highspeed black holes or neutron stars on (almost) head-on collision course and kinetic energy

First: I don't think this is a duplicate question. There are related question on mergers of black holes that orbit around each other etc., so please read on.

I'm having a hard time picturing what might happen in the following scenario:
Assume two black holes of the same size on an almost frontal collision course with a very high relative speed of x km/h (replace x with whatever would be necessary to enable the scenarios described below).

If their event horizons don't "touch" I'd assume their courses will change considerably but it would be a normal flyby - right ?

But what happens if their event horizons "touch", if their event horizons "overlap" just a few meters ?

On the one hand both objects have a massive kinetic energy with opposite directional vectors. And on the other hand nothing can escape below the gravitational radius.

Where does all the kinetic energy go ? Would the two black holes extremely deform, like creating a long string before they collapse into spherical form?

And what if in a similar scenario one of the two objects is a neutron star. Would the neutron star be ripped apart when it scrapes the black hole on high-speed flyby ?

• 1.000.000 km/h is not that impressive, less than 0.1% of c ;) Feb 5, 2016 at 14:04
• I once got a baseball between the legs and the kinetik energy of these maybe 80 km/h was quite impressive. Feb 5, 2016 at 14:10
• My point is that you must have a velocity of close to the speed of light in order to not be captured by the black hole when close to the event horizon. With that snail-speed, they are simply going to merge anyway. Feb 5, 2016 at 14:14
• @TheVoid You are talking nonsense. Black hole mergers are quite well understood, and don't result in the consumation of the universe Feb 7, 2016 at 17:02
• Event horizons do not have a fixed shape. They are deformed by any massive bodies nearby, especially other black holes. As the BHs get close to each other, their event horizons will begin to deform. If the EHs merge, it's a done deal, they're gonna merge all the way. astronomy.stackexchange.com/questions/31989/… May 23, 2019 at 7:08

I think it's a fun question, and I can answer some of it.

If their event horizons don't "touch" I'd assume their courses will change considerably but it would be a normal flyby - right?

While the relativistic speeds and time dilation might change things a bit, a flyby is still a flyby. They would either fly past each other, the dense objects would change direction as a result, but the combined kinetic energy and momentum would remain constant.

Second option is they enter into orbit around each other. Pretty much the same with any two massive objects passing near each other.

But what happens if their event horizons "touch", if their event horizons "overlap" just a few meters?

With classic (non Kerr) black holes, if the event horizons touch the black holes have no option but to merge. The event horizon is directly proportional to the radius, so when the two event horizons touch it, as that happens, no longer two black holes but one black hole. The mass of the two objects combined has an event horizon that circles both of them.

For Kerr black holes this question is more complicated and I'm not sure but I think it's the same. Once the event horizons touch it's no longer two separate black holes but one bigger one.

On the one hand both objects have a massive kinetic energy with opposite directional vectors. And on the other hand nothing can escape below the gravitational radius.

When you're talking about event horizons, gravity always wins. Kinetic energy cannot exceed the speed of light, so it loses.

Where does all the kinetic energy go ? Would the two black holes extremely deform, like creating a long string before they collapse into spherical form?

A long string doesn't make any sense. A temporarily non-round event horizon as the holes merge seems possible, but think of a merger of two stretched balls, not a string. Each black hole is centered around it's "singularity", those shapes might warp some as the holes collide or spiral into each other. As an FYI, direct collisions would be rare. Spiraling into each other is much more common.

The kinetic energy gets absorbed inside the black hole. It can't, by definition of the black hole, escape. Total momentum is likely preserved.

And what if in a similar scenario one of the two objects is a neutron star. Would the neutron star be ripped apart when it scrapes the black hole on high-speed flyby ?

A few points to consider regarding a black hole. Anything that falls within a black hole's photon-sphere is unlikely to ever escape, so one of the magical distances to consider is 1.5 times the radius of the black hole where all orbits are destined to fall into the black hole. If the black hole and neutron star are of similar size and the neutron star passes close to the event horizon and relativistic speed, then there's an interesting scenario where some of the neutron star (at close to the speed of light) would be outside the photon-sphere and have the momentum to escape and some of it would not. Neutron stars are bound together very tightly, but the tidal forces would be very strong and it's possible that some of the neutron star material could get torn off in this hypothetical scenario. Would the entire neutron star be torn apart? Maybe. It's hard to say. The math in that hypothetical is way above my pay-grade.

If the neutron star is much smaller than the black hole, then it's likely inside the photon-sphere and it will spiral into the black hole, perhaps breaking apart in the process into an accretion disk, perhaps not, but it will get absorbed into the black hole if it's entirely within the photon-sphere, even at nearly the speed of light.

The problem with this hypothetical is that it's pretty much impossible. Objects the size of stars don't accelerate at nearly the speed of light relative to other near by stellar mass objects. What actually happens is described in the first answer to your question, the two dense objects would either have sufficient relative velocity to fly past each other or they would get caught into a mutual orbit that would likely lead to a merger. In the actual universe, a close to the event horizon fly-by between a neutron star and a black hole would result in a merger of the two. In theory, with enough kinetic energy the neutron star could fly close to and still fly past the black hole, but that much relative velocity probably never happens.

People smarter than me should feel free to correct anything I got wrong, but I thought this one was a fun one to answer.

• Nice answer, but you might like to update it a little, now that LIGO has observed a BH merger. I'm a little puzzled what "Kinetic energy cannot exceed the speed of light" is supposed to mean. Relativity limits speed, but not KE. OTOH, KE will be consumed as an energy input to the BH merger, although some energy & momentum will be emitted as gravitational waves. BTW, check out the BH merger sim video I linked here. May 23, 2019 at 9:07

If the two black holes miss are more than a few Schwarzschild radii apart at closest approach then what will happen will look very much like the pure Newtonian solution -- similar to a close encounter between two planets or stars -- but with some small perturbations to the orbits due to GR and some energy lost to gravitational radiation.

If they go much closer than that, the GR effects become much larger. Firstly the trajectories change, so they may "bend" or "spiral" into one another (quotes because saying anything geometric about what happens near a black hole where space and time are so curved risks being misleading). As they do so, when they get close enough the event horizons will merge rapidly deforming to enclose all the space that was previously inside either of them, and some more. The resulting event horizon will then quickly settle down to one of the standard symmetrical forms, radiating a lot of gravitational waves in the process. The energy and angular momentum of the initial situation will end up either in the spin and mass of the final black hole, or in those gravitational waves.