Observation of matter falling into Black Holes

[ObjectivelyRational]

This is not true, in theory. The correct description is subtle.

1) You will continue (in theory) to receive em signal from said infalling matter forever, long after the gravitational radiation from its absorption by the BH was received. In practice, you won't because no detector can detect an em signal with a wavelength of e.g. 1 light year (or photon with a frequency of 1 cycle per year).

2) But there is, even in principle, no inversion of timing, as you describe it.

The explanation is that this long delayed relic photon was emitted by some particle of infalling matter when it was a tiny fraction of a Planck length from the stabilized horizon. The gravitational radiation you observed earlier was generated by spacetime distortions further away from the horizon than this. All gravitational radiation you observe is generated by phenomena occurring outside the horizon. Since it was generated further away from the horizon than the photon in (1), you receive it earlier.

So I am a little confused.

I understand that contributions to that gravitational wave are generated outside the horizon, we do not observe with LIGO any process occurring "inside" the event horizon of any black hole. So too, any photon observed at LIGO must have been generated outside the event horizon.

I referred to "specific portions" for greater precision, to identify for example a single atom, or a positron-electron pair, or a bit of plasma, or some such from which a photon is emitted and having its own matter energy density from which some particular contribution to the total gravity wave originates (the total wave being due to contributions from all of the matter and energy density).

I assume that from any particular specific portion of infalling matter, any photon and any propagating wave of spacetime that emanates from that specific portion (at the same some local time t... and I am imagining a generalized Huygens principle conceptually applies here?) travels away from that specific portion at the same speed (the speed of light) and in the same "directions" (through the spacetime influenced by all other mass energy in the universe), so that they would reach LIGO at the same time and from the same direction (of course they are emanating in all directions but I assume here they do so together... there is no "dispersion" between the em waves and the gravity waves (and here I assume truly empty space between LIGO and the BH). What I am understanding from your response is that the infalling matter collectively creates a more detectable wave whose maximum reaches LIGO first and diminishes more sharply and prior to the theoretical observation of the final photons from various specific portions of the matter and before these become too low in frequency to detect... and that this does not contradict with light and gravity waves traveling together at the speed of light.

 

[PeterDonis]

(the total wave being due to contributions from all of the matter and energy density).

For a black hole merger, there is no matter or energy density. Black holes are not made of matter. They are made of spacetime curvature. Even for the case of a neutron star merger, where there is matter and energy density present, the matter and energy density is not the primary source of the gravitational waves; the spacetime curvature is. So your assumption here is not correct.

I assume here they do so together... there is no "dispersion" between the em waves and the gravity waves

It's not a matter of "dispersion"; it's a matter of the EM waves and the gravitational waves not having the same source. See above.

 

[pervect]

Is it safe to say:

1. For any specific portion of infalling matter directly in line of sight between you and the cog of the bh, "after stabilization" no photons emitted directly towards you from that specific portion of the infalling matter (straight line path) can reach you (it being beyond the event horizon). (or better no photons can even be directed toward you... or there is NO towards you)

For a purely classical black hole (no Hawking radition and no BH evapoartion), once the portion of infalling matter crosses the event horizon, no signal emitted from the matter itself can ever reach the external universe by the definition of what an event horizon is.

As others have noted, the idea of the "center of gravity" isn't quite right.

2. Any contribution to the gravity wave you detect caused by that specific portion of infalling matter

Gravity is non-linear, therefore you can't describe the total signal as the sum of signals from "specific potions" of infalling matter. I believe it is incorrect to talk about the signal due to a "specific portion" of the infalling matter in the strong field case you are describing. In the weak field case one can get away with it as an approximation, but not in a strong field case.

It's wrong to ascribe all signals directly to matter. The right way to do things is to solve the Einstein field equations. Matter causes space-time to curve. The curved space-times interact, in a nonlinear matter, even in regions where matter isn't present.

As another poster has pointed out, in a black hole-black hole merger, which is one of the best studied cases, there isn't technically any matter in the simulation. There is only space-time geometry, and an excluded point that represents the singularity - nothing that can really be called matter. But it is the interaction of the two space-time geometries that is studied in this case.

We know a lot about the GW's emitted by binary inspirals, they have been studied in detail, so I will try to describe the three phases of what happens during such an inspiral. Black-hole black-hole inspirals are one case, neutron star-black hole inspirals have also been studied, I believe. The later does contain matter, so it applies to your question.

The first part of the inspiral can be handled by post-netwonian approximations to GR analytically. During this phase, as the inspiraling black holes get closer and closer, the gravitational wave emission increases as the two black holes orbit each other closer and closer , faster and faster. This generates a characteristic chirp, the amplitude and frequency both increase with time.

The second part requires numerical simulation of the strong field Einstein equations. This is very numerically intensive.

The third part involves the ring-down of the black hole. This ringdown phenomenon is also expected if matter falls into a bh. The infalling matter "excites" the space-time around the black hole. Even after coalescence is regarded to have occurred (and I'm not quite sure white criteria / coordinates are used to determine "before" and "after" in this contex), the ringdown emits gravitational waves.

I suspect this is the key part of your question, unfortunately I don't have an answer to it. Conceptually, the simulations wind up describing a four dimensional space-time geometry that represent the entire process, using, for instance, the "block universe" philosophy. Separation of the 4-d geometry into "before" and "after" is a matter of choice, and the choice is made for convenience, which in this case is efficiency of the calculation process.

It is reasonably likely that the notion that simultaneity, "before and after", depends on human choices and is not dictated by physics may not be familiar to you. This comes out of special relativity, and is known as "the relativity of simultaneity". In fact, the relativity of simultaneity is one of the key stumbling blocks for a lot of people when learning SR. This post is already too long to go into more details about the topic, so I'll simply point out it's existence. There have been many threads on this topic, and I'm sure there will be many more.

Because of the relativity of simultanetiy, splitting up this 4d geoemtry into spatial slices that has a "before" and an "after" requires some conventions as to how to do this. These conventions are not physics, they're just a way of organizing our thinking in familiar terms. Pragmatically, the choices made are just the ones that make the computations reasonably efficient. But I don't know any details.

A description recapping the three phases of the merger can be found in wiki, and a number of papers. Wiki is probably a good starting point. https://en.wikipedia.org/w/index.php?title=Binary_black_hole&oldid=920102125

 

[ObjectivelyRational]

Thank you this was very informative. Inspired me to look through my old textbooks.

Turns out they have more info in them than I remembered...

Thank you to everyone who took the time to reply.