Should a black holes binary system in fase of imminent merge shrink the inner parts of the event horizons of both black holes where they directly face each other? So the 'singularities' have the inner part of the event horizons (the parts of both event horizons that face each other) closer to them than the outer part (the parts of both event horizons that are far from the center of rotation) as their gravities subtract themselves at the inner parts of horizons but add up at the far parts of the horizons?
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asked May 29, 2022 at 10:21
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$\begingroup$ ligo.org/science/Publication-GW190521 and ligo.caltech.edu/video/ligo20160211v3 $\endgroup$– anna vCommented May 29, 2022 at 10:55
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$\begingroup$ @annav That is a bad video to see what happens to the horizons. Here is a good one: youtube.com/watch?v=Y1M-AbWIlVQ&feature=youtu.be $\endgroup$– safesphereCommented May 29, 2022 at 23:15
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$\begingroup$ “So the 'singularities…” - A singularity is the future of the horizon and forms after all possible horizons have merged. There are no singularities in two merging black holes before they merge. $\endgroup$– safesphereCommented May 29, 2022 at 23:36
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$\begingroup$ “their gravities subtract themselves at the inner parts of horizons” - You are confusing the gravitational acceleration with potential. While accelerations do subtract, the potentials add up (in a non linear way). $\endgroup$– safesphereCommented May 30, 2022 at 2:27
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Good question. Between the two you stay where you are. On their COM you will not be accelerated. What look the force field and potential look like of two point masses in general? Take a look:
You can conclude that the horizon surfaces "bump" to each other and get smaller indeed. In between them there is no gravity at all! But the potential is lowered, while no force is exerted in you, apart from tidal effects. So if two identical BH approach you from both dides and you stay in their middle, your time will slow down wrt far away observers. You will be engulfed by both horizons and the holes will fall on your head and you will become part of the singularity. Or better you become the singularity. Luckily, we're not made of point particles.
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$\begingroup$ “the horizon surfaces ‘bump’ to each other and get smaller indeed” - They extend to each other like two opposite magnets. Once they touch, the whole thing is a single horizon. See the video in my link above. $\endgroup$ Commented May 30, 2022 at 2:31