# A How Black Holes eat Gravitational Waves

#### .Scott

Homework Helper
Summary
Is it fair to say that all energy from a Gravitational Wave that enters the photon sphere of a Black Hole is destine to become part of that BH?
Is it fair to say that all energy from a Gravitational Wave that enters the photon sphere of a Black Hole is destine to become part of that BH?

And other parts that remain just outside of the photon sphere would experience gravitational lensing? Perhaps focusing the GW to an area of much greater intensity.

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#### Drakkith

Staff Emeritus
2018 Award
As far as I understand things (which is a very limited understanding I have to admit), the gravitational wave causes the event horizon to oscillate in such a way as to re-emit the same wave. The end result is that the gravitational wave appears to pass over the BH without losing any energy.

Someone correct me if I'm wrong please.

#### .Scott

Homework Helper
As far as I understand things (which is a very limited understanding I have to admit), the gravitational wave causes the event horizon to oscillate in such a way as to re-emit the same wave. The end result is that the gravitational wave appears to pass over the BH without losing any energy.

Someone correct me if I'm wrong please.
So the energy from the Gravitational Wave makes it all the way to the event horizon and back?
Can I use this to measure the speed at which the gravitational wave traverses the event horizon? Since the EH is at extreme time dilation, wouldn't that effectively terminate the travel of that portion of the Gravitational Wave and the energy it is carrying?

#### Drakkith

Staff Emeritus
2018 Award
So the energy from the Gravitational Wave makes it all the way to the event horizon and back?
Can I use this to measure the speed at which the gravitational wave traverses the event horizon? Since the EH is at extreme time dilation, wouldn't that effectively terminate the travel of that portion of the Gravitational Wave and the energy it is carrying?
I don't think I know enough to begin to answer these questions. Sorry!

#### Heikki Tuuri

A gravitational wave is a moving Riemann curvature deformation in spacetime. It travels at the speed of light.

Far from the source, it is a quadrupole wave. That is, it is the waveform generated by two parallel dipole transmitters whose phase differs by 180 degrees.

If you wave your fist, then the fist is a dipole transmitter of gravitational waves. The other dipole is that part of Earth's crust which moves to the opposite direction from the fist. Far away, it looks like a quadrupole wave.

Close to a black hole, a gravitational wave will progress like an electromagnetic wave. Some of the wave will be scattered back. Some of the wave will follow the null geodesics to the horizon and beyond.

The black hole will devour the energy just like it would devour the energy of an electromagnetic wave.

#### Drakkith

Staff Emeritus
2018 Award
The black hole will devour the energy just like it would devour the energy of an electromagnetic wave.
Really? I was under the impression that this didn't happen. I guess I was mistaken.

#### PeterDonis

Mentor
Is it fair to say that all energy from a Gravitational Wave that enters the photon sphere of a Black Hole is destine to become part of that BH?
No. The photon sphere is not the boundary inside which everything ends up inside the hole; that's the horizon. Photons and gravitational waves propagating radially outward can escape from anywhere above the horizon.

Photons and gravitational waves that are not propagating radially outward can be captured by the hole (meaning, their trajectories will end up putting them inside the horizon) further out than the horizon; but the photon sphere is not a hard boundary there either. Actually, if you imagine an observer "hovering" at a gradually decreasing altitude above the horizon and trying to emit photons in all directions, the range of directions at which emitted photons will escape to infinity continuously gets narrower (starting, when the observer is very far away from the hole, from all directions except the set of directions that point directly at some part of the area on the observer's sky occupied by the hole). The photon sphere is the altitude at which the range of directions is exactly 180 degrees--any photons emitted tangentially (exactly perpendicular to radially outward) at that point remain in closed orbits about the hole. For lower altitudes than that, the range of directions narrows further, approaching a limit at the horizon of no directions at all (because at the horizon photons moving exactly radially outward stay at the same radius).

#### .Scott

Homework Helper
No. The photon sphere is not the boundary inside which everything ends up inside the hole; that's the horizon. Photons and gravitational waves propagating radially outward can escape from anywhere above the horizon.
A gravitational wave entering the photon sphere will not be radiating outwards. And unlike photons, it cannot be reflected. So unless there is some kind of diffraction or refraction possible, I think my statement stands.

Also what about the gravitational lensing? It would seem that a BH should be able to concentrate a portion of a gravitational wave into a smaller region.

#### .Scott

Homework Helper
Actually, if you imagine an observer "hovering" at a gradually decreasing altitude above the horizon and trying to emit photons in all directions, the range of directions at which emitted photons will escape to infinity continuously gets narrower (starting, when the observer is very far away from the hole, from all directions except the set of directions that point directly at some part of the area on the observer's sky occupied by the hole). The photon sphere is the altitude at which the range of directions is exactly 180 degrees--any photons emitted tangentially (exactly perpendicular to radially outward) at that point remain in closed orbits about the hole. For lower altitudes than that, the range of directions narrows further, approaching a limit at the horizon of no directions at all (because at the horizon photons moving exactly radially outward stay at the same radius).
I like that description because it brings up another question:
I'm go to use "full escape" to mean that both the spacecraft and any reaction mass it jettisons end up back outside the photon sphere. If we were not talking about a relativistic, frame dragging environment, I would expect that if I was orbiting just inside the photon sphere, I should be able to jettison half my mass to the side (perpendicular to the orbit) and both me and that reaction mass would end up escaping. But since this maneuver does not create an immediate "outward vector" for either myself or the reaction mass, I'm pretty sure it would not work within the photon sphere. So a "full escape" from the photon sphere is not possible. There is always something sacrificed.

