Gravitational distortion of black holes

[Jon Richfield]

Unlike other people, I find black holes puzzling. Let's consider some black holes of modest size, say a few solar masses:
Suppose we have a smallish black hole rotating significantly (read: spinning like its angular momentum represents a large fraction of the energy equivalent of its rest mass or even exceeds it. Don't ask me how it got that way! Maybe some imps were having fun by accelerating it with light beams...?)
As I understand it, that spin could not tear it apart (but please prove me wrong!) but what I would love to know is: What would it do to the shape of the event horizon, and why wouldn't it?

OK, having got that out of the way, now suppose we have two black holes of about that size. Suit yourself about their sidereal rotation, but they are quite close together, say with their event horizons separated by a few km.
Possibly their sidereal rotation could most conveniently match their orbital period round each other. OK?
Now, what would the shape of their individual event horizons be?
It seems to me that at their point nearest to each other, their event horizons should contract, because their gravitational fields should counter each other, and the tidal effects should be pretty confusing. Not at all the the same as the effect if we had two masses of say, mercury or other molten metal orbiting each other at a close separation.
No?
Why not?
Thanks for any helpful replies, just so that I know what to expect next time I see any of these things.

Jon

 

[Nabeshin]

Last few seconds of this movie should help you, sorry it's right at the end and you might have to play it a few times to see.

 

[Chronos]

Black holes possesses no 'special powers'. Until you get very near the event horizon they look like any other massive object in the universe.

 

[Jon Richfield]

Nabeshin,
Much appreciated. Although I played and downloaded that one a few times, it always stopped before there was any visible distortion or contact, but I did explore a few other animations from the same site and the general picture seems to have been that the event horizons elongated towards each other as they approached and finally were enveloped in a larger event horizon. The larger horizon was the bit I understood most comfortably.

This puzzles me. If I got it right, and those animations got it right too, then I am not sure how

Chronos

justifies his remark about BHs being unspecial. Consider the Earth-moon system, which certainly "possesses no 'special powers'", right? Now, if I get into my magic NASA spaceship and direct my trajectory to closely miss the far side of the moon, or the side of the Earth away from the moon, I'll expect to find that the resultant field is greater than if the other body were absent. But, if I were to skim the *near* side of each body, I should expect to find that the gravitational attraction towards the individual centres of mass would be *reduced*.
Right so far?
OK, now my tame imps get to work and magically squeeze each of these two bodies till they each form very, very tiny black holes. (Somewhere I have the formulae for their radii, but let's ignore the details, I am sure you can supply the sordid details.)
Now, those two event horizons would be exerting the same gravitational effects on each other's gravitational contours or isogravs or whatever one might call them, as before. After all, they are and were pretty well spherically symmetrical at all times. Right again?
So, if I then sent my little spacecraft through the same trajectories as before the collapse, it should still follow the same paths, right?

And so far, very Newtonian, still right?

OK, so now the question gets more interesting (to me at least. You folks might by now be properly bored, so forgive!)

I now get my supercharger going and make sure that my spaceship is very strongly braced against tidal forces. Then I repeat the passes, going nearer and nearer, until I find the stresses get to be uncomfortable and accordingly I stop and assess my observations.
I still expect to be able to skim the bodies more closely on the INSIDE passes than on the OUTSIDE passes.
Why am I wrong? (OK, OK, the animations showed me to be wrong, but...)
Sorry to be so obtuse, but as a non-physicist I feel I have a licence! :-)
And thanks again for your replies,

Jon

 

[Nabeshin]

Nabeshin,
Much appreciated. Although I played and downloaded that one a few times, it always stopped before there was any visible distortion or contact, but I did explore a few other animations from the same site and the general picture seems to have been that the event horizons elongated towards each other as they approached and finally were enveloped in a larger event horizon. The larger horizon was the bit I understood most comfortably.

This puzzles me. If I got it right, and those animations got it right too, then I am not sure how

Sort of. I think it depends on the conditions of the merger. For example, in that video I posted before, the horizons pancake in a direction perpendicular to the line connecting them before merging (not shown). However, in the case that the black holes do not orbit, but instead simply fall into each other, you are right the horizons elongate towards each other before forming a common "peanut shaped" horizon. You can see both situations in the first video here:
http://www.black-holes.org/explore2.html

 

[Chronos]

By the time you get near enough to either black hole to experience the forces you are describing, you will be within millimeters of the original center of mass.

 

[Jon Richfield]

Chronos,

A few mm? OK, I'll buy a few mm for tidal forces if you say so.

