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Thread: Can gravitational waves escape from a Black Hole?

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    Can gravitational waves escape from a Black Hole?

    I know that we can detect the gravitational waves from 2 BH merging, but I'm wondering something a bit more specific. Lets say you had a supermassive BH, and then you had 2 stellar mass BH that are falling into the supermassive one and are on a trajectory to collide and merge inside the event horizon of the supermassive BH. Would the gravitational waves that resulted from that merger make it outside the event horizon of the BH? What if the merger happened only just inside the event horizon of the supermassive BH such that the singularities of the 2 stellar BH were inside the event horizon of the supermassive BH but their event horizons were overlapping the event horizon of the supermassive BH (I hope that made sense)? Would any gravitational waves be detected then? Thanks!

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    Quote Originally Posted by Dave241 View Post
    I know that we can detect the gravitational waves from 2 BH merging, but I'm wondering something a bit more specific. Lets say you had a supermassive BH, and then you had 2 stellar mass BH that are falling into the supermassive one and are on a trajectory to collide and merge inside the event horizon of the supermassive BH. Would the gravitational waves that resulted from that merger make it outside the event horizon of the BH? What if the merger happened only just inside the event horizon of the supermassive BH such that the singularities of the 2 stellar BH were inside the event horizon of the supermassive BH but their event horizons were overlapping the event horizon of the supermassive BH (I hope that made sense)? Would any gravitational waves be detected then? Thanks!
    If I am not mistaken, as the two smaller black holes fall in, there will not be overlapping event horizons but rather a merged event horizon that is strongly deformed from being spherical and rapidly changing its shape. As the shape is changing the combined system will be emitting gravitational waves that actually carry off some of its total mass. As the infall continues this deformed combined event horizon will "ring down" and return to being spherical, with the gravitational-wave emission diminishing as the ringing subsides. I have no means of figuring what the smaller bodies would look like to a hypothetical observer falling in with them during the period between falling through the original supermassive Schwarzschild radius and being spaghettified toward the center.

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    Quote Originally Posted by Dave241 View Post
    Would the gravitational waves that resulted from that merger make it outside the event horizon of the BH?
    Possibly if it was modeled with mathematical degeneracy as a single or multiple degenerate triangle(s). Wikipedia had a separate page on it many years ago but most of the details seem to have been removed when the pages were merged because their Triangles page appears to makes no mention of it now.

    Google probably describes it in the simplest way.
    An example of a definition that stretches the definition to an absurd degree. A degenerate triangle is the "triangle" formed by three collinear points. It doesn't look like a triangle, it looks like a line segment. A parabola may be thought of as a degenerate ellipse with one vertex at an infinitely distant point.
    https://en.wikipedia.org/wiki/Degeneracy_(mathematics)

    Think of the 'pea and cup' trick where the pea can travel in a straight line but is technically in 2 cups at the same time at the moment it is being transferred from one to the other.

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    Gravitational waves emitted inside the event horizon will not escape - they'll propagate towards the singularity.
    You can't have overlapping event horizons - the supermassive black hole's horizon will move outwards to merge with the event horizons of the infalling black holes.

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    Quote Originally Posted by grant hutchison View Post
    Gravitational waves emitted inside the event horizon will not escape - they'll propagate towards the singularity.
    You can't have overlapping event horizons - the supermassive black hole's horizon will move outwards to merge with the event horizons of the infalling black holes.
    This is kinda what I picture of the merging EHs (about equal in mass), though the circularity at the boundary is likely too circular. [Just bubbles afterall.]

    bubbles combined.jpeg

    I assume that the surface area of the merged BH will be less than the sum of the original two. Is this right? [I'm still curious how to address this dramatic entropy change without a touch of violence.]
    Last edited by George; 2018-Sep-28 at 02:55 PM.
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    Some very interesting shapes appear during a black hole merger. Page back and forth here, for example.
    The surface area of the final black hole event horizon can only be equal to or greater than the combined area of the event horizons of the merging holes - how much greater depends on the mass lost in gravitational waves during the merger.

