View Full Version : Black Holes, and Hoops

WaxRubiks

2010-Apr-27, 03:35 PM

In another thread a while back it was said that if you imagine a beam of light traveling close to a high gravitational object, like a neutron star, and imagine that that beam(say a laser beam) was surrounded at intervals by hoops, then even though that beam would really be curved, you could look down the path and see a straight line of hoops.

Well I would like to know if you did the same to a beam of light leaving or entering the event horizon what the path would really be, even though you would only see a straight tube of hoops.

http://farm4.static.flickr.com/3563/4557470377_27a34c85d1_o.jpg

I don't know where the even horizon is supposed to be on the original depiction of a black hole, but I have put in the tube of hoops from the edge of the black circle.

What would be the real path of a beam of light traveling through these hoops, as viewed from above?

grant hutchison

2010-Apr-27, 04:25 PM

You've provided the relevant diagrams yourself, when discussing the magnification of the event horizon by the curved light paths.

Are you expecting something different this time?

Grant Hutchison

WaxRubiks

2010-Apr-27, 04:29 PM

I'm just curious as to how much the event horizon is magnified, and what its real size is.

grant hutchison

2010-Apr-27, 04:52 PM

I seem to recall giving quite a detailed response to this question the last time you asked. I generated this graph (http://www.ghutchison.pwp.blueyonder.co.uk/relativity/blackholeview.jpg) for you, showing the apparent radius as seen by a free-falling and a stationary observer, compared to what we might expect from simple Euclidean trigonometry.

Was there a problem with all that?

Grant Hutchison

WaxRubiks

2010-Apr-27, 05:03 PM

well, that graph didn't show the factor by which the event horizon was magnified at 100 Schwarzschild radii...

The factor by which it would be magnified by would drop the closer one got, I suppose.

grant hutchison

2010-Apr-27, 05:11 PM

well, that graph didn't show the factor by which the event horizon was magnified at 100 Schwarzschild radii...About 2.6 for a stationary observer. A freefaller from infinity is getting a bit of relativistic aberration, so sees a magnification of just 2.3. As you get farther away, both observers converge on that 2.6 figure.

Grant Hutchison

WaxRubiks

2010-Apr-27, 05:14 PM

thanks

something for me to think about.

grant hutchison

2010-Apr-27, 05:21 PM

All of this (including diagrams of the light paths) was available in the paper (http://www.spacetimetravel.org/licht/licht.html) by Ute Kraus I linked to last time.

The limit magnification of 2.6 for a distant stationary observer is just the impact factor of the photon sphere, as Kraus describes. In exact figures, it's equal to 1.5*sqrt(3).

Grant Hutchison

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