Are black holes spherical during merger?

  • I've been thinking about black holes, specifically during the final moments before two merge. I'm wondering if black holes, or I guess more specifically their event horizons, are always spherical. It seems to me that in the moments before two merge, their respective event horizons will be stretched, somewhat like how the Moon causes our ocean's tides. I have drawn a (poor) diagram of what I think they may look like. Notice how the event horizons are closer to the singularity on the inner side, this is because the gravity from each black hole is in opposition. The event horizons are further from the singularity on the outer side because the gravity from each black hole adds up.
    enter image description here


    One problem with this question is that, by definition, a black hole is a place where space and time are quite distorted and things are generally happening rather quickly. So simply asking what shape the event horizons are at a particular moment is not really a well-defined question. Defining which events are happening at the same time is a somewhat arbitraru process depending on the observer, while defining "shape" meaningfully needs quite a bit of differential geometry. The SXS simulations (https://www.black-holes.org/) make an attempt and you can read their papers for the details.

  • Florin Andrei

    Florin Andrei Correct answer

    2 years ago

    No need to guess. There's solid research done in this field. Even Wikipedia has some info:




    As two black holes approach each other, a ‘duckbill’ shape protrudes
    from each of the two event horizons towards the other one. This
    protrusion extends longer and narrower until it meets the protrusion
    from the other black hole. At this point in time the event horizon has
    a very narrow X-shape at the meeting point. The protrusions are drawn
    out into a thin thread. The meeting point expands to a roughly
    cylindrical connection called a bridge.




    https://en.wikipedia.org/wiki/Binary_black_hole#Shape



    There are research papers with images showing the results of calculations of the shape of the event horizons during merger. Here's an example:



    enter image description here



    The image above is taken from this paper:



    On Toroidal Horizons in Binary Black Hole Inspirals




    We examine the structure of the event horizon for numerical
    simulations of two black holes that begin in a quasicircular orbit,
    inspiral, and finally merge. We find that the spatial cross section of
    the merged event horizon has spherical topology (to the limit of our
    resolution), despite the expectation that generic binary black hole
    mergers in the absence of symmetries should result in an event horizon
    that briefly has a toroidal cross section.



    +1 Lovely pictures. I appreciate how the xyz-axes in the corners contribute absolutely nothing.

    @user28113: The black holes started on the YZ plane.

    I think you mean XZ plane... but yeah, they really don't add anything useful haha.

    @user28113 The coordinates make sense in the context of the simulation described in the paper. These are the actual results of numeric analysis - not "an artist's impression" of the phenomenon.

    The diagram seems to assume that a black hole is rubber-like; a rubber sphere, if you will. I only point this out because most here assert that a black hole isn't solid in any way (bar, I assume, the alleged singularity), and that you wouldn't even know if you passed the event horizon. So, are black holes rubbery spheres or what, mate? With all due respect.

    @WhitePrime Black holes are basically just powerfully distorted spacetime. At the singularity our math blows up so it's pointless to talk much about that. The event horizon is the boundary where things get different in many ways - but it's not a line drawn in the sand, nor is it a "solid object". It's more like the Equator - you know it's there, you can measure and calculate it, but there is no white line on the ground that says "Equator". The shape of the event horizon is influenced by rotation, other massive bodies nearby, etc. It would be spherical for a static, isolated black hole.

    @Florin Andrei But, in descriptions of black hole mergers, it's always asserted that they 'wobble' before quickly regaining shape.

    @WhitePrime They do, yes. But rubber balls are not the only things that can "wobble". Spacetime itself can wobble. Particles in a magnetic trap could wobble. Entire universes could wobble if conditions are right. "Wobbling" simply means there's a force that opposes a deformation, and it brings the system back to the initial point, but it overshoots and is deformed in the opposite direction, and then it's brought back again, etc. Many things can do this.

    Square smoke rings wobble. As for the boundary that is called the event horizon, it is simply the demarcation of a region of space inside of which we, being on the outside, cannot assign a "when" to any event that occurs on the inside. Stuff happens in there, but we'd need to wait an infinite amount of time to see it.

    FWIW, there's a nice image and a short but gorgeous video of a simulated merger here, courtesy of the Max Planck Institute for Gravitational Physics. However, that sim makes a couple of major simplifications, as mentioned in the text.

    But if black holes distort spacetime, then XYZ axes really don't mean anything at all. :’’’(

    @FlorinAndrei : You may need a different example than the Equator.

    @biziclop Not true. The distortions are not arbitrary, they can be calculated precisely.

    @biziclop Because the planet's spherical, latitude and longitude lines on a map really don't mean anything at all.

    @user28113 This may well be an artifact of the program used to visualize the graph.

    @FlorinAndrei BTW, there *is* a line on the ground marking the Equator, at the El Mitad Del Mundo monument in Ecuador. Huge tourist attraction: everyone wants a photo of them with one foot in each hemisphere! Unfortunately, some 260 years after the site was first marked, the advent of GPS revealed that the *real* exact 0° latitude is about 200m away... but there's now a line there too, at the Inti Nan museum :-)

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