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View Full Version : Blackholes: Infinite Fall vs. Evidence of Gobbling?



CBrachyrhynchos
2007-Jul-06, 05:36 PM
Ok, yet another twisty black hole question.

General relativity predicts that intense gravity causes time dilation. A research team recently announced that this solves one of the information parodoxes of black holes. It takes an infinite amount of time for matter to fall into a black hole due to increasing time dilation. But it takes a finite amount of time for the black hole to evaporate. Therefore no information is really lost because nothing really crosses the event horizon.

However, we have evidence of periodic gobbling of matter by the supermassive black hole at the core of our galaxy (via "light echos"). How would this work?

Noclevername
2007-Jul-06, 05:40 PM
However, we have evidence of periodic gobbling of matter by the supermassive black hole at the core of our galaxy (via "light echos"). How would this work?


It just gets sucked too close for us to percieve it. What happens to it after that is anyone's guess.

nauthiz
2007-Jul-06, 06:08 PM
General relativity predicts that intense gravity causes time dilation. A research team recently announced that this solves one of the information parodoxes of black holes. It takes an infinite amount of time for matter to fall into a black hole due to increasing time dilation. But it takes a finite amount of time for the black hole to evaporate.


Turns out that's a bit of an oversimplification - I got tripped up by it when I first heard about this, too. What it is is that it takes an infinite amount of time for the matter to fall in as seen by an outside observer. When you're falling in, you won't notice yourself slowing down at all.

That said, I'm still a bit lost as to what the research team actually found - the paper was way over my head. I believe what's happening is an interaction between time dilation and the black hole's evaporation whose upshot is that the event horizon always recedes from you at least as fast as you're approaching it. So it's not that it takes an infinite amount of time to get to where the event horizon is, it's that by the time you get there it's moved.

Twinsun
2007-Jul-06, 07:33 PM
WOW that's interesting ... like a time capsule ... it preserves it, not devours it ... even though it might modify its physical state of the matter

Grey
2007-Jul-06, 09:16 PM
General relativity predicts that intense gravity causes time dilation. A research team recently announced that this solves one of the information parodoxes of black holes. It takes an infinite amount of time for matter to fall into a black hole due to increasing time dilation. But it takes a finite amount of time for the black hole to evaporate. Therefore no information is really lost because nothing really crosses the event horizon.As others have pointed out, that infinite time to fall in is only for distant observers. Someone falling in measures a finite amount of time passing on their own clock as they go. But also, the infinite time to fall in depends on a black hole that lasts forever. If you add in evaporation due to Hawking radiation after some finite length of time, you'll find out that it no longer takes an infinite amount of time for something else to fall in. You'll see that it finally reaches the event horizon just at the same moment as the black hole evaporates.

CBrachyrhynchos
2007-Jul-06, 10:30 PM
As others have pointed out, that infinite time to fall in is only for distant observers. Someone falling in measures a finite amount of time passing on their own clock as they go. But also, the infinite time to fall in depends on a black hole that lasts forever. If you add in evaporation due to Hawking radiation after some finite length of time, you'll find out that it no longer takes an infinite amount of time for something else to fall in. You'll see that it finally reaches the event horizon just at the same moment as the black hole evaporates.

I got that. The paradox that bothers me involves this insight combined with the second observation. As distant observers we watch a black hole capture gas from a companion object. As that gas spirals in, it becomes heated producing X-rays. The time dilation predicted by general relativity means that the observed duration of this event should last for the lifetime of the black hole (or at least longer than our ability to observe it). The effects of time dilation should to us as an external viewer "smear out" that event in slow motion.

but observationally we can describe describe the activity of black holes as episodic, based on the existance of "light echos" surrounding supermassive black holes.

I suppose one way around this is to propose that the X-ray events we observe from black holes happen at a sufficient distance that time dilation effects are not that big of a deal. But do we have any evidence regarding the dynamics of black hole accretion to support this?

