Time Dilation & Black Hole Mergers: Exploring Ringdown Gravitational Waves

[zhermes]

Time dilation and black-hole--black-hole mergers, and ringdown gravitational waves

An observer far away from an event horizon never sees a particle cross the event horizon. How does this effect the apparent merger of two black holes?

Also, I've seen that the gravitational waves during the ringdown phase (post-merger) are still periodic. How can this be so, when the trajectory of each BH must be radially inward once it passes the event horizon?

 

[bcrowell]

I could be totally wrong, but it seems to me that the answer to both of these is probably the same. We think of a black hole as having all its "stuff" concentrated at the singularity at the center, but that is only because our usual definition of "stuff" is anything that contributes to the stress-energy tensor. But gravitational fields themselves can carry energy, even though they don't contribute to the stress-energy tensor. In one of these merger processes, you have a region of spacetime that is strongly disturbed, with gravitational waves propagating around in it. These waves have their own dynamics, which continue regardless of the causal disconnection from the region inside the event horizon.

 

[K^2]

Also, I've seen that the gravitational waves during the ringdown phase (post-merger) are still periodic. How can this be so, when the trajectory of each BH must be radially inward once it passes the event horizon?

Black holes merging is a bit above my pay grade, but a "small" point mass falling into a black hole will not fall radially in after passing event horizon. It spirals in. Why do you think two singularities will fall onto each other radially?

 

[bcrowell]

Black holes merging is a bit above my pay grade, but a "small" point mass falling into a black hole will not fall radially in after passing event horizon. It spirals in.

This is incorrect. If the point mass is dropped from rest, it falls in radially, not in a spiral. (One way to see this is that there is nothing to break the axial symmetry.)

 

[Naty1]

An observer far away from an event horizon never sees a particle cross the event horizon. How does this effect the apparent merger of two black holes?

(a) You cannot see the apparent nor absolute horizon of any black holes, merging or not. There is nothing to see..it is a mathematical boundary. If you deal with Leonard Susskinds's "stretched horizon", the degrees of freedom just above the apparent or absolute horiozn, then a particle or merging black holes would be seen to spread out over the merging horizon...but in the

(b) The "particle never crossing" is the view from a great distance, a stationary non accelerating observer, essentially at infinity...such a perspective does NOT hold near the horizon of a single black hole nor merging black holes.

You question is analogous to asking (in special relativity): If two observers in relative high speed motion see each other's clocks are running slower than there own, which is correct? They both are.
or analogous in general relativity, "If two distant observers each within different gravitational potentials observe each other's clocks are running different from their own, which is correct? Again, they both are.

Since "stretched horizons are not typically discussed here that I have seen, here is what Susskind says about them:

Black Hole Complementarity
Leonard Susskind, THE BLACK HOLE WAR

Complementarity

(p238) Today a standard concept in black hole physics is a stretched horizon which is a layer of hot microscopic degrees of freedom about one Planck length thick and a Planck length above the event horizon. Every so often a bit gets carried out in an evaporation process. This is Hawking radiation. A free falling observer sees empty space.

(p258) From an outside observer’s point of view, an in falling particle gets blasted apart….ionized….at the stretched horizon…before the particle crosses the event horizon. At maybe 100,000 degrees it has a short wavelength and any detection attempt will ionize it or not detect it!

(p270)…. eventually the particle image is blurred as it is smeared over the stretched horizon and….and the image may later be recovered in long wavelength Hawking radiation. (I think this means scrambled information.)

 

[Naty1]

Of possible interest:

Experimental Clues...

Black hole pairs
Almost every galaxy has a black hole with a mass of one million to one billion times that of the sun. A super-massive black hole, of more than 4 million solar masses, is located in the center of our own Milky Way galaxy. As the universe has evolved, galaxies often collide and merge, creating larger galaxies. This has led to the supposition that galaxies in mid-merge should have a two great black holes (a pair) orbiting one another. Expectations were, that this should be a common observation, hand in hand with mid merge collisions. However, observation has not validated this supposition; only a few orbiting pairs had been found. When observation did not match expectation, this posed problems for theories of how galaxies merge and grow.[10][11]

These statistics have been recently altered. 33 pair of super-massive orbiting black holes were recently discovered. The first 32 pair by the DEEP2 Galaxy Redshift Survey conducted with the Keck II Telescope on Hawaii’s Mauna Kea. This survey determined which black hole was moving toward Earth at which time. When the black hole moves toward Earth, its light is blue-shifted, meaning it has a shorter wavelength. Orbiting pairs were identified by looking for instances when one black hole was blueshifted and the other redshifted. The pairs orbit each other at 200 km per second, at several thousand light years apart.[10][11]

Intermediate mass black hole
In this image, X-rays from Chandra X-ray Observatory are shown in blue and are overlaid on an optical image from the Hubble Space Telescope... Chandra X-ray Image of the intermediate black hole event, (NGC 1399), without the Hubble Space Telescope overlay. Credit: X-ray: NASA/CXC/UA/J. Irwin et al; Optical: NASA/STScI ----... evidence is accumulating that a black hole, one thousand times more massive than the sun, has caused the destruction of a white dwarf star. It appears that the white dwarf is heating up as it falls toward the black hole. This event creates an intense stellar astrophysical X-ray source, called an ultraluminous X-ray source

 

[Polyrhythmic]

That's interesting, may I ask you for the source of those quotes?

 

[Naty1]

Looks like I forgot to post the source...Wikipedia...

I just did a quick search and could not find it again...both quotes were from one article as I recall...

I've never seen much of a description of black holes combining...and these were interesting but easily subject to misinterpretation like

"When the black hole moves toward Earth, its light is blue-shifted, meaning it has a shorter wavelength..."

Huh??..Black holes giving off light??

No, they must mean it's the radiation from infalling matter accelerating into the horizon...but outside the horizon... such radiation is a key clue to black holes...

 

[DrGreg]

Looks like I forgot to post the source...Wikipedia...

Ten seconds of googling reveals the source to be American Astronomical Society 215th meeting on Wikipedia.

Always a good idea to name your source when quoting!

 

[K^2]

This is incorrect. If the point mass is dropped from rest, it falls in radially, not in a spiral. (One way to see this is that there is nothing to break the axial symmetry.)

And who said anything about dropping things from rest? Any realistic situation will involve a rather high amount of angular momentum, be it a BH merger or a "small" object falling in.

 

[Passionflower]

Any realistic situation will involve a rather high amount of angular momentum, be it a BH merger or a "small" object falling in.

In any realistic situation it is darn difficult for a small object to actually fall into a black hole.

 

[PAllen]

This seems to be one of the major recent efforts on this:

Phys. Rev. Letters summary:
http://arxiv.org/abs/0909.2867

Longer Phys. Rev. D article by the same collaboration:

http://arxiv.org/abs/1005.3306

The references link to other key papers, most seem available in arxiv.

 

[K^2]

In any realistic situation it is darn difficult for a small object to actually fall into a black hole.

You mean in terms of cross-section? I won't argue with that. The OP's question was why the gravity waves are still periodic, suggesting he believes the merger is radial after the singularities are within common event horizon. I'm asking if there is actually any reason to think so, and merely using small object as an example where I know the answer.

 

[debojoti]

I am a new guy in this field...just wanted to know under what conditions does the radial or spiral acceleration of the masses takes place from the event horizon of the black hole...means when does spiral takes place and when the radial takes place...??