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Thread: Accuracy of a black hole's "inner horizon" and "space falling faster than light"

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    Accuracy of a black hole's "inner horizon" and "space falling faster than light"

    In this video, Professor Andrew Hamilton says some things which sound plausible, as well as a couple of things which do not.

    Comments?

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    The issues he brings up have (IIRC) been discussed in the ATM thread on "RussT's rotating black hole", it's 4 pages to read through, but it gives some nice information by Ken (about space falling faster than light) and publius (about the inside of a rotating black hole - inner horizon).

    ETA:
    KenG was saying that it is an easy coordinate choice to say that space itself is falling faster than light, it is equivalent to other choices, but an easy one to conceptually work with.

    I think the discussion came to the conclusion that chances are way too high that we can't trust our theoretical predictions on what would happen one the 'inside' of a Kerr (rotating) black hole. Publius adding that any disturbance (matter falling in etc) in a Kerr black hole provide an unstable deviation - whereas for a 'normal' nonrotating black hole, the deviation would be stable, it would return to the 'baseline' by itself.

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    He's offering an interpretation of the metric which seems to be fairly common: a way of imagining how a photon (travelling locally at the speed of light) can hover at the event horizon for an external observer. "Space" is going inwards as fast as the photon is going outwards.

    The inner horizon he mentions is a feature of the Kerr metric for rotating black holes. It's a surface at which matter and energy "piles up" as he describes, also called the Cauchy horizon. The familiar outer horizon seems to form in a predictable way, but the Cauchy horizon, although present in the maths, is sensitive to the nature of the collapse that forms the black hole, and may not actually form.

    ETA: I copied out some stuff from a reference source, relating to the Cauchy horizon, here.

    Grant Hutchison

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    Quote Originally Posted by caveman1917 View Post
    The issues he brings up have (IIRC) been discussed in the ATM thread on "RussT's rotating black hole"...
    No. If this were true, I wouldn't be bringing them up.

    Quote Originally Posted by grant hutchison View Post
    He's offering an interpretation of the metric which seems to be fairly common: a way of imagining how a photon (travelling locally at the speed of light) can hover at the event horizon for an external observer. "Space" is going inwards as fast as the photon is going outwards.
    Again, no. What's with you guys? You want to pass this off as a previously asked question so you don't have to think? Come on!

    Conditions:

    1. Free-falling observer.

    2. Rotating BH - may or may not be.

    What I'm looking for, as exceptionally well-stated in the OP, is this (restated from the OP): "In this video, Professor Andrew Hamilton says some things which sound plausible, as well as a couple of things which do not.

    Comments?"

    Avoid the video, folks. Please comment on Professor Hamilton's view of what's inside a black hole, if you would, please. And please refrain from ascribing to my own OP things which either aren't there, or are simply ancillary in nature, perhaps being coincidental from previous posters.

    I don't care if they're coincidental - Let's focus on my question, instead - what you think of Professor Hamilton's video, and how he describes black holes.

    Thanks.

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    As Grant and Caveman said, these points were discussed in very recent threads. There is nothing that Grant or Caveman said that deserved that response of yours.

    The professor describes the common (hybrid coordinate) picture of "space falling at light speed" at the horizon, then goes on to describe the features of the inner Cauchy horizon of a Kerr hole, and Grant and Caveman responded accordingly.


    -Richard

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    Quote Originally Posted by mugaliens View Post
    2. Rotating BH - may or may not be.
    Must be. The description in the video is concerning the Cauchy horizon, which only exists with rotating black holes.

    I don't care if they're coincidental - Let's focus on my question, instead - what you think of Professor Hamilton's video, and how he describes black holes.
    Could it be that you have missed the part where he specifies he is talking about a Kerr black hole? This is not a description of black holes in general - and neither does he claim so.

    He starts of with some general "easy way to think of a black hole as a region where space is falling in faster than light" (direct quote). One could take this to mean from an outside observer, given the context of the point in the video it is brought up.
    No suprises there.
    Then there is (~1min) a 'break' and he starts describing what would happen if you'd fall into a rotating black hole.
    Which is exactly the same what Grant pointed you to, and starting from that post the whole thing was already dissected in the ATM thread.