Another followup question is would the effects of general releativity in black hole accretion clouds also result in smearing the spectra? Would matter at different parts of the gradient have different red-shifts?

nauthiz
2007-Jul-06, 10:45 PM
You're talking about light echoes in terms of what was mentioned in this UT post (http://www.universetoday.com/2007/01/11/light-echoes-from-our-supermassive-black-hole/), right?

I don't believe those X-ray bursts are evidence of matter actually crossing the event horizon. X-rays are produced as the matter becomes superheated in the accretion disk.

I don't think, the echoes were something special about the black hole. What made them cool is that they allowed us to detect an event that we otherwise would never have seen because the primary radiation reached us before we had X-ray telescopes.

publius
2007-Jul-06, 10:47 PM
Let's look at the time dilation factor (see the other thread about this here, where I got to playing). At r = 2R, two Schwarzschild radii, the stationary time dilation is only about 70%. At the photon sphere, r = 3R/2, that factor is

dT/dt = sqrt[1 - 2/3] = 1/sqrt(3) ~58%. Proper stationary clocks are not even yet down to 1/2 that of the asymptotic observer, yet this the radius where (local) circular orbit speed is 'c'. So, things are locally flying in at very high speeds there, but the time dilation isn't all that much.

The extreme time dilation from that to 0 happens in that last 1/2 R! That is something to appreciate. All the action of "freezing" happens in that last little bit (according to our asymptotic sense of distance).

-Richard

antoniseb
2007-Jul-06, 10:47 PM
This is a related idea: Imagine that there is a stellar-mass concentration of mass (that we are referring to as a black hole) and a test particle (let's say an electron for the sake of clarity) is on a path to hit/cross the event horizon. At some point, an outside observer would see the electron slow down to almost a stop (if that kind of observation were possible). So the test particle appears to be just outside the event horizon for an extended time.

Now, imagine that a second 'black hole' collides with the first. Is the test particle now inside an event horizon?

publius
2007-Jul-07, 01:09 AM
This is a related idea: Imagine that there is a stellar-mass concentration of mass (that we are referring to as a black hole) and a test particle (let's say an electron for the sake of clarity) is on a path to hit/cross the event horizon. At some point, an outside observer would see the electron slow down to almost a stop (if that kind of observation were possible). So the test particle appears to be just outside the event horizon for an extended time.

Now, imagine that a second 'black hole' collides with the first. Is the test particle now inside an event horizon?

Modelling scenarios like that are what separates the pros from the pikers like me. That is doing some real General Relativity. The EFE is complex enough, but what makes it really complex, I mean, really, really, really complex, are dymanic situations like this. Mass-energy responds to space-time by moving around, and as it does, changes space-time.

The equations become very difficult, and even stretch numerical techniques to the breaking point. It has been done, however, and black hole mergers are something that has been modelled. There is some stuff online about it, and I'll try to find some of the good stuff later when I get around to it.

But to answer your question, no the electron sitting there frozen doesn't ever go in. What happens is quite weird and complex. Before you even worry about that, imagine the merger of two spherical balls of gravitationally bound fluid.

During the merger, you would loose spherical symmetry, and that fluid would do all sorts of interesting things during the process, but the end result would be a bigger sphere of fluid.

That's basically what happens with two spherical black holes merging. The asymptotic state is a spherical black hole of the sum of the two original hole masses (with certain assumptions).

But the dymanic intermediate state is a complex thing. During the merger, spherical symmetry is lost. The event horizons become distorted, and merge, sort of squeezing out and touching.

Assume those black holes were originally formed from a collapse event. The asymptotic observer would see a spherical chunk of mass frozen near its own horizon. Now imagine he sees two of those balls of frozen stuff moving linearly towards each other. During the merger, the frozen stuff, which is just nearly frozen, still barely moving, every so slowly, getting slower and slower, changes its state of motion a bit during the non-spherical phase as they get close and being to "touch". All the crazy stuff of strong field gravity, frame-dragging, etc, etc, come into play.