But how does that affect the answer to the question? For one thing, it shouldn't greatly affect the normal trajectories till I get close. Are you saying that if I send micrometre-sized diamonds or laser beams on trajectories closer and closer to the BHs, that their behaviour will invert somewhere close to the last mm or so?

Thanks for your patience,

Jon

 

[Ich]

The event horizon is the boundary from which nothing can escape to infinity. The presence of a second mass certainly doesn't help things escape to infinity.
That said, event horizons are tricky to define in dynamic circumstances, and behave strangely. For example, if you add matter to a black hole, the EH would expand before the matter actually reached it.

 

[Jon Richfield]

The event horizon is the boundary from which nothing can escape to infinity. The presence of a second mass certainly doesn't help things escape to infinity.
That said, event horizons are tricky to define in dynamic circumstances, and behave strangely. For example, if you add matter to a black hole, the EH would expand before the matter actually reached it.

Wow! Now there you have me gobsmacked! When you say:"The presence of a second mass certainly doesn't help things escape to infinity"
my immediate reaction was to ask you to justify that, because for example, we could in principle use the presence of the moon overhead to assist takeoff into orbit and thence to escape velocity from Earth.
The analogous situation over a black hole should be to partly negate the local gravitation, which should reduce the local radius of the EH...

However, if the approach of another, not yet absorbed, mass increases the local radius of the event horizon of a BH by the mass equivalent of the potential energy, that would explain the expansion.
Do I understand your point? If not, please elaborate.

Thanks,

Jon

 

[Ich]

we could in principle use the presence of the moon overhead to assist takeoff into orbit and thence to escape velocity from Earth.

Then you are in orbit. The orbit is not infinity. It's harder to escape the earth-moon system than Earth alone. That's a question of potential, and potentials always add, never cancel each other.
(of course a swingby maneuver may help you escape by increasing your kinetic energy. But the EH is the place where you can't escape no matter what your kinetic energy is, so this doesn't change the picture.

However, if the approach of another, not yet absorbed, mass increases the local radius of the event horizon of a BH by the mass equivalent of the potential energy, that would explain the expansion.
Do I understand your point?

Sorry, I don't exactly understand what you are saying. Did my explanation above help?

 

[Jon Richfield]

Then you are in orbit. The orbit is not infinity. It's harder to escape the earth-moon system than Earth alone.

Phew, I am beginning to hate BHs; they are obviously out to get me!

But Ich (it is remarkably hard to say that! I am not German, but it still feel like saying "But listen I!" BTW, have you read the book "The Mind's I" by Hofstadter and Dennett? GREAT stuff! Just don't start it when you don't have the time. It takes a lot of thinking as you read.) I assumed in that example that we start out with the Earth/moon system, so it does not increase the difficulty. Given that you are on one body of a two-body system (not a BH!) you can choose an optimal trajectory to get into orbit, and my guess is that gravity would be at its friendliest between the two bodies. If each body had an atmosphere, the atmosphere would bulge most drastically between them, wouldn't it?
In fact, it should be possible in principle to have the bodies sharing a combined atmosphere as long as they were stably in mutually synchronous orbit. No? This would create an extremely interesting evolutionary situation incidentally!

But never mind that. Ignore the atmosphere for now. Yes, I understand about the potential energy required to get out of orbit once you have got into orbit, and I wasn't thinking of slingshotting.

Mind you, it occurs to me that if I did use the opposing gravitational fields to get into orbit, I probably would already be using a sort of slingshotting, wouldn't I? I would be affecting the orbit of the moon in the process, surely?

That's a question of potential, and potentials always add, never cancel each other.

Really? Universally perhaps, but locally? Whether gravitationally or electrically, one can get level nodes where gradients oppose surely? What about at the point where Earth and Moon gravity cancel out (The L1 point?) Have I misunderstood something? Why do we get tidal forces in opposition to the attraction of Earth's gravity?

But the EH is the place where you can't escape no matter what your kinetic energy is, so this doesn't change the picture.

Yes, I accepted that anyway. But OK, let's imagine that We have a BH with a diffuse interior, but a lowish density. "How do we get such a BH?" you ask?
Seems to me that if the BH were say a billion LY in radius and looked like our observable universe, only a few orders of magnitude denser, that should meet our requirements. Somewhere near the centre we have a smallish mass masking the singularity (sort of! ) we launch a rocket from the central mass. Given that there is an EH, we know that we will not get through, but the question is not escape, but to get as high as possible, so surely by launching projectiles in all directions and exercising a few trillion years' of patience, we could deduce where there were massive bodies outside the EH by seeing how high our various missiles get?