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    Quote Originally Posted by grant hutchison View Post
    Some very interesting shapes appear during a black hole merger. Page back and forth here, for example.
    Those are interesting and a bit surprising in their structure. Thanks.

    The surface area of the final black hole event horizon can only be equal to or greater than the combined area of the event horizons of the merging holes - how much greater depends on the mass lost in gravitational waves during the merger.
    Is this also true given the significant mass loss in a BHs merger? I don't see how the net EH could not be less.

    [Added: Nevermind. I had already worked this out after the LIGO discovery. The EH size from the 36 solar mass + 29 solar mass more than doubled their original combined sizes. The 3 solar mass loss to the GW only reduced it about 9%.]
    Last edited by George; 2018-Sep-28 at 04:55 PM.
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    Quote Originally Posted by George View Post
    Is this also true given the significant mass loss in a BHs merger? I don't see how the net EH could not be less.
    Remember the area of the event horizon is proportional to M2. If we ignore all the constants, then a a pair of black holes, each with mass 1, would have a combined event horizon area of 2. But if losslessly merged, they would have an event horizon area of 4.

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    Quote Originally Posted by grant hutchison View Post
    Remember the area of the event horizon is proportional to M2. If we ignore all the constants, then a a pair of black holes, each with mass 1, would have a combined event horizon area of 2. But if losslessly merged, they would have an event horizon area of 4.
    Yep, I tried to make the correction above before you posted.

    Still, for that event, the 9% reduction to the EH size suggests the entropy was reduced and this is still hard for me to think there wasn't more than a nice sinusoidal gravity wave generated. A refrigerator's lowering of entropy produces even greater heat. "Where's the heat?" (a takeoff of "Where's the beef?" commercials, which you might not have seen).
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    Quote Originally Posted by George View Post
    Still, for that event, the 9% reduction to the EH size suggests the entropy was reduced ...
    I don't know why you think that. There's a large increase in event horizon area after the merger, which is a large increase in entropy.

    (36+29-3)2/(362+292) = 1.8

    Grant Hutchison
    Last edited by grant hutchison; 2018-Sep-28 at 05:23 PM.
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    Quote Originally Posted by grant hutchison View Post
    I don't know why you think that. There's a large increase in event horizon area after the merger, which is a large increase in entropy.

    (36+29-3)2/(362+292) = 1.8
    What I am wondering is whether or not it could be viewed as a two-step process where the EH increase is 1.98x (no 3 mass loss just yet) then the GW emerges lowering the EH to 1.8x? It would all seem, I suppose, to happen simultaneous to us, but with GR time dilation internally could we not imagine that, for the masses themselves, first a huge increase then suddenly ending with a large decrease separately? And if so, "where's the heat?" -- from the decrease -- perhaps like the grand finale in a fireworks show?
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    Quote Originally Posted by George View Post
    What I am wondering is whether or not it could be viewed as a two-step process where the EH increase is 1.98x (no 3 mass loss just yet) then the GW emerges lowering the EH to 1.8x? It would all seem, I suppose, to happen simultaneous to us, but with GR time dilation internally could we not imagine that, for the masses themselves, first a huge increase then suddenly ending with a large decrease separately? And if so, "where's the heat?" -- from the decrease -- perhaps like the grand finale in a fireworks show?
    I see no reason to see it as a two-step process rather than as a continuously evolving merger process.