That suggests to me that information isn't abruptly lost as you cross the event horizon. Instead, there is a continuous loss of information as an object travels from the photon sphere to the event horizon.

#### PeterDonis

Mentor
A gravitational wave entering the photon sphere will not be radiating outwards.
Depends on where it's coming from. If it's coming from a black hole merger, it will be moving outwards at the photon sphere of the newly merged hole.

If it's coming at the photon sphere from outside, then yes, it will be moving at best tangentially so it will end up falling into the hole.

Note that in all of this we have been implicitly assuming that the wavelength of the gravitational wave is much smaller than the size of the hole (roughly its horizon radius). For waves of comparable wavelength to the hole's size, things get much more complicated.

what about the gravitational lensing? It would seem that a BH should be able to concentrate a portion of a gravitational wave into a smaller region.
Waves that get gravitationally lensed by the hole will be focused on a point way beyond the hole (roughly the same distance from the hole as the wave source, but on the other side). They won't be focused on the hole itself, any more than an ordinary lens focuses light coming into it on itself.

if I was orbiting just inside the photon sphere
There are no free-fall orbits inside the photon sphere.

a "full escape" from the photon sphere is not possible. There is always something sacrificed.
In the sense that you need rocket power to keep from falling into the hole inside the photon sphere (because there are no free-fall orbits there), and the reaction mass ejected by a rocket that is escaping will not itself escape, yes, this seems intuitively plausible, but I have not done the math to check it.

That suggests to me that information isn't abruptly lost as you cross the event horizon. Instead, there is a continuous loss of information as an object travels from the photon sphere to the event horizon.
The information loss problem has nothing to do with anything we've discussed; it's a quantum problem, not a classical problem, and everything we've discussed in this thread is classical.

As far as the quantum information loss problem is concerned, nobody even knows for sure how or where the quantum information in question is stored since we don't have a theory of quantum gravity. So there is no way to even check your statement at the quantum level. (I have not seen anything like your suggestion in the literature I have read, but there is a lot that I have not read.)

#### .Scott

Homework Helper
Waves that get gravitationally lensed by the hole will be focused on a point way beyond the hole (roughly the same distance from the hole as the wave source, but on the other side). They won't be focused on the hole itself, any more than an ordinary lens focuses light coming into it on itself.
That's not how a normal convex lens would work. Light from infinity is focused closer than light from a nearby source. And it is certainly possible for a convex surface of a lens to focus light to a point within the glass.

#### PeterDonis

Mentor
it is certainly possible for a convex surface of a lens to focus light to a point within the glass.
Well, as I've already said, light that is coming into the photon sphere from outside will fall into the hole, yes. But if you're talking about gravitational lensing in the usual sense of that term, you're talking about light that is going to be visible to an observer on the other side of the hole from the source, so it's not falling into the hole.

If you want to use the term "gravitational lensing" to describe the fact that photons falling into the photon sphere (as opposed to the horizon) from outside will fall into the hole, I can't stop you, but I don't think that's the usual use of that term.

#### .Scott

Homework Helper
Well, as I've already said, light that is coming into the photon sphere from outside will fall into the hole, yes. But if you're talking about gravitational lensing in the usual sense of that term, you're talking about light that is going to be visible to an observer on the other side of the hole from the source, so it's not falling into the hole.

If you want to use the term "gravitational lensing" to describe the fact that photons falling into the photon sphere (as opposed to the horizon) from outside will fall into the hole, I can't stop you, but I don't think that's the usual use of that term.
In a ball lens, the difference between the outside of the glass and the focal "point" where the light (or gravitational wave) is focused to is dependent on the index of refraction and the balls diameter.

When the index of refraction is 2 or more, light from infinity is focused to a point within the lens.
That would very roughly model the photon sphere.
So I would expect that light or gravitational waves above the photon sphere would be modeled by lower indexes of refraction - and be focused onto regions above the photon sphere at different elevations - dependent on how close they got to that sphere.

I only mention this because it would be another feature of the BH environment.

#### pervect

Staff Emeritus
I suppose a GW of the right frequency could make the black hole "ring", as you suggest. Intuitively, I'd expect if the GW was of a high enough frequency, it could be treated by geometric optics, and would get absorbed. But I've never seen a thorough analysis of the question, my intuition could be incorrect.

#### PeterDonis

Mentor
When the index of refraction is 2 or more, light from infinity is focused to a point within the lens.
That would very roughly model the photon sphere.
Again, if you want to call this "gravitational lensing" I can't stop you, but it's not the usual use of that term. I agree that it happens--as I've already said, photons coming in to the photon sphere from outside will get captured by the hole.

"How Black Holes eat Gravitational Waves"

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