# Direct collision of two black holes at 0.999 c

• B
The relative speed of two supermassive black holes moving directly towards each other is 0.999 c. What happens when the two black holes collide directly (so the black holes aren't orbiting each other) at such high velocity? Where does all that energy go and how would it effect space time/what would the merger look like? What happens if they hit at a slight angle such that their event horizons would make contact but there isn't a direct hit.

## Answers and Replies

supermassive black holes
Why black holes?

timmdeeg
Gold Member
T Where does all that energy go and how would it effect space time/what would the merger look like? What happens if they hit at a slight angle such that their event horizons would make contact but there isn't a direct hit.
After the merger the newly formed black hole is deformed and will loose energy by radiating away gravitational waves until it is spherical symmetric.

PAllen
Science Advisor
Several cases of this are shown as movies in

https://www.black-holes.org/explore/movies

As to some of your questions:

Comparing head on collision of two BH of different relative velocity (but otherwise identical), the two with larger relative velocity would produce a larger resulting BH. The extra energy goes into the size of the BH.

If the horizons touch, they will merge. However, the details are extremely complex, and I do not personally know of a paper analyzing this case.

Several cases of this are shown as movies in

https://www.black-holes.org/explore/movies

As to some of your questions:

Comparing head on collision of two BH of different relative velocity (but otherwise identical), the two with larger relative velocity would produce a larger resulting BH. The extra energy goes into the size of the BH.

If the horizons touch, they will merge. However, the details are extremely complex, and I do not personally know of a paper analyzing this case.

THe movies were very interesting. I find it odd that the black holes oscillate back and fourth after a direct collision. Almost like two blobs of water colliding in one of the international space station videos. Doesn't that suggest that the black hole isn't a singularity but has actual stuff with volume? If it was just an infinitesimal singularity how could it oscillate like that according to the videos?

PAllen
Science Advisor
A black hole is not defined by a singularity. It is defined by an event horizon. The singularity is inside the horizon and is not part of the ‘universe’. The presumption is that since physical quantities approach infinity on approach to the singularity, that some new theory takes over and avoids this. Note also that the singularity is a time for matter inside the horizon, not a place. But all this happens well inside the event horizon which is what defines the BH. The event horizon is defined by where outgoing light cannot escape but is not forced towards the singularity either.

PeroK
Ibix
Science Advisor
2020 Award
THe movies were very interesting. I find it odd that the black holes oscillate back and fourth after a direct collision. Almost like two blobs of water colliding in one of the international space station videos. Doesn't that suggest that the black hole isn't a singularity but has actual stuff with volume?
Clearly not. Those are simulations using general relativity, the very theory that predicts that the interior is vacuum. You'd need direct imaging of a real black hole merger that didn't look like the videos to provide evidence for your conclusion.
If it was just an infinitesimal singularity how could it oscillate like that according to the videos?
You aren't looking at simulations of the singularity (I've no idea how you'd even draw it in this kind of presentation), you are looking at simulations of the event horizon. The event horizon isn't a thing, it's a place - like "the altitude at which geosynchronous satellites orbit" is a place. It's the place where you can't get out of the black hole no matter how hard you try. What you are seeing is that point-of-no-return evolving as the black hole emits gravitational radiation and settles into its final form. There's no matter wobbling around here.

Clearly not. Those are simulations using general relativity, the very theory that predicts that the interior is vacuum. You'd need direct imaging of a real black hole merger that didn't look like the videos to provide evidence for your conclusion.
You aren't looking at simulations of the singularity (I've no idea how you'd even draw it in this kind of presentation), you are looking at simulations of the event horizon. The event horizon isn't a thing, it's a place - like "the altitude at which geosynchronous satellites orbit" is a place. It's the place where you can't get out of the black hole no matter how hard you try. What you are seeing is that point-of-no-return evolving as the black hole emits gravitational radiation and settles into its final form. There's no matter wobbling around here.

Right, I understand that the movies show only the event horizon. My confusion is that because the event horizon, like you said, is not even a thing, then how could it be oscillating? THe only thing I could think of with my admittedly limited understanding is that the event horizon shape is determined by the distribution of matter inside the black just like a gravitational field of a planet would be determined by the mass distribution of the material inside the planet. I realize this analogy is probably much too simplistic. However GR says there is no distribution of matter, it exists in a point.

If all the mass of a black hole is "located" in a singularity as described by GR, then it couldn't have a mass distribution in any sense of the word so I don't see how its possible to have oscillations from a point. Maybe you could explain how a merged singularity can produce an oscillating event horizon. It seems like once the black holes merge then the event horizon should be entirely spherical, not fluctuating between an ellipsoid and a sphere.

PAllen
Science Advisor
Right, I understand that the movies show only the event horizon. My confusion is that because the event horizon, like you said, is not even a thing, then how could it be oscillating? THe only thing I could think of with my admittedly limited understanding is that the event horizon shape is determined by the distribution of matter inside the black just like a gravitational field of a planet would be determined by the mass distribution of the material inside the planet. I realize this analogy is probably much too simplistic. However GR says there is no distribution of matter, it exists in a point.