The asymptotic result of that is bigger ball of frozen stuff now at a larger radius of the new ball at the end. Sounds crazy, but it works.

Such events radiate enormous amounts of gravitational radiation. As crazy as it sounds, a merger can, under certain conditions, give off a *linear* chunk of momentum in that radiation, pushing the merged black hole off against its own radiation.

Taking our merging fluid example, it would look as though momentum wasn't conserved. The merged ball of fluid had a different momentum than the sum of its parts. The difference went to gravitational radiation.

Don't ask me how that all works, because I don't know. :lol: All I can say is space and time do things our minds just can't imagine.

-Richard

publius
2007-Jul-07, 01:20 AM
Here are some papers on the linear "recoil" kick of black hole mergers:

http://www.citebase.org/abstract?identifier=oai%3AarXiv.org%3Aastro-ph%2F0701887&action=cite****s&cite****s=cocitedby

Note this can happen with inspiralling mergers, too. And, things have been modelled with Kerr (spinning) black holes as well. "Binary rockets", pushing off against their own gravitational radiation flux.......

-Richard

publius
2007-Jul-07, 02:13 AM
The numerical relativity group of the Einstein Institute at the Max Planck Institute (lots of institutes there, apparently :) ), has been doing a lot of work on such simulations:

http://numrel.aei.mpg.de/

They have some movies under the "images" tab. They are impressive looking, but I have no idea what's really being visualized. :lol: The movies are huge. I'm currently trying to get a rotating collapse simulation to download. If you've got only dial-up, I wouldn't even bother.

Search on "black hole merger animation" and you'll find some others. Again, some movies, but it's hard to tell just what is being visualized. Other than the vague notion of space-time shaking like a bowl full of jelly.

-Richard

publius
2007-Jul-07, 05:27 PM
The profanity filter here gets ridiculous in its zeal. I noticed that link I posted didn't give what it was supposed to, and that's because of some "****" in the URL. The string is supposed to be cites_hits, with the underscore removed which looks like a dirty word. THe profanity filter renders that as cite****s.

So when you click on it, go to the address bar and replace the asterisks with that particular dirty word looking string. :)

Anyway, the linear recoil kick can be fairly high -- 500km/s

-Richard

publius
2007-Jul-07, 05:38 PM
Just to give you an idea of how numerically complex this work is, here's a quote about the numerical relativity group's work:



The Cactus code performs a direct evolution of Einsteinís equations, which are a system of coupled nonlinear elliptic hyperbolic equations that contain thousands of terms if fully expanded. Consequently, the simulation resource requirements are enormous just to do the most basic of simulations. The simulations have been limited by both the memory and CPU performance of supercomputers as they attempt to move from calibrating against analytic black hole solutions to non-analytic astrophysically relevant cases in full 3D. The spiraling merger is just such a non-analytic case.

These simulations must use more than one-third of the NERSC IBM SPís available aggregate memory of 4.3 TB in order to achieve the resolution required to accurately simulate these phenomena. This simulation uses 1.5 TB of memory and more than 2 TB of disk space for each run. These runs typically consume 64 of the large-memory nodes of the SP (a total of 1,024 processors) for 48 wall-clock hours at a stretch. The simulation can use all 184 nodes, but this would only allow simulations that are fractionally larger than using the large-memory nodes due to memory/load-balancing issues.

NERSC provided access to a special queue to improve turnaround, opened ports to allow remote steering and Grid access, and provided consulting support for 64-bit integration and code debugging. In the space of two months, this simulation consumed 700,000 CPU hours, simulating three-fourths of a full orbit before coalescence. In the near future, this project could use 10 TB of disk for each run, 5 TB of uniform, user-available memory, and 15 million CPU hours.



Note it took 700,000 CPU hours to simulate *3/4* of an orbit before merger................that shows just how complex the EFE is.