View Full Version : Does the diameter of an EH expand when an observer approaches it?

2009-Nov-15, 01:32 AM
Because of relativistic effects ... does an EH seem to expand as an observer gets closer to it or hovers near it compared to observing it from outside of its relativistic effects?

Frog march
2009-Nov-15, 04:12 AM
Light curves towards a black hole as it gets closer, but any observer on that light path will see the black hole's event horizon(or matter falling in close to the apparent event horizon) on a tangent to that path, then I think that the black hole will look smaller the closer one gets, as far as I can see. If that is ATM, I'd like to know why.

ETA: or maybe, now I come to think about it, the black hole occupies the same arc the closer one gets.....

grant hutchison
2009-Nov-15, 01:39 PM
Depends on the observer.
A hovering observer at the photon sphere (1.5 Schwarzschild radii) sees the black hole event horizon fill half the sky: so it looks bigger than simple Euclidean geometry would predict. A free-fall observer who started from infinity will see the event horizon span less than 90 degrees until he has crossed the event horizon: so it looks smaller than simple Euclidean geometry would predict. Both observers see the event horizon spanning more sky the closer they approach the black hole.
These are optical effects. They don't change the Schwarzschild radius.

Grant Hutchison

2009-Nov-15, 08:01 PM
Thanks for the answers and interesting ones none the less ... but I also realized a simple mistake I made about an hour after I posted this .. .for some reason I forgot the space contraction was only parallel with the force of gravity and not in the other directions ... uggg ...

grant hutchison
2009-Nov-15, 09:37 PM
Actually, I need to correct myself, too. :)

The free-faller sees the apparent diameter of the event horizon as being smaller than the angular size observed by a stationary observer in the same position. (That's a simple function of relativistic aberration.)
But for most of his journey he still sees the event horizon as being wider than would be predicted by simple flat-space geometry. Only when he is falling very quickly, close to the hole, does he see an apparent diameter less than that predicted by Euclidean geometry. The cross-over from "bigger" to "smaller" happens at about two Schwarzschild radii, if I'm doing the maths correctly.

Grant Hutchison