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    Quote Originally Posted by Hornblower View Post
    I see no reason to see it as a two-step process rather than as a continuously evolving merger process.
    Agreed, but this is also true for a fireworks display, right? Wouldn't it necessarily require the EH to first become large, perhaps initially greater than 2x given Grant's cool links to modeling of the merging event, but ending (thus along a sequence of time that may be quite long at the EH?) where the ending includes a burst of a GW and a loss of entropy?
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    Quote Originally Posted by George View Post
    Agreed, but this is also true for a fireworks display, right? Wouldn't it necessarily require the EH to first become large, perhaps initially greater than 2x given Grant's cool links to modeling of the merging event, but ending (thus along a sequence of time that may be quite long at the EH?) where the ending includes a burst of a GW and a loss of entropy?
    I don't see the need.

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    The gravitational radiation is emitted while the black holes approach each other, and while the event horizon is asymmetrical (as the peanut shaped event horizon rings down towards symmetry around the rotation axis). So mass is lost in the form of gravitational radiation before, during and after the horizon merger, but not once the event horizon has reached its equilibrium shape.

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    And to be clear, a gravitational wave cannot travel outwards past the event horizon.

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    Quote Originally Posted by grant hutchison View Post
    The gravitational radiation is emitted while the black holes approach each other, and while the event horizon is asymmetrical (as the peanut shaped event horizon rings down towards symmetry around the rotation axis). So mass is lost in the form of gravitational radiation before, during and after the horizon merger, but not once the event horizon has reached its equilibrium shape.
    Ok, so I guess another way to say it is that the wave (mass loss) transpires while the EH is enlarging, and not as if there is a last gasp in the form of a humongous wave pulse (lower entropy event). Logical, but I did so which for some fireworks. Oh well, it does better explain why I never got traction with this when the LIGO news created waves, so to speak. [Even my puns barely make a noise. ]

    At least neutron mergers are more dramatic, especially if the accretion disks are significant.

    Thanks again, all!
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    Quote Originally Posted by grant hutchison View Post
    Gravitational waves emitted inside the event horizon will not escape - they'll propagate towards the singularity.

    Quote Originally Posted by JCoyote View Post
    And to be clear, a gravitational wave cannot travel outwards past the event horizon.
    Thanks for the answers guys! So for my little thought experiment, it would seem the answer is that gravitational waves will be produced when each BH crosses the event horizon of the SMBH, but no additional gravitational waves will be emitted when the 2 BH merge inside the event horizon of the big SMBH.

    My reason for asking this is because we can obviously still feel the gravity of the singularity outside of the event horizon, so I wasn't sure if that meant that gravity waves could also get out of the event horizon too.

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    I would not say "gravity of the singularity", as that tends to motivate the thinking of something "getting out" by crossing the event horizon. I think of gravity as an artifact of the curved spacetime that goes with a concentration of mass, and the gravitational signature of a collapsing spherical body reaches its final state as soon as the body has contracted to being inside its Schwarzschild radius. For something non-spherical, such as our three merging black holes, we temporarily have a misshapen combined event horizon which "rings down" and soon becomes spherical. As I see it the churning spacetime around this system is the source of outgoing gravitational waves. My hunch is that a description of the fate of the two small black holes is going to be more complicated than a simple collision just inside the original Schwarzschild radius of the big one.

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    Quote Originally Posted by Dave241 View Post
    Thanks for the answers guys! So for my little thought experiment, it would seem the answer is that gravitational waves will be produced when each BH crosses the event horizon of the SMBH, but no additional gravitational waves will be emitted when the 2 BH merge inside the event horizon of the big SMBH.

    My reason for asking this is because we can obviously still feel the gravity of the singularity outside of the event horizon, so I wasn't sure if that meant that gravity waves could also get out of the event horizon too.
    Well, keep in mind that the EH is where causality and information transfer go to die. IOW the EH is itself, the last possible form of gravitational information before the cutoff: a "no exit" sign.

    IMO asking if gravity borne information can "pass" an EH is kind of like asking, can light reflect off a rainbow. Not meant snarkily, it is a literal comparison. Rainbows are an artifact of light and water. EH is an artifact of information and gravity.
    Last edited by Noclevername; 2018-Sep-30 at 03:11 AM.
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