    Now here's something interesting (for those who followed the ATM thread) he says (~1:10)
    If that black hole is rotating - and surely all of them do

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    Quote Originally Posted by mugaliens View Post
    Let's focus on my question, instead - what you think of Professor Hamilton's video, and how he describes black holes.
    He describes them very well, and completely plausibly, for reasons that have been provided already.
    The only question in your OP is "Comments?" which is a little difficult to "focus" on. I chose to address the two implied questions in your thread title, and it seems others have done the same thing.
    If that's not what you wanted to hear about, perhaps you need to frame some more specific questions. However, given the gracelessness of your responses so far, I won't be participating further.

    Grant Hutchison

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    Ok, more to the point, I understand GR's warping of space-time and geodesics, but I'm uncertain as to how it's possible for space to fall faster than light. Is it a misstatement, in that the warping of space-time cannot exceed lightspeed any more than anything else can exceed it (i.e. it's asymptoptic at c), or is it that gravity can indeed warp space-time to an extent greater than c?

    I'm assuming the latter. It's just that the former seemed more consistant with "nothing exceeds c," thought upon thinking about it, I can see that it doesn't jibe with the idea of an EH simply being the point where gravitational distortion actually equals c.

    But then this brings into question another statement the professor made, that once inside the EH gravitational distortion lessens. This doesn't sound plausible, for if gravity is concentrated at the singularity, the closer one gets, the greater the distortion. In fact, it seems that once inside the EH, each successive depth experiences the same EH-life effects all the way down to the singularity at the center. Thus, the EH seems to be more like a shell-like effect extending from the EH surface to the singularity center.

    Yet this is nothing like how the professor described it. It's not like how it's been described here on BAUT, either, where most answers have been "we really don't know."

    It's the disparity between these three camps which motivated me to ask what you folks thought about the professor's video and provide a response.

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    I am by no means an expert on GR, but i'll give it a shot.

    First of all it is important to understand that the limit at c is only a local limit. Meaning that any observer can not measure anything going above c, in his local coordinate system (ie his local 'patch' of space-time).

    Quote Originally Posted by mugaliens View Post
    Ok, more to the point, I understand GR's warping of space-time and geodesics, but I'm uncertain as to how it's possible for space to fall faster than light.
    Let's put this in context, the coordinate system where it is thought that space falls faster than light is that relative to an outside observer. It is how 'we' (standing a good deal away from this EH) can conceptualise what is going on at the EH. Let's however consider an observer that is on the EH. He can not measure anything going faster than c, since his local coordinate system takes space as stationary. The limit of c is that nothing can move faster than c relative to its local coordinate system, and this 'rule' isn't broken in this case. There is nothing preventing space itself from going faster than light.

    Many other examples exist here. Take for instance the inflation period, that was space expanding (moving) faster than c. And even still now, places far enough away from us would be moving >c relative to us. But that is again space itself expanding, if you were on such a galaxy, locally you wouldn't move faster than c relative to your own 'patch' of space.

    Someone even got the idea to use this effect for making a warp drive, see alcubierre drive.

    or is it that gravity can indeed warp space-time to an extent greater than c?
    This is a tricky one.
    Gravity is nothing more than the curvature of space-time in the presence of energy. This curvature is static as long as the energy content producing it doesn't change. The curvature of spacetime is not a process with some speed, it is a static way of describing the geometrical background. It would be like asking what the speed is of the curvature of earth.
    But it is a curvature of spacetime - not just space and that's why if one curves it enough, one gets all sorts of funny effects. Such as space moving faster than c, spatial dimensions and time dimension switching places, etc.
    The thing that is limited to c is changes to this curvature. For example suppose we add some mass to the black hole, then this change of the curvature will propagate at c.