Or, if we were to be too stingy to create BH universes for our experiment, then suppose we took a couple of mingy little BHs, a few hundred solar masses each, of roughly equal mass, still far apart, but orbiting each other (and of course slowly approaching each other through orbital decay, emitting gravitational waves and so on).

OK. Now, our spaceship lies on their common ecliptic, right? We happen to want to pass them with minimal expenditure of fuel, en route to a destination also on that ecliptic, but on the other side of their common centre of mass equivalent. We have plenty of fuel, but it is expensive and we wish to conserve it. Also we are in a hurry. Yes? I propose that our most economical trajectory would be (with appropriate synchronisation of course!) smack between them. Meanwhile, we might be exchanging laser messages with our friends on the other side. We also would be sending our messages by similar (but different) routes.

Similarly, suppose our problem were with two BHs of significantly different mass, but the rest of the problem were unchanged. In particular, assume that the combined centre of mass were in space between them, not inside either BH. It seems to me that our strategy would remain the same, except that we would pass nearer to the smaller BH (Not through the combined centre of mass, as we would do when the BHs were of equal mass and the point of zero resultant gravity coincided).

No?

Of course, in both cases our course would not be straight, but would waver according to the BHs' orbiting. In the case of the differing BH masses, we might have to do a lot of chasing of the point of gravitational neutrality.

Not that in neither case do we go anywhere nearer to any EH than we must.

Now, obviously we have other options in principle. For instance, we could chicken out and detour around in any direction depending on the practical details. But I reckon that we would have to steer further from the nearest BH if we stayed in the ecliptic, than we would if we passed between?

Still steering clear of EHs all the time.

Am I missing something?

Sorry, I don't exactly understand what you are saying.

Can't say I blame you. Let's try again.

You said:

For example, if you add matter to a black hole, the EH would expand before the matter actually reached it.

If I understood you correctly, that implied that the approaching mass must have added to the effective mass of the BH even before it reached the EH. In other words the increasing potential energy conversion would have been what caused the bulging of the EH, no? Surely only an increase of mass equivalent, whether in the form of energy or actual mass, could affect the EH?

Did my explanation above help?

If I have been making sense, then yes, definitely and thank you muchly. If not, thank you for your patience so far!

Cheers,

Jon

 

[Ich]

But Ich (it is remarkably hard to say that! I am not German, but it still feel like saying "But listen I!"

Hmm, strange, this kind of difficulty has been reported to me by several persons. I could never reproduce the effect, however, it always seems natural to call myself Ich.
Maybe it is because you are not I, but still - sloppily - refer to you as I. Such misbehaviour on your side is bound to create confusion.

If each body had an atmosphere, the atmosphere would bulge most drastically between them, wouldn't it?

Yes, because this point is at a relatively low potential. This is where things want to go to, not run away from.

In fact, it should be possible in principle to have the bodies sharing a combined atmosphere as long as they were stably in mutually synchronous orbit.

It's also possible for BH to share a common EH, at least for some milliseconds.

That's a question of potential, and potentials always add, never cancel each other.

Really? Universally perhaps, but locally? Whether gravitationally or electrically, one can get level nodes where gradients oppose surely? What about at the point where Earth and Moon gravity cancel out (The L1 point?)

Potential is what I'm drawing in the attached diagram.
You simply add them. The resulting potential (green) is at each point smaller (more negative) than the potential of a single body.
It is easier to get to a point with smaller potential, but for the same reason it's harder to escape from this point to infinity. When you add a second body, it's harder to escape to infinity from every point.
Escape to the other black hole doesn't count as escape. You have to get away to be outside the horizon.

...we launch a rocket from the central mass.

That's not how it works. You can't move freely within a BH and then bounce against the horizon from the inside.
It is not wrong to say that the inward direction inside a BH is timelike. That means: every material object will move toward the singularity with the same certainty as it moves into the future. There is no EH visible from the inside - information will still reach you from the outside -, but no matter what you do, you'll end up in finite time in the singularity.

Now, our spaceship lies on their common ecliptic, right? We happen to want to pass them with minimal expenditure of fuel, en route to a destination also on that ecliptic, but on the other side of their common centre of mass equivalent. We have plenty of fuel, but it is expensive and we wish to conserve it. Also we are in a hurry. Yes? I propose that our most economical trajectory would be (with appropriate synchronisation of course!) smack between them.

In Newtonian physics, with unbounded speed, yes. In relativity: not necessarily. Time dilation may let you cross the dense region sluggishly (as seen from the outside), so you may want to avoid it if you're in a hurry. The extreme example being a direct hit of a BH there.

