Gravitational lensing paradoxon

[mersecske]

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.

 

[yuiop]

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.

 

[Troponin]

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?