    But then this brings into question another statement the professor made, that once inside the EH gravitational distortion lessens. This doesn't sound plausible, for if gravity is concentrated at the singularity, the closer one gets, the greater the distortion. In fact, it seems that once inside the EH, each successive depth experiences the same EH-life effects all the way down to the singularity at the center. Thus, the EH seems to be more like a shell-like effect extending from the EH surface to the singularity center.
    Once again, it is imperative to consider that the professor is describing a rotating black hole.
    The difference is that the singularity is not localized in a single point, but more like a circle or torus. Massive framedragging should also occur.
    This particular kind of black hole seems to have two different horizons, and that's where the effect of 'lessening' of curvature comes from.
    In a nonrotating black hole (such as you seem to be thinking off) this indeed does not happen.

    You may want to review the Kerr metric which describes rotating black holes such as the one the professor was talking about.

    Yet this is nothing like how the professor described it. It's not like how it's been described here on BAUT, either, where most answers have been "we really don't know."

    It's the disparity between these three camps which motivated me to ask what you folks thought about the professor's video and provide a response.
    There is no disparity between the camps, they are simply talking about different things.

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    Finally - a good response!

    Quote Originally Posted by caveman1917 View Post
    I am by no means an expert on GR, but i'll give it a shot.

    First of all it is important to understand that the limit at c is only a local limit. Meaning that any observer can not measure anything going above c, in his local coordinate system (ie his local 'patch' of space-time).
    So, at the EH, our stationary observer is observing matter falling in at an asymptotically velocity equivalent to c, and right on c's heels, if not having just latched onto them as both matter and energy pass our stationary, and thus accelerating observer.

    Let's put this in context, the coordinate system where it is thought that space falls faster than light is that relative to an outside observer. It is how 'we' (standing a good deal away from this EH) can conceptualise what is going on at the EH.
    Ok. To us it appears both light and ordinary matter are travelling precisely at c, but only at the moment they pass through the EH.

    Let's however consider an observer that is on the EH. He can not measure anything going faster than c, since his local coordinate system takes space as stationary. The limit of c is that nothing can move faster than c relative to its local coordinate system, and this 'rule' isn't broken in this case.
    But if spacetime is falling faster than c, and the observer is stationary, and matter within that spacetime is falling at a rate relative to that spacetime...

    My head's beginning to spin, again.

    There is nothing preventing space itself from going faster than light.
    Along with the matter freely falling within it?

    You see my quandry, here. Yes, I'm familiar with the thought scenario of three rockets, all of which are travelling in a straight line, but the 2nd is .5 c faster than the 1st, and the 3rd is .5 c faster than the 2nd. I get it. What I'm having a difficult time with is translating this to our friendly neighborhood black hole's EH with respect to boh free-standing as well as free-falling observers (oh, bungee jumping - not my forte).

    Many other examples exist here. Take for instance the inflation period, that was space expanding (moving) faster than c. And even still now, places far enough away from us would be moving >c relative to us. But that is again space itself expanding, if you were on such a galaxy, locally you wouldn't move faster than c relative to your own 'patch' of space.
    Ok, so put simply, the non-conflict with space-time expansion faster than c beyond the CMB is little different (if at all different) than the +c space-time expansion (stretching, acceleration, etc.) resulting from local space-time warping due to the black-hole.

    I suppose the question then becomes, since we know local BH effects are caused by gravity, what of observable universe space-time expansion - are they also a reflection of gravity?

    This is a tricky one.
    Hmm...

    Gravity is nothing more than the curvature of space-time in the presence of energy. This curvature is static as long as the energy content producing it doesn't change. The curvature of spacetime is not a process with some speed, it is a static way of describing the geometrical background. It would be like asking what the speed is of the curvature of earth.

    But it is a curvature of spacetime - not just space and that's why if one curves it enough, one gets all sorts of funny effects. Such as space moving faster than c, spatial dimensions and time dimension switching places, etc.

    The thing that is limited to c is changes to this curvature. For example suppose we add some mass to the black hole, then this change of the curvature will propagate at c.
    Ok, so the change of propogation is limited by c, but the warping of spacetime is not...

    ? Something's not jibing, here...

    Once again, it is imperative to consider that the professor is describing a rotating black hole.

