gravitational lensing in astrophysics
  • Learn about the differences between space-space and spacetime diagrams
USEFUL FOR

Astronomers, physicists, and students of general relativity who are interested in the implications of gravitational lensing and the behavior of light in curved spacetime.

mersecske
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Let us assume that two light rays are started at the same time symmetrically (towards the left and towards the right side of the star) which are diffracted due to the gravitational effect of a star and they meet each other at the same place behind the star. The meeting is the same event, therefore the world-lines of the two light rays cross each other twice. How it is possible? Because a light ray goes on the surface of the light cone, which separates the causality regions in general relativity.
 
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mersecske said:
Let us assume that two light rays are started at the same time symmetrically (towards the left and towards the right side of the star) which are diffracted due to the gravitational effect of a star and they meet each other at the same place behind the star. The meeting is the same event, therefore the world-lines of the two light rays cross each other twice. How it is possible? Because a light ray goes on the surface of the light cone, which separates the causality regions in general relativity.

I am not sure why you think this is any more paradoxical than passing two diverging light rays through a suitable glass lens so that they converge on a focal point. Happens all the time in cameras, telescopes, etc.

The diagram of the diverging rays going around a massive body and converging on a point is essentially a space-space diagram, while light cones are normally depicted in space-time diagrams, so there is no conflict here because they are different situations.

In a spacetime diagram of a light cone, with time on the y-axis and distance on the x axis, the physical situation is two rays going in opposite directions parallel to the x axis. The diagram does not depict a physical "light cone" in space.

You should also bear in mind that in the curved spacetime of gravitational field, the spacetime diagram of a light cone is warped or curved, especially near a black hole and is not a neat cone consisting of null paths diverging in straight lines at 90 degrees to each other.
 
Last edited:
kev said:
I am not sure why you think this is any more paradoxical than passing two diverging light rays through a suitable glass lens so that they converge on a focal point. Happens all the time in cameras, telescopes, etc.

Agreed, unless I'm missing something?
 

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