If I understood you correctly, that implied that the approaching mass must have added to the effective mass of the BH even before it reached the EH. In other words the increasing potential energy conversion would have been what caused the bulging of the EH, no?

The approaching mass makes it harder for an object near the BH to escape: it woud have to overcome its attraction too on most of its journey outward, and will benefit from it only in the first part of it (as long as it's inside the incming shell).
That means that said object may be inside the EH (i.e. can't escape), even before the other mass reached it. Remember, the EH is no some physical boundary the presence of which you could somehow detect. It's the "virtual" boundary of a region which is defined by a criterion that is evaluated at future null infinity, i.e. far away, far in the futurel. If you see light there from a point, it was obviously outside the EH, if not, is was inside. That's nothing you can determine at the EH itself.

 

[stevebd1]

Here are a couple of links to other videos showing black holes merging-

http://numrel.aei.mpg.de/Visualisations/index.html

http://www.nasa.gov/vision/universe/starsgalaxies/gwave.html

 

[Jon Richfield]

Well Ich, I am for some reason wondering whether I have fallen foul of Bohr’s clarity exhortation: "Never express yourself more clearly than you are able to think." I don't know how clearly I have expressed myself, but I am sure it was much more clearly than I was able to think.

That's not how it works. You can't move freely within a BH and then bounce against the horizon from the inside.
It is not wrong to say that the inward direction inside a BH is timelike. That means: every material object will move toward the singularity with the same certainty as it moves into the future. There is no EH visible from the inside - information will still reach you from the outside -, but no matter what you do, you'll end up in finite time in the singularity.

That time-like principle is very striking. For a “solid” BH, one with a mass equivalent in the range of say a few billion solar masses it is very believable. However, a thought springs somewhat laboriously to my to my somewhat laborious mind: the larger the EH, the lower the density of the BH, right? In fact, round about the radius of our observable universe, the density would be within a few orders of magnitude of our universe.

No?

Well, if so, what happens to our singularity and our progress towards it? A Newtonian view would certainly permit in principle, that a mix of solids and gases could follow indefinite dynamic trajectories much like the trajectories of the galaxies we see about us. In such a BH there could be time for consciously subjective observers to evolve before they get swallowed up. (After all, if you gathered enough of our galactic-cluster stuff within a radius of a few tens of billion light years, the presence of solid and gaseous materials with intervening space would not prevent the constitution of an EH, right?) Why should a relativistic view deny this? Why should a relativistic (or even Newtonian) view deny the possibility that ordinary solar BHs could form within our common EH? (Not that that last item seems to me to be very important!)

I won’t ask you what our singularity would look like inside such a BH “bubble universe” would look like, though I would love to know, but I accept that there would be one, presumably about at our bubble centre of mass-equivalent.

I also cannot see why in principle such a bubble BH could not form, containing nothing but photons (though the light intensity should make it an unhealthy place to raise an ecology) but contemplating its nature beats my limited comprehension even without taking my mathematical illiteracy into account. Imagining what happens to the photons at the singularity is positively scary if one gets too graphic.

It is easier to get to a point with smaller potential, but for the same reason it's harder to escape from this point to infinity. When you add a second body, it's harder to escape to infinity from every point.
Escape to the other BH doesn't count as escape. You have to get away to be outside the horizon.

That is common cause, as long as one starts INSIDE an EH. But my fundamental question was about
a) whether external gravitational fields could distort an EH, and
b) in what way.

You have patiently pointed out that one cannot approach it from inside anyway, so that is irrelevant for a start. But in my other questions I was assuming that I started from outside all EHs in question, possibly from quite a generously safe distance, and certainly never cross an EH.
You also have stated that the distortion of the EH is the OPPOSITE from what I had expected, that where I had expected it to shrink locally, it would instead bulge locally. If I understood correctly, this would be because of the mass equivalent of increased local potential energy (correct me if I got that one wrong!)

There is no EH visible from the inside - information will still reach you from the outside

That makes sense, but it raises yet another question. I would expect the incoming light to be viciously blue-shifted, right? And yet, it seems to me that the tidal effect of the gravitation would tend to “stretch” incoming photons the same as it would stretch any other incoming entity, thereby increasing its wavelength, and reducing its energy, which makes no sense. Am I missing something else that should be obvious?

In Newtonian physics, with unbounded speed, yes. In relativity: not necessarily. Time dilation may let you cross the dense region sluggishly (as seen from the outside), so you may want to avoid it if you're in a hurry. The extreme example being a direct hit of a BH there.