    The difference is that the singularity is not localized in a single point, but more like a circle or torus. Massive framedragging should also occur.
    Well, the framedragging explains a lot with respect to local variations of gravity differing from that of a static, non-charged, non-rotating black hole, but...

    This particular kind of black hole seems to have two different horizons, and that's where the effect of 'lessening' of curvature comes from.
    Or perhaps an EH which is based upon the movement of the observer?...

    In a nonrotating black hole (such as you seem to be thinking off) this indeed does not happen.

    You may want to review the Kerr metric which describes rotating black holes such as the one the professor was talking about.
    Thanks. I'm on it.

    There is no disparity between the camps, they are simply talking about different things.
    Ok, I'm more or less getting this, now. For some reason, a couple of years ago I never made the connection between expansion and local gravitational acceleration, but it appears they're the same, no?

    If so, this brings me back to my previous question concerning the mechanism of expansion, the the deeper I look at this the less I'm buddy to the idea it's due to "dark energy," but rather an idea I had much earlier which explains it but is not widely accepted by the mainstream (thus my not bringing it forth here).

    Thanks, folks.

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    Quote Originally Posted by mugaliens View Post
    So, at the EH, our stationary observer is observing matter falling in at an asymptotically velocity equivalent to c, and right on c's heels, if not having just latched onto them as both matter and energy pass our stationary, and thus accelerating observer.



    Ok. To us it appears both light and ordinary matter are travelling precisely at c, but only at the moment they pass through the EH.



    But if spacetime is falling faster than c, and the observer is stationary, and matter within that spacetime is falling at a rate relative to that spacetime...

    My head's beginning to spin, again.



    Along with the matter freely falling within it?

    You see my quandry, here. Yes, I'm familiar with the thought scenario of three rockets, all of which are travelling in a straight line, but the 2nd is .5 c faster than the 1st, and the 3rd is .5 c faster than the 2nd. I get it. What I'm having a difficult time with is translating this to our friendly neighborhood black hole's EH with respect to boh free-standing as well as free-falling observers (oh, bungee jumping - not my forte).
    It's always important to be consistent from what observer we are looking at things.

    Let's visualise it in another way. You know those electric moving stairs one finds at malls and so? (i don't know the english term for them).
    At airports you also get 'flat' ones, not stairs. Like a moving sidewalk. You know what i mean?

    Let's say that this sidewalk contains an observer A (a person), together with some luggage (free falling matter) and a flashlight.
    Let's also say this sidewalk has a different speed at every point, at the beginning of the 'track' it is stationary relative to the ground next to it. It always goes faster and faster until it reaches a point where it goes at c - and here we draw a line next to it on the ground saying 'EH'. And beyond that it even goes faster than c.

    Now let's consider what happens from the perspective of some other observer B standing on the stationary ground at the beginning of this sidewalk. He sees A (together with his stuff) starting to move away from him. At the point where say the speed of the sidewalk is 0.5c, A puts on his flashlight and some photons start moving back towards B. These will always move at a local speed of c (relative to the point of the sidewalk where they are at that moment). From B's perspective they will arrive 'late', they needed more time to cross the distance between A and B than would be suggested by c. Their speed is c - vs (vs is the speed of the sidewalk at that point) - in the usual manner the speed of someone running on a moving sidewalk is v - vs. However at all points along the way a local observer will measure c, since that observer will also be moving with the sidewalk at -vs, the 'vs' terms thus cancelling out. That is what is meant by c being only a local limit. B would think light only travelled at 0.5c at the start, but that's not a problem - it only locally needs to travel at c.
    You could also think of the redshift the light incurred from A to B as the extra energy loss it needed to overcome the movement of the sidewalk.

