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Thread: Event Horizon Shape

  1. #1
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    Event Horizon Shape

    Hi everyone.

    If a black hole was in a binary system, I was wondering would the event horizon remain spherical or would it be elongated due to tidal forces.

    Can this tell us anything about the internal structure? If it distorts, then internally cannot be a singularity, as a point would not feel tidal forces. If it remains spherical, would this prove a singularity?

    Some years ago, LIGO detected two black holes of super-stellar mass merging. Can gravitational waves tell us if the event horizons were distorted in the process?

    Many thanks.

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    Yes, there is a distortion of the event horizon, similar to, but not identical to, what we see with solid bodies.
    The shape of the singularity isn't affected, just the trajectories of photons in the vicinity of the event horizon. In essence, the presence of an additional mass nearby means that photons which would otherwise be able to escape to infinity are instead doomed to head for the singularity instead.

    There was an interesting series of papers a few years ago, which include some visualizations of the event horizon shape under tidal gravity.
    Part 1
    Part 2
    Part 3

    (Just scroll past the algebra to reach the diagrams. Notice in Part 3 that the event horizon shape for very rapidly rotating black holes can't be visualized in normal Euclidean space, even before we apply tidal effects.)

    Grant Hutchison

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    Quote Originally Posted by sdsperth View Post
    Hi everyone.

    If a black hole was in a binary system, I was wondering would the event horizon remain spherical or would it be elongated due to tidal forces.

    Can this tell us anything about the internal structure? If it distorts, then internally cannot be a singularity, as a point would not feel tidal forces. If it remains spherical, would this prove a singularity?

    Some years ago, LIGO detected two black holes of super-stellar mass merging. Can gravitational waves tell us if the event horizons were distorted in the process?

    Many thanks.
    There are some nice videos about the shape of the event horizon as two black holes merge. You are right. They do not stay spherical during the merger. They (it) do(es) return to spherical shortly after the merger. I believe that you are right to think that LIGO detects this.
    Forming opinions as we speak

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    Quote Originally Posted by antoniseb View Post
    There are some nice videos about the shape of the event horizon as two black holes merge. You are right. They do not stay spherical during the merger. They (it) do(es) return to spherical shortly after the merger. I believe that you are right to think that LIGO detects this.
    Yes, there would be no ringdown phase to the gravitational wave signature if the paired black holes didn't form a transiently distorted event horizon before settling into equilibrium.

    Grant Hutchison

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    Quote Originally Posted by grant hutchison View Post
    Yes, there is a distortion of the event horizon, similar to, but not identical to, what we see with solid bodies.
    Grant Hutchison
    Thanks Grant. Is it fair to say that if the event horizon of a black hole in a binary system is not distorted by tidal forces that there is indeed a singularity inside? I hear theories of degenerate matter and even ideas of matter smeared out across the event horizon. Surely the latter would be subject to said tidal forces?

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    Quote Originally Posted by sdsperth View Post
    Thanks Grant. Is it fair to say that if the event horizon of a black hole in a binary system is not distorted by tidal forces that there is indeed a singularity inside?
    I think "tidal forces" is perhaps the wrong expression when it comes to event horizons. The event horizon isn't an object, it's a locus of spacetime separating regions from which photons can escape and regions in which all photons are drawn to the singularity. The presence of another mass shifts the location of the event horizon because it changes the shape of spacetime. It doesn't matter whether or not there's a "physical" singularity at the centre of the black hole; what matters is the combined spacetime curvature produced by the black hole and the gravity of the second object. If the event horizon didn't respond to the presence of a nearby mass, there would be something wrong with General Relativity.

    Grant Hutchison

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    Quote Originally Posted by sdsperth View Post
    Thanks Grant. Is it fair to say that if the event horizon of a black hole in a binary system is not distorted by tidal forces that there is indeed a singularity inside? I hear theories of degenerate matter and even ideas of matter smeared out across the event horizon. Surely the latter would be subject to said tidal forces?
    A point-source singularity and a self-gravitated sphere of degenerate matter would both produce the same shape of event horizon, IIRC.

    As far as matter "smeared out" I'm not at all familiar with that concept so I am not certain of the specifics. It seems unlikely based on current knowledge of gravity.
    "I'm planning to live forever. So far, that's working perfectly." Steven Wright

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    Quote Originally Posted by Noclevername View Post
    A point-source singularity and a self-gravitated sphere of degenerate matter would both produce the same shape of event horizon, IIRC.
    Hi Noclevername
    I'm with you on this, but if it's a sphere of degenerate matter, can that sphere be deformed by tidal forces, and if so, will the event horizon also be deformed. My thinking is that a singularity cannot be deformed and so the event horizon shape might tell us something about the internal structure (albeit very difficult to observe).

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    Quote Originally Posted by sdsperth View Post
    ... if it's a sphere of degenerate matter, can that sphere be deformed by tidal forces, and if so, will the event horizon also be deformed. My thinking is that a singularity cannot be deformed and so the event horizon shape might tell us something about the internal structure (albeit very difficult to observe).
    If the resulting collapsed matter is not a singularity, it will likely be spinning and be in the form of a disk. In about 25 years facilities similar to LIGO, but much more sensitive, will begin to set limits on the nature of what is inside the event horizons of stellar mass black holes from merger events. The ALIGO+ that will be online about 2024 will show a little more detail in the shape of the GW signals, and will be able to rule out a few of the more extreme models of structure within the event horizon, but it will be a few decades before really satisfying measurements of that can be made.
    Forming opinions as we speak

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    Quote Originally Posted by antoniseb View Post
    The ALIGO+ that will be online about 2024 will show a little more detail in the shape of the GW signals, and will be able to rule out a few of the more extreme models
    Thanks antoniseb. That sounds incredible. This is truly a golden age.

