# what happens in overlapping event horizons?

Recent thought experiment. If we assume anything inside an event horizon can’t escape, what would happen if two black holes were in orbit so that their event horizons over lapped?

Seems like if something fell into the overlap it’d be pulled equally hard from each direction. In another thread it was explained to me that inside an event horizon space recedes toward the center at a faster speed than light, therefore matter can’t escape.

However in this case that explanation gets confusing. It implies space would recede faster than light in both directions. Can it?

Let’s say the black holes orbited such that over lap was balanced for equal pull in both directions at a point between them. What would happen if I aimed a laser at this point? Would it get get stuck between them or would it escape?

I think the likeihood is that you’ll find that anything caught between the two black holes is still mving toward both singualrities as the black holes would coalesce.

So there isn’t a possible stable orbit where two singularities have overlapping event horizons, but their centers of mass are outside of each others event horizon?

I guess that could invalidate the hypothetical, but if there is a stable orbit, no matter how unlikely, let’s assume it for this.

Exactly — event horizons can’t overlap in the way you’re thinking. Rather, the two join together not unlike the T-1000 reconstituting itself. And if you’ve got two black holes closer together than their (isolated) Schwarzchild radii, then they’ll almost certainly coalesce. In fact, it’s impossible for anything (black hole or otherwise) to stably orbit another black hole closer than about three times the Schwarzchild radius.

two black holes coalescing is incredibly difficult to model, but on the other hand the event horizon signifies the static limit of the black hole so if it was inside the event horizons of two black hole logically it must be moving towards both singualrities.

I have wondered what the shape of the event horizons look like for black holes near but not touching. They certainly don’t stay spherical just until they touch, but do they “reach out” towards each other? Just after they touch, is the shape sort of a dumb-bell? Does it depend on whether they’re moving directly towards each other or spiraling in?

It seems like you’d need to answer this to give a [del]good[/del] ETA: complete answer to the OP.

Yes certainly the shape of the event horizons would be affected, though if anything I’d expect they’d shrink away from each other to some extent rather than reach out towards each other (but that’s just a WAG).

Like I said though modelling two black holes coalescing is a incredibly complicated, the kind of thing that physicists use supercomputer time to run numerical solutions.

I know there have been simulations run though.

And even with supercomputers, it’s only in the past few years that folks have even figured out how to do it at all. As in, before that, it wasn’t just that it took an impractically long time to model; it just couldn’t be done at all. They had to massage the equations in a very fancy way to even bring it into the realm of supercomputing.

All that said, one can use some fairly basic principles to conclude that the event horizons must distort towards each other, not away. But don’t ask me the shape of the distortions.

I don’t disagree as it was a WAG, but can you expand on this?My intial feeling is that you’d bexpect a certain degree of cancelling between the ‘pull’ of the two black holes (which you would ceratinly see if part of the region betwen them was almost flat.

Well, that’s certainly true for boring old Schwarzschild black holes, but rotating and charged ones may have stable orbits inside their horizons – some people even think those regions are stable enough to accommodate whole planets (though that’s certainly somewhat out there, speculation-wise).

I’ve got no idea in what sense a singularity could orbit another inside a black hole, though – I’m pretty certain that in the long run (possibly a rather short long run), you’re gonna end up with a rotating black hole with a ring-shaped singularity, but as has been said, how exactly that happens is the stuff of sophisticated computer simulation.

Think potential, not force. As for why I said they’d have to distort towards each other, if they distorted apart, then you’d get a discontinuity that seems unphysical when all of a sudden they got close enough to merge. You’ve also got issues with the Second Law of Black Hole Thermodynamics: The total area of event horizons can’t (classically) decrease (it can decrease in Hawking radiation, but only by dumping an equivalent amount of entropy into the emitted radiation).

That does make sense, I suppose one way of looking at it a quasi-Newtonian way would be the centre of mass lying somewhere between the two holes would have it’s own escape velocity for an object to escape to infinity, at some point when the two holes are sufficently close this will go to create a region of space which there will be no worldlines out to infinity from the centre of mass.

I should expand on that, basically event horizons are global not local properties, so I was incorrect to think about the local effect of the gravity of the two BHs on some point between them.

Thanks everybody for your thoughts on this!

Okay so to sum the interesting discussion, my premise of over lapping event horizons is a false premise. They would instead merge, creating areas where space was so warped there was no outside path and even light bends back on its self, an exaggerated manor of how an orbit is straight line through curved space.

So a couple of questions I’m left with are, where does the light go? Newton understanding says an object would accelerate toward the center of mass. However there’s two (possibly 3) center of masses in the system, and so the term is ambiguous. Further if Newtonian physics doesn’t give way to Relativistic physics here then I’m your drunk uncle Sue.

If I were to guess I’d say what is going on is the place where the event horizons merged is the center of mass for the entire system which is light and objects would fall towards. Sort of like how the earth-moon system has 3 center of masses, the earth, the moon, and the point they both orbit. Is that correct?

A related question. What level of math is needed to understand this? I’m going to take calculus I next fall. How far away am I? Poking around I’ve read Relativity is based on something called a Riemannian Metric Tensor, which describe distortions in space. How far away am I?

For a rough mental picture, this is probably about right. However, I feel obliged to point out that the very notion of “center of mass” involves how masses are located in space, and when space itself becomes curved it can be hard (if not impossible — anyone know how to define this notion?) to actually point to some spot in space and say, “the center of mass is right there.”

You’ve got a bit of time left, I’m afraid. Most general relativity textbooks assume that you’re familiar with multi-variable calculus (sometimes known as vector calculus), which at most educational institutions I’ve been at is the third semester-long calculus course you take. Special relativity, on the other hand, can be described just using high-school algebra (and maybe a tiny bit of calculus for the most advanced stuff) — so if you want to learn about time dilation, length contraction, twin paradoxes, and all that cool stuff, you’re probably ready now.

Ahh I see. Layman’s explanations can’t always be precise. I know I’ve had to use a few metaphors in computers that were pretty rough, but as precise as the other person could handle, which is why I need the math to get better explanations.

Well I plan to study calculus on my own over the summer. I’ve found the academic class system isn’t a good fit. A recent pit thread is testament to this. What did help me greatly with trig recently was giving up on the academic book as directed by the class, and supplementing it with three other books, and wikipedia of all things.

So what I plan to do this summer is work ahead on figuring out calculus, finding the intuitive explanations and then expanding them into the rigorous explanations, and applications. If calculus and vectors is the gold standard, than I’ll see how close I can get.

Thanks!

Really, once you understand multivariable calculus, differential equations, and linear algebra (usually presented as algebra on matrices), you can tackle pretty much everything. It’s all just applications of one or more of those.

So what you’re saying is multivariable calculus is the gateway drug to the universe. Pretty cool!

I would figure an L1 Lagrange point between the singularities exists regardless of event horizon overlappage.

L1 is a gravitic equilibrium point, albeit an unstable one: drop a baseball onto the point of a cone and it just rolls downhill, but drop the ball into a crater and it settles on the bottom.

What are the Lagrange points of two black holes in proximity to each other?

I imagine that the notion of “Lagrange points” isn’t well-defined for black holes in close proximity. The two holes themselves aren’t even in equilibrium; how can one define “equilibrium” for a fourth body added to the system? And no, “fourth” wasn’t a typo: The first three bodies are the two holes and the gravitational field.