    Now let's say A has reached our little line on the ground, the EH. The sidewalk is now moving at exactly c. A shines his flashlight again. Now from B's perspective light will appear stationary: 'v - vs'; v = c; vs = c. But again, locally there's no problem. A is standing on the sidewalk, so the vs term dissapears. You could think of the photon being stationary at the EH, but A himself moving (with the sidewalk) at c - once again the relative speed of the photon is locally c. It is however impossible at this point for A to remain stationary (to B). He would have to run at exactly c relative to his sidewalk to do this, but he can't accelerate that much. Hence the EH being the point of no return.
    From B's perspective A would be moving at c (due to the sidewalk - but still). And this can't be. However B can never see this happen - the photons (and thus information) on this can never reach back to B - they are stationary at the EH.

    From the moment things would get 'fishy' - the EH cuts of causal contact preventing that from appearing to B.

    Now let's consider A going beyond the EH. The sidewalk will now be moving >c. If B could see this, he would think A is moving faster than light. But once again no photons can reach back to B - so the problem never occurs. The specifics at the EH will always 'save the day'.

    If you'd do the scenario again, but from the perspective of A, you'd see it all plays out perfectly again.


    Ok, so put simply, the non-conflict with space-time expansion faster than c beyond the CMB is little different (if at all different) than the +c space-time expansion (stretching, acceleration, etc.) resulting from local space-time warping due to the black-hole.

    I suppose the question then becomes, since we know local BH effects are caused by gravity, what of observable universe space-time expansion - are they also a reflection of gravity?
    No, i only said that to give other examples of space moving faster than c, to point out the concept isn't that weird at all. I didn't mean to imply that the causes of these different examples are related - they aren't.

    Ok, so the change of propogation is limited by c, but the warping of spacetime is not...
    You're probably having troubles because you consider it a 'warping' - which implies a process occuring in spacetime - it is not. It is a static property of spacetime.
    That's why it's easier to consider it in the correct terms, a 'curvature' of spacetime.

    Consider having a piece of paper. We can define 'curvature' in this case as a number saying how 'far away' it is from being flat.
    We start with a flat paper - the curvature thus being 0. Now start crumbling it, this is changing its curvature (making it non-flat) - these changes can only propagate at c.
    When you have crumbled it plenty, put it back on the table. We might say the paper now has a curvature of say 10. But that is a static property. If you don't touch the paper anymore, it just remains sitting there with a curvature of 10, there is nothing moving. The curvature remains 10, nothing whatsoever happens to it that we can ascribe a speed to.

    Or perhaps an EH which is based upon the movement of the observer?...
    An EH is always based upon the movement of the observer. Even in perfectly flat spacetime, an observer that has a constant acceleration in some direction will see an EH 'pop up' behind him.
    But with these comparisons we are always considering free-falling observers, and the effect of having 2 horizons is certainly there. Not considering the uncertainty with the Kerr metric behind the first EH - it is likely the description is wrong at that point.

    Ok, I'm more or less getting this, now. For some reason, a couple of years ago I never made the connection between expansion and local gravitational acceleration, but it appears they're the same, no?

    If so, this brings me back to my previous question concerning the mechanism of expansion, the the deeper I look at this the less I'm buddy to the idea it's due to "dark energy," but rather an idea I had much earlier which explains it but is not widely accepted by the mainstream (thus my not bringing it forth here).
    I'll repeat here that i only meant those as seperate examples of space moving faster than c, not that they are related in any other way.

    Thanks, folks.
    You're welcome.

    As a parting thought though, you can catch more flies with honey than with vinegar

    ETA: remember that this way of putting it 'space moving faster than c' is only an easy coordinate choice B can take to conceptualize what's going on - many other coordinate choices are also possible, just a lot harder to work with conceptually.
    Last edited by caveman1917; 2010-Aug-08 at 09:49 PM.

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    Hmm, very interesting visualisation.

    I'm suddenly seeing black holes surrounded by moving sidewalks! ;-)

    Further to that;
    -If spacetime itself gets stretched and pulled into a black hole, to an external observer even exceeding the speed of light, would that happen to some extent with all objects that give off gravity?

    Seems like spacetime behaves a bit like plate techtonics then, Accelerating expansion creates more spacetime that then gets pulled in by the "subduction zones" of gravity.
    Moving sidewalks all around..
    No wonder the large scale structures of the universe looks like bubbles.. :-)

    /Peter

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