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    Inspiral, coalescence, ringdown; ah, the poetry of black hole mergers.

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    Maybe this is what you all are talking about, but if two black holes are merging, are they always on the verge of merging and never merged?
    The moment an instant lasted forever, we were destined for the leading edge of eternity.

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    I am kind of asking is it possible for a singularity to ever form since time slows down so much that the actual singularity could never form.
    The moment an instant lasted forever, we were destined for the leading edge of eternity.

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    Quote Originally Posted by Copernicus View Post
    Maybe this is what you all are talking about, but if two black holes are merging, are they always on the verge of merging and never merged?
    No, they merge. We have observational evidence of that now, in the form of the ringdown signal from gravitational wave detections.
    The whole thing about "time stops at the event horizon" is a red herring, because the event horizon is what changes size and shape. So the region of spacetime where the Schwarzschild time coordinate shoots off too infinity is the thing that moves.

    "That infalling object can never reach the event horizon, because time will slow to a halt before it reaches the event horizon.
    "Yikes. The event horizon just got bigger and engulfed the falling object."

    Quote Originally Posted by Copernicus View Post
    I am kind of asking is it possible for a singularity to ever form since time slows down so much that the actual singularity could never form.
    Time doesn't slow down for the stuff forming the singularity. What "really" happens is a matter for local observers.

    Grant Hutchison

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    What shape would the event horizon be if a black hole did not spin?
    I know that I know nothing, so I question everything. - Socrates/Descartes

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    Quote Originally Posted by DaCaptain View Post
    What shape would the event horizon be if a black hole did not spin?
    Spherical. That's the classic Schwarzschild metric.

    Grant Hutchison

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    Quote Originally Posted by grant hutchison View Post
    Spherical. That's the classic Schwarzschild metric.

    Grant Hutchison
    I take it this sphere is the same weather the BH is spinning or not?
    I know that I know nothing, so I question everything. - Socrates/Descartes

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    Quote Originally Posted by DaCaptain View Post
    I take it this sphere is the same weather the BH is spinning or not?
    It gets complicated, because there are various coordinate choices to describe a rotating black hole, and some (according to my understanding, at least) produce a fixed radius for the outer event horizon, and some produce an ellipsoid, flattened at the poles. And if you look at the curvature of the event horizon, then you can consistently embed the horizon shape in Euclidean space for slowly rotating black holes, and it looks like an ellipsoid. But there's a threshold of rotation rate above which the curvature becomes negative at the black hole's poles, and you produce a shape that you can't display in "flat" Euclidean space.

    (You can make different coordinate choices for a non-rotating black hole too, of course, but they all produce a spherical event horizon.)

    Grant Hutchison
    Last edited by grant hutchison; 2020-Sep-01 at 01:07 AM. Reason: Bracketed

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    Quote Originally Posted by grant hutchison View Post
    But there's a threshold of rotation rate above which the curvature becomes negative at the black hole's poles, and you produce a shape that you can't display in "flat" Euclidean space.
    Hmm, so are you saying the event horizon looks like a donut?
    I know that I know nothing, so I question everything. - Socrates/Descartes

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    Quote Originally Posted by DaCaptain View Post
    Hmm, so are you saying the event horizon looks like a donut?
    Nope. Donuts (torii) are 3D, easily pictured shapes. A Non-Euclidean from is not so easy to visualize.
    "I'm planning to live forever. So far, that's working perfectly." Steven Wright

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    Quote Originally Posted by DaCaptain View Post
    Hmm, so are you saying the event horizon looks like a donut?
    No, definitely not. It absolutely doesn't have a hole in the middle. Spacetime is so strongly curved around rapidly rotating black holes that the event horizon has a shape you simply can't portray in flat Euclidean space. The curvature of the event horizon near the poles is concave, rather than convex, but the radial coordinate of the event horizon doesn't increase towards the poles. So if you wanted to model the curvature, you'd give the event horizon polar spikes--but if you modelled the radial coordinates there would be no spikes. So there's no way you can assign such an object a consistent shape that you could carve out of a block of wood or mould in plastic.

    Grant Hutchison

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    Not related to a event horizon shape but are there colors that a black hole progresses through before it's black? Or is it instantly black? Do all colors of light get effected by gravity the same?
    I know that I know nothing, so I question everything. - Socrates/Descartes

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    I assume you're talking about a stellar-mass black hole, forming from a collapsing star? The light from the infalling surface is progressively red-shifted, with all frequencies affected in the same proportion. That doesn't mean that it would appear red, however--it depends on the shape of the spectrum that is shifted into the visible spectrum. Very hot black bodies have a self-similar spectrum up to very high frequencies, so the redshifted spectrum is still blue-dominated through a wide range of redshifts, and doesn't even change colour very much. You might therefore see the surface dim into invisibility while still appearing blue. There would be a lot of physics involved in working out exactly what the appearance would be, I imainge.

    Grant Hutchison

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