# Could it be really true that light can't escape from a black hole if we illustrate it with geodesic lines?

If we consider the black hole with geodesic lines, as in this illustration of geodesic lines,

I believe that at a given moment, since the light follows its geodesic lines, it will emerge outside the black hole.

If this is true that light can't escape from black hole, then does it mean that this representation with geodesic line is wrong ?

If the light escapes from black hole, it could still be compatible with the fact that we don't see the light, because light could emerge at a completely different angle. Not seeing the light is not a proof for stating that the light does not emerge, since the light could emerge in another direction.

If this schematic would be a genuine illustration of the behaviour of the black hole, it would be clear that light emerge : just imagine the line quoted "5" that goes very deep : at a given moment, even if we wait centuries, the light will go up, since the geodesic lines enter the well and exit the well.

Even if you would say for example : there is singularity : the well is infinite (is it ?), then still, the light would emerge, after an infinite time.

What concretely means that there is singularity ? If this means "actually, we don't know", then I don't understand why people say "we know that light does not emerge".

Don't shout on me : I am of course not a specialist of black holes...

• at a given moment, the light will follow its geodesic That doesn’t make sense in English. – G. Smith Oct 9 at 20:47
• the geodesic lines enter the well and exit the well This is false, since any geodesic crossing the horizon will proceed to hit the singularity. – G. Smith Oct 9 at 20:50
• Geodesics cannot be integrated through a singularity. The curvature is infinite there. – G. Smith Oct 9 at 20:51
• Where does that diagram come from? (You should give attribution for any diagrams posted on Stack Exchange sites). All timelike and lightlike geodesics that touch the event horizon cross it and then proceed towards the singularity and terminate there. They can't come back out again. – PM 2Ring Oct 9 at 21:24
• Unfortunately the site with the diagram is ignorant. It describes spacetime geodesics as trajectories in space. This is wrong. For example: "Geodesic 4 falls into the gravity well and intersects itself as it comes out." - This is nonsense. A geodesic cannot intersect itself without traveling back in time, certainly not in a black hole. None of the lines on your diagram are geodesics. They are trajectories in space, but not in time. – safesphere Oct 10 at 6:56

## 1 Answer

We don't know for certain that light could never emerge from a black hole, but all our current theories say that it never will.

Your suggestion that light might emerge from a black hole 'in another direction' is ingenious, but even if that were possible (and the theory says it is not), then all light leaving black holes would have to do so 'by the back door', so to speak. It would be rather difficult to understand why light should escape from a spherical black hole in just one direction, and, even if we conceded that, it would be a spooky coincidence if all light escaping from all black holes happened to do so in a direction pointing away from us.

• Very useful. Thank you. Problem solved. – Mathieu Krisztian Oct 9 at 21:36