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When Black Holes Collide
EricTheGreen writes "CNN.com reports on a pair of black holes in a mating dance that can only end badly for both of them. Fortunately they've still got several million years for the emotional rush to wear off and realize what a terrible mistake they're both making..."
Something I always wondered: When two black holes are close together, then something that has exactly the same distance to each of them should not fall into either one. What happens when they are so close that their event horizons overlap? Shouldn't there always be some flat zone between them that is not part of either event horizon? So how can they merge?
There's a difference between the strength of a gravitational field and a gravitational gradient. It's like at the center of the Earth. The gravitational gradient there (relative to the Earth's field) is zero, but the force of all that overhanging rock is pretty high. You wouldn't float there comfortably with no force acting on you. You'd be squished.
And that's in a conventional, Nwtonian view of gravity, which is where most people are comfortable thinking about these things. In the relativistic world things get a bit more complicated. The gravitational field itself has energy, and energy at sufficiently high densities has an appreciable mass equivalence and so itself gravitates. At high enough values, like at the event horizon of a black hole, this kind of positive resonance causes the equations describing the system to diverge and the solutions go to infinity, and this divergence is called a singularity.
The event horizon isn't a physical thing, it's the point where the divergence is assured. You can't really think of a black hole as a single hard little ball agt the center of a black hole surrounded by black empty space up to the event horizon, though I believe that's now most people think of it. All spatial and temporal points within the event horizon are indistinguishable - but it's be somewhat misleading to say that they're all the same point either, because the equations that describe those points can't be solved rationally since they contain infinities and it's like asking how infinity +1 is different from infinity + 2.
If you were able to maneuver in space such that you were always equidistant from two black holes of identical mass, you would float around comfortably as long as the bh's were sufficiently far from you. As they approached, you'd feel significant tidal stretching. As the bh's got closer, you would be stretched further, and smaller regions even closer to that exact midpoint would feel increased stretching. At the point where they merged, even the infinitestimal point at the exact center would be stretched to infinity (that one zero volume point could not resist the force that was stretching it out to fill the volume of the whole universe). Of course, this is a somewhat poetic way to describe events that cannot really be described because the physical equations contain infinities and have no meaningful interpretations.
At times like that, poetry is all you can do. It's hard to resist making analogies with this scenario and the creation of the universe, but such analogies, like any other analogy what talk about on or inside the event horizon of a black hole, are meaningless here. But it's still fun.
In theory, there's no difference between theory and practice. In practice, there is.
Cheers,
-l
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The event horizon of a black hole can be thought of as the surface from which no information (particles, energy, whatever) can escape. It's the event horizon because it's where observable events (time) ends; you can't see what happens inside a black hole.
Now, merging black holes. If you're in the exact center (or maybe not the very exact center, since black holes drag space-time around them and other funky effects), then maybe you don't get "pulled" into either black hole before the merger. But you still can't escape the combined system, which is the point where the event horizon swallows you up.
To think of it another way, if the system were Newtonian, and consisted of point masses, then you could balance perfectly between the two. But at some point, the field becomes so strong that you can't escape that balance point; if you try to leave, no matter how powerful your engines, both black holes will act to pull you back. (Similar to what happens at the L1 Lagrange point.) At this point, that balance point has been enveloped by the event horizon.
The event horizon is a surface that encloses a volume that simply describes a region of space-time where events (which, as far as we know, are limited by the speed of light) can no longer observed. As such, it's not really a physical boundary, but a mathematical one. An object crossing the event horizon wouldn't notice until it tried to get out. Otherwise, there's nothing special about it.
Of course, this all assumes continuity, and we know the actual universe is quantum, and once you add quantum in, you get funky effects like Hawking radiation. But we haven't solved the quantum gravity problem yet, and Einstein's theory is the best we've got for now.
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There's a difference between the strength of a gravitational field and a gravitational gradient. It's like at the center of the Earth. The gravitational gradient there (relative to the Earth's field) is zero, but the force of all that overhanging rock is pretty high. You wouldn't float there comfortably with no force acting on you. You'd be squished.
ouch! no. At least, not if you assume spherical symmetry. Baby analytical mech. example: the uniform sphere. Gravitational force is linear inside, going to zero.
You'd be squashed, alright, but not by gravity. It's the pressure in all that rock around you that you have to watch for. But if you manage to stabilize the hole you supposedly dug in the center of the Earth against the surrounding pressure, then you'd be floating quite comfortably.