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Black holes bending light

by PhantomOeo
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PhantomOeo
#1
May7-09, 12:14 AM
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The reason I heard that black holes are black is because any light that trying to leave the black hole's gravity gets sucked in by the massive amounts of gravity.

So this implies that light can curve or even reverse direction if enough gravity is present. If this is the case then what stops a black hole from acting as a slingshot? I am asking if a black hole could cause light coming from earth to bend around it (like an asteroid slingshoting around a planet) coming back to earth? To us it would look like a earth-like planet on the other side of the galaxy or universe but in reality we would be looking at earth millions of years in the past (i.e. no signs of civilization or anything else that would indicate that it is earth not another inhabitable planet)
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tiny-tim
#2
May7-09, 05:04 AM
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Hi PhantomOeo! Welcome to PF!

A black hole has a "photon sphere" of radius 3M (where 2M is the Schwarzschild radius, of the event horizon), at which photons (light) can orbit the black hole for ever.

A photon which just misses the photon sphere will go in an ellipse, and the more it just misses it, the more eccentric the ellipse.

In a limiting case, yes, a photon could more or less go back the way it came

but very few photons would do that,

and there'd be no focussing (unless you could place a "mask" near the black hole), so they'd be swamped by all the other photons from paths of different eccentricity.
George Jones
#3
May7-09, 09:10 AM
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Quote Quote by tiny-tim View Post
A photon which just misses the photon sphere will go in an ellipse, and the more it just misses it, the more eccentric the ellipse.
The only closed orbits orbits around spherical black holes for both massive particles and massless photons are circles. The only bound orbits for photons are circles, while bound, non-closed orbits exist for massive particles.

If gravity is fairly weak, the bound, non-closed orbits of massive particles are almost closed ellipses, but nothing like this exists for the trajectories of photons. The photon sphere circular orbits are at an unstable equilibrium of the effective potential, and a small perturbation will either start the photons spiraling into the black hole or out to infinity.

tiny-tim
#4
May7-09, 06:14 PM
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Black holes bending light

Hi George!

Yes, you're right I'm being stupid.

The photon sphere circular orbits are unstable, and there are no other closed orbits.

I should have said that photons going near enough to the black hole can wind round the black hole many times before coming out again

a black hole would act as a lens giving rise to n ring-shaped images of a background star, each ring corresponding to light which had been bent 1,2,3,..n times around, for some positive integer n (which depends on the distance beyond the black hole)

and it would act as a mirror giving rise to n ring-shaped images of an observer, in the same way.

(all amazingly faint, of course, and jumbled up with images of everything else )
Thanks for the help!
Division
#5
May27-09, 02:03 AM
P: 49
If light doesn't have mass, why does the Black Hole bend it?

The accretion disc is matter trapped in the Black Hole's gravity, slowly going in to the event horizon. If light is trapped along with matter in the accretion disc, shouldn't light contain some kind of mass?

I might be missing something here, but it is a question that has been on my mind for a long time.
tiny-tim
#6
May27-09, 04:49 AM
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Hi Division!
Quote Quote by Division View Post
If light doesn't have mass, why does the Black Hole bend it?
Mass in energy, energy is mass, so light has mass.

Light doesn't have rest-mass.
The accretion disc is matter trapped in the Black Hole's gravity, slowly going in to the event horizon. If light is trapped along with matter in the accretion disc, shouldn't light contain some kind of mass?
Light is not trapped in the accretion disc.

And the accretion disc is not "trapped in the Black Hole's gravity" any more than the Earth is trapped in the Sun's gravity. Orbits in the accretion disc are stable the accretion disc itself however generates (and therefore loses) energy, probably through ordinary or magnetic viscosity (see http://en.wikipedia.org/wiki/Accretion_disc), causing it to gradually spiral in.
malawi_glenn
#7
May27-09, 05:31 AM
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The light follows geodesics in space-time, and massive objects (well anything that has energy) curves space-time.

Curvature is proportional to the energy-momentum tensor, not mass.
qraal
#8
May28-09, 04:00 AM
P: 775
So why is the photon sphere at 3M? What causes the circular orbit to be there? If photons behaved like massy particles it'd be at M, assuming Newtonian gravity applied to an object travelling at c.
malawi_glenn
#9
May28-09, 09:04 AM
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the difference is that light follows null-geodesics
qraal
#10
May28-09, 03:12 PM
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Quote Quote by malawi_glenn View Post
the difference is that light follows null-geodesics
And? How did they compute that?
malawi_glenn
#11
May28-09, 03:13 PM
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Quote Quote by qraal View Post
And? How did they compute that?
what? that light has null geodesics or where the photon sphere is located around Schwarzchild BH?
qraal
#12
May28-09, 05:36 PM
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Quote Quote by malawi_glenn View Post
what? that light has null geodesics or where the photon sphere is located around Schwarzchild BH?
Sorry I wasn't clearer. I meant the radius of the photon sphere - why is the geodesic wrapped in a circle at 3M?
qraal
#13
May28-09, 06:11 PM
P: 775
Oddly enough Wikipedia has a decent entry on the Photon Sphere and actually derives it...

Photon Sphere

...though it's all in GR tensor notation that I'm really not sure how to translate. At least the equations themselves, extracted from the tensor, aren't inscrutable.
malawi_glenn
#14
May29-09, 12:39 AM
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I hope that question will come on my GR exam next friday lol
ngjingyi
#15
May30-09, 08:15 AM
P: 19
how do something overcome the huge amount of gravity of black hole?


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