If all the mass of a black hole is "located" in a singularity as described by GR, then it couldn't have a mass distribution in any sense of the word so I don't see how its possible to have oscillations from a point. Maybe you could explain how a merged singularity can produce an oscillating event horizon. It seems like once the black holes merge then the event horizon should be entirely spherical, not fluctuating between an ellipsoid and a sphere.
A boundary defined by the criteria that it is the boundary of where light can escape to infinity can easily oscillate. Your understanding is not just limited, it is simply wrong. In classical GR a BH more than a few days old is pure vacuum. The mass has left the universe, in some sense. However, the horizon remains, as does the interior excluding the singularity. The horizon is determined by the mass and energy that went into the BH in the past.

The videos show the evolution of the horizon for different merging scenarios. These are the predictions of GR. Your understanding of GR is simply incorrect. If you have any desire to understand real GR, a good starting point is:

https://arxiv.org/abs/gr-qc/9712019

Ibix
Science Advisor
2020 Award
My confusion is that because the event horizon, like you said, is not even a thing, then how could it be oscillating?
Consider a point such that the distance from your left hand, to the point, to your right hand is 2m. The set of all such points forms an ellipsoid around your hands. Clap your hands together; the ellipsoid collapses into a sphere. Now clap your hands repeatedly and the surface oscillates smoothly between a sphere and an ellipsoid. All I need to do is put together an animation showing that surface oscillating.
THe only thing I could think of with my admittedly limited understanding is that the event horizon shape is determined by the distribution of matter inside the black just like a gravitational field of a planet would be determined by the mass distribution of the material inside the planet.
The gravitational field depends on the stress-energy tensor, which includes mass, momentum, pressure, and angular momentum. And it doesn't only depend on what it is now ("now" is a slippery concept in GR), but on what it was elsewhere in the past. And the gravitational field affects the stress-energy distribution (loosely: matter moves due to gravity) which affects the gravitational field. It's the nature of that mutual interaction that makes GR maths hard.
However GR says there is no distribution of matter, it exists in a point.
There are two spinning singularities merging. The surface can't go directly from two smooth featureless spheres to one smooth featureless sphere - you never see that kind of discontinuous behaviour. It takes a while for the surface to transition from one state, that's all. It isn't due to matter slopping around, it's due to the history of how the singularities came together (see my previous paragraph).

Also, GR doesn't say that all mass is located at a point in a black hole. As @PAllen says, the singularity is not part of the universe as modelled by GR. We assume that this is a failing of GR, since that doesn't make too much sense. But nevertheless, the interior of the black hole as modelled by GR is vacuum and its event horizon oscillates. You don't need matter slopping around.
Maybe you could explain how a merged singularity can produce an oscillating event horizon. It seems like once the black holes merge then the event horizon should be entirely spherical, not fluctuating between an ellipsoid and a sphere.
See above - it just takes a while for the two spheres to settle down into one.

PeroK
Science Advisor
Homework Helper
Gold Member
2020 Award
It seems like once the black holes merge then the event horizon should be entirely spherical, not fluctuating between an ellipsoid and a sphere.

That's why you need mathematics. Physics isn't what might seem to be the case if you casually think about something for a minute of two. Physics is about having an evidence-based theory and working through the mathematics.

weirdoguy and Ibix
Ibix
Science Advisor
2020 Award
That's why you need mathematics. Physics isn't what might seem to be the case if you casually think about something for a minute of two. Physics is about having an evidence-based theory and working through the mathematics.
@arusse02 - note that Einstein published general relativity in 1915. Kerr published the solution describing a single isolated rotating black hole in 1963. We aren't joking about the time this stuff takes to work out.

m4r35n357 and PeroK
The relative speed of two supermassive black holes moving directly towards each other is 0.999 c. What happens when the two black holes collide directly (so the black holes aren't orbiting each other) at such high velocity? Where does all that energy go and how would it effect space time/what would the merger look like? What happens if they hit at a slight angle such that their event horizons would make contact but there isn't a direct hit.

Some fraction of the kinetic energy becomes gravitational waves, rest collapses into a black hole.

(I decided to ignore the fact that there already existed two black holes, those are are so small, compared to the huge kinetic energy and the huge black hole that would be formed if that kinetic energy collapsed into a black hole)

Let's incorrectly assume that all of the kinetic energy becomes gravitational waves. Those gravitational waves will collapse into a black hole, unless they are produced during a very long time, so that the energy density of the waves stays low enough for there to not be a collapse.

timmdeeg
Gold Member
My confusion is that because the event horizon, like you said, is not even a thing, then how could it be oscillating?
In short, a empty volume defined by a "shape" can oscillate.

The geometry of the event horizon is not determined by a "distribution of matter", but instead by the mass ##M## of the black in its singularity. The black hole contains vacuum inside the event horizon because its metric is a so called vacuum solution of Einstein's field equations. The event horizon of a static black hole (sloppy said its "shape") is given by the Schwarzschild radius ##r##. Photons emitted radially outwards at ##r =2 M## which means emitted at the event horizon don't escape nor do they fall into the singularity. Therefor as photons "stay" at the event horizon this horizon is a light-like surface. The event horizon of a static black hole has a spherical symmetric geometry. - In contrast the event horizon of the newly formed black hole after the merger of two black holes is deformed and oscillates until it is spherical symmetric.

PeroK
That's why you need mathematics. Physics isn't what might seem to be the case if you casually think about something for a minute of two. Physics is about having an evidence-based theory and working through the mathematics.

RIght and i'm not asserting that i'm correct or that I have some insight, just that I didn't understand.