Well Ich, we may be at cross purposes here. I accept that the BHs might be too close together for the pilot who knows his craft to risk the interior journey, hurry or no hurry. But for purposes of the exercise it is reasonable to assume that the BHs are well apart. I did in fact say: “...suppose we took a couple of mingy little BHs, a few hundred solar masses each, of roughly equal mass, still far apart, but orbiting each other...”

I grant that “far apart” is a bit vague, but it was meant to suggest that Buck Rogers would be reasonably sure of being able to duck between without having to go relativistic or risk being torn apart by tidal forces.
Bear in mind that the object of the gedankenexperiment was to establish how close to the nearest BH Buck could safely chart his course, depending on whether he went round or smack between. My bet was that if going between was at all practical, it would be the most economical course and would clip the nearer BH most closely.
Did I get that one right?

Thanks for your patience and sorry to be still on at you!

Cheers,

Jon

 

[Jon Richfield]

Here are a couple of links to other videos showing black holes merging-

Thanks Steve, some of those were about as helpful as my by now dizzy mind could assimilate!

Go well,

Jon

 

[Ich]

Hi Jon,

But my fundamental question was about
a) whether external gravitational fields could distort an EH, and
b) in what way.

Ok, I think I see what part of the puzzle I forgot to explain: potential.

I assume you are familiar with potential in the Newtonian theory. In certain circumstances, you have a similar concept in GR.
There, it is a number between 0 and 1. It's 1 far, far away (where the Newtonian potential would normally be set to 0), and it's less in the presence of gravity.
The potential in GR is related to the "flow of time" at a certain point. 1 is the reference, so the number tells you how fast clocks are ticking relative to a clock at infinity.
That means that "time stands still" where the potential becomes 0. That's the EH.
You can't simply add the potentials in GR, but still, if you add matter, the potential at any point becomes less, not more. So the EH is larger in the presence of a second mass.

This is related to your question about the fastest route through a BH cluster: You're already moving near c, so, unlike Newtonian theory, you won't get faster by gravitational attraction. Instead, you enter a region where time passes slower, so you are effectively going slower for an outside observer. You'll want to stay away from that region, but not take a long detour. You'll end up going almost along a "null geodesic", the curved path of light in gravitational lensing.

I would expect the incoming light to be viciously blue-shifted, right? And yet, it seems to me that the tidal effect of the gravitation would tend to “stretch” incoming photons the same as it would stretch any other incoming entity, thereby increasing its wavelength, and reducing its energy, which makes no sense. Am I missing something else that should be obvious?

The tidal effects are not very important for infalling things. Normally, you can neglect them near the EH.
Infalling light is blueshifted for static observers, and redshifted for infalling observers. That's a matter of velocity.

 

[Jon Richfield]

Ok, I think I see what part of the puzzle I forgot to explain: potential.
...
a number between 0 and 1. It's 1 far, far away (where the Newtonian potential would normally be set to 0), and it's less in the presence of gravity.
The potential in GR is related to the "flow of time" at a certain point. 1 is the reference, so the number tells you how fast clocks are ticking relative to a clock at infinity...
You can't simply add the potentials in GR, but still, if you add matter, the potential at any point becomes less, not more. So the EH is larger in the presence of a second mass...

Well Ich, that was in fact helpful, and I really hope you realize how much I appreciate your trouble and patience in this matter. Apart from anything else, it is interesting in a way to see how deeply such a simple concept in Newtonian terms differs diametrically from the consequences of the concepts of GR.
It might be a salutary exercise for a post-graduate to construct a coherent BH theory based on Newtonian axioms. It probably would come out closer to what one finds in SF scenarios.

Infalling light is blueshifted for static observers, and redshifted for infalling observers. That's a matter of velocity.

That was obvious even to me, but it unexpectedly raised a point that I had not thought of before. However, I think I now have a slightly better grasp. Possibly you could verify or correct the following?

Blue- and red-shift in terms of who is moving in which direction always seemed obvious, both in energy and frequency. No problem in either Newtonian or Einsteinian terms. F=MA rules OK!

But if I were stationary in a gravitational gradient, then the consequence of receiving red light from higher up the gradient, or blue light from below, might mean that I receive green light form both, but then it would seem that light from one side had lost cycles (not frequency, but actual cycles) while light from the other direction had gained! Not possible surely?

Now, forcing myself to think about it more carefully, it seems to me that my error lay in forgetting to take into account the fact that time also changes within that gradient, and in the same proportion as frequency. The red light beam contains just as many cycles as before, but with my slower clock, they seem to arrive in a shorter period of time, and hence are blue-shifted.

OK, I still am no GR theorist, but I feel I am closer to comprehension of some of the basics!

Many thanks,

Jon