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tommac
2011-Apr-14, 07:32 PM
Can a stable orbit exist inside of an event horizon of a black hole for say a planet or star?

Noclevername
2011-Apr-14, 09:59 PM
Any matter would be spaghettified (http://en.wikipedia.org/wiki/Spaghettification) by tidal stress long before you got close enough to see if the EH had an "underside."

(IIRC the event horizon is like a rainbow, it changes location depending on where you view it from.)

Nowhere Man
2011-Apr-14, 10:16 PM
No. As I understand it, all world lines within the event horizon intersect the center. In other words, there's nowhere to go but down.

Also, the event horizon is where the escape velocity is c. A bit higher up is a region where the orbital speed is c. So even outside the event horizon, there is a region where no matter can have a stable orbit.

Fred

slang
2011-Apr-14, 10:19 PM
Can a stable orbit exist inside of an event horizon of a black hole for say a planet or star?

I don't think so. See this bit of wiki (http://en.wikipedia.org/wiki/Schwarzschild_metric#Orbital_motion). Or try looking up "Innermost Stable Circular Orbit".

baskerbosse
2011-Apr-15, 12:07 AM
Can a stable orbit exist inside of an event horizon of a black hole for say a planet or star?

I would think not.
-Correct me if I'm wrong but at the event horizon escape velocity is lightspeed, past the event horizon you would need to exceed lightspeed just to remain stationary.


Peter

WayneFrancis
2011-Apr-15, 07:57 AM
Isn't anything inside the photon sphere unstable? Anything inside the EH has no orbit. I think things also get really complicated with rotating black holes because of the extreme frame dragging effect.

tommac
2011-Apr-15, 12:56 PM
This is not true for all black holes. From what I understand for SMBH there is little tidal force at the EH and passing through it is non eventful.

Spaghettification only happens on smaller black holes where the tidal forces at the EH are signifigant.


Any matter would be spaghettified (http://en.wikipedia.org/wiki/Spaghettification) by tidal stress long before you got close enough to see if the EH had an "underside."

(IIRC the event horizon is like a rainbow, it changes location depending on where you view it from.)

tommac
2011-Apr-15, 01:02 PM
isnt that relative to the EH rather than the singularity? Couldnt we fall through the EH at an angle that would catapult us out past the singularity, but not out past the EH, only to get slingshotted back?


I would think not.
-Correct me if I'm wrong but at the event horizon escape velocity is lightspeed, past the event horizon you would need to exceed lightspeed just to remain stationary.


Peter

baskerbosse
2011-Apr-16, 03:13 AM
isnt that relative to the EH rather than the singularity? Couldnt we fall through the EH at an angle that would catapult us out past the singularity, but not out past the EH, only to get slingshotted back?

No, I don't think so.
Since escape velocity at EH is c, orbital speed is also c at EH.
Further in, gravity increases, so maintaining orbit would exceed c and therefore not possible.


Peter

Nowhere Man
2011-Apr-16, 03:56 AM
Correction. Orbital velocity at the event horizon is not c. The region where c is the orbital velocity is the photon sphere (http://en.wikipedia.org/wiki/Photon_sphere) (as stated by WayneFrancis above), and for a nonrotating black hole is 3/2 of the Schwarzchild radius. Rotating black holes are more complicated.

This doesn't change the fact that within the event horizon, or even within the photon sphere, you can't have a stable orbit. And once inside the event horizon, your next destination is the singularity.

Fred

swampyankee
2011-Apr-16, 03:04 PM
No. You can't have a stable circular orbit within 3 times the Schwarzchild radius, at least for non-rotating black holes. For rotating black holes, I suspect that the least radius for a stable orbit will depend on orbital inclination. For charged black holes? Who knows?

Jeff Root
2011-Apr-17, 11:05 AM
... at the event horizon escape velocity is lightspeed, past the event
horizon you would need to exceed lightspeed just to remain stationary.
isnt that relative to the EH rather than the singularity? Couldnt we fall
through the EH at an angle that would catapult us out past the singularity,
but not out past the EH, only to get slingshotted back?
You are in serious danger at the photon sphere, in deep trouble
inside the photon sphere, lost at the event horizon, and flushed
down toward the singularity inside the event horizon. The farther
in you go, the harder you are pulled in. Not only do orbits become
impossible, your spiral downward should become more and more
nearly a straight-line zoom to Hell and spaghettification without
meatballs.

-- Jeff, in Minneapolis

caveman1917
2011-Apr-18, 02:07 AM
For a Schwarzschild black hole, the minimum radius is 3rs. For a Kerr black hole, things depend on the angular momentum of the black hole, and the angular momentum of the test particle in each direction, see here (http://202.38.64.11/~jmy/documents/publications/Wilkins1972prd5_814.pdf). It's interesting to note that for an extremal Kerr black hole (J/Mc = rs/2) there are stable orbits all the way to the event horizon.

baskerbosse
2011-Apr-18, 04:18 AM
Correction. Orbital velocity at the event horizon is not c. The region where c is the orbital velocity is the photon sphere (http://en.wikipedia.org/wiki/Photon_sphere) (as stated by WayneFrancis above), and for a nonrotating black hole is 3/2 of the Schwarzchild radius. Rotating black holes are more complicated.


Oh... -yes, sorry. Of course you're right.
Even worse for the poor guy trying to orbit..! ;-)

Peter