# If Gravity travels at c

by OSalcido
Tags: gravity, travels
 P: 2,050 That's actually a difficult question: - it *will* end up being still spherically symmetric (google "no hair theorem"), albeit slowly moving in the direction of the momentum you threw in. - you will never actually see the small piece of mass reach the event horizon (due to time dilation). - as the mass approaches, the "event horizon" isn't well defined (mathematically, it's a global rather than local concept). - the finer details still aren't all known, basically because the precise equations are so difficult to extract accurate solutions from. There is a closely related question, of what happens to the electric field if a charge is thrown into a black hole. In that case I think the finer details can all be worked out, and you see that as an electric charge approaches the black hole, the event horizon practically takes on a like charge, so externally it makes little difference whether the charge is "just outside" the horizon or even "in the singularity".
P: 2,341
 Quote by Brinx Consider a non-rotating black hole, with a nice spherically symmetric event horizon.
Let's say uncharged and isolated (no other mass present), so that we can model the initial situation using a portion of the Schwarzschild vacuum solution.

 Quote by Brinx If one drops some mass 'into' the black hole from a specific direction, what will be the resulting gravitational field of the now slightly bigger black hole?
It is often helpful to first study the analogous Newtonian question. Here, there is a tidal tensor which can be compared directly with that electrogravitic or tidal tensor used in gtr. In Newtonian theory it is, in a vacuum region, simply by $E_{jk} = \Phi_{,j \, ,k}$ where $\Phi$ is the Newtonian gravitational potential http://en.wikipedia.org/w/index.php?...oldid=28781955 (or more generally, by the traceless part of the Hessian). So answering the question comes down to how the potential changes. In a vacuum region, the potential is just a harmonic function, and since we are dealing with an isolated system (central object plus smallish mass) it vanishes asymptotically. As the smaller object approaches its gravitational field distorts that of the big one. Since Newtonian gravitation is governed by a linear field equation, the Poisson equation, the net potential is simply the sum of the two original potentials. So at this point, you might want to add two point mass Newtonian potentials and animate some contour plots, then follow suit for the Hessian.

In general relavity, as the two objects near each other, we expect strong fields to bring nonlinearity into play, so that the predictions of gtr will differ greatly from those of Newtonian gravitation in various ways. However, it should already be clear at this point that one thing you can expect during the "approach phase" is that the field may retain approximal axial symmetry but certainly won't be spherically symmetrical.

In both Newtonian gravitation and gtr it is useful to have some way of describing precisely the "shape" of the field. In the case of an isolated system, as in our situation, the answer is multipole moments. If you haven't seen these before, you might take a moment (no pun intended) to read about the elementary kinds of moments used everywhere in mathematics, including weak-field gtr, which is an approximate theory governed by the "linearized EFE". In fully nonlinear gtr a more sophisticated kind of multipole moment is appropriate (there is a standard notion, given by competing mathematical definitions which turn out to be largely equivalent).

One of the most essential differences between Newtonian gravitation and gtr is that gtr is a true relativistic field theory of gravitation, and thus it predicts the existence of gravitational radiation. In particular, when the multipole moments of an isolated system are appropriately time varying, gravitational radiation will be emitted from the system. This condition is satisfied in our situation.

Now, there is a principle, discovered long ago by Richard Price and others, to the effect that when a smallish object falls into a black hole, after the collision and merger, the field may be briefly distorted (in particular, the horizon might be distorted and wrinkled), but the hole "radiates away" these distortions in the form of gravitational radiation which moves out at the speed of light and leaves behind an "smooth and symmetrized" region. The result is that after all the fuss has died down, you have a somewhat larger hole, but if no angular momentum was introduced during the merger, it will still be modeled by a Schwarzschild vacuum.

 Quote by Brinx Before you say 'simply spherically symmetric again, only a bit stronger', let me elaborate.
I am oversimplifying above, incidently. In fact much more can be said about the time sequence which the radiation will follow, how strong it will be, and so on. A huge amount of work has been done on such problems, so quite a bit is known by now about what gtr predicts in such merger scenarios.

 Quote by Brinx I'd think that the last position from which the gravity field of the infalling mass is 'updated' for an external observer lies at the event horizon.
Which is not static in this situation.

 Quote by Brinx That, after all, is the place from which the changes in the gravitational field brought about by the infalling mass can still be propagated outward. After the mass passes the event horizon, its position can no longer be measured, by any means including via gravitational waves. So, then we get a slightly asymmetric gravitational field as a result: the initial spherically symmetric gravitational field of the black hole (centered, presumably, at the center/singularity of the black hole), plus the small addition of the gravitational field of the infalling mass (or rather, the 'fossil field' of the mass from the moment it passes the event horizon), of which the center resides at the point on the event horizon through which the mass fell. The sum of these fields isn't spherically symmetric anymore, it'd seem. Does my line of reasoning make sense?
Comparing with what I said above, sounds about right.

 Quote by Brinx Is the conclusion of a resulting non-spherically-symmetric gravitational field, if valid, problematic in any sense?
Well, much is known, but not everything which might happen is well understood yet. Merger scenarios continue to be the subject of intense research. Because of these typically have little or no symmetry, much of the work involves numerical simulations, and it turns out to be highly nontrivial to concoct numerical integration schemes which remain stable sufficiently long to model the "approach, merger, radiative smoothing" scenario sketched above.

One thing which is thought to be "well understood" from simulations is the idea that in some merger scenarios, the gravititational radiation emitted from the system might be asymmetric, basically because the smallish object, roughly speaking, will suddenly plunge into the (distorted) horizon of the hole. In some situations this radiation can carry off very substantial amounts of energy and momentum. The result is that the new hole should be "kicked" by the recoil of the outgoing gravitational radiation! As a result, one should apparently expect to find holes speeding out of their parent galaxies as the result of such mergers. But as someone recently mentioned, a current mystery is that this hasn't yet been observed.

 Quote by cesiumfrog - as the mass approaches, the "event horizon" isn't well defined (mathematically, it's a global rather than local concept).
In principle, the event horizon would generally be well defined but it is always defined in "teleological" fashion. That is, knowing the locus of the event horizon requires roughly speaking knowledge of the entire future history. Thus, numerical simulations have to use "horizon detectors" based on local (as in local neighborhood) notions. One fact worth mentioning is that in the static Schwarzschild vacuum, the world sheet of the horizon (static and spherically symmetric!) happens to be generated by a Killing congruence. This is related to the fact that the covariant derivative of certain scalar curvature invariants vanishes at the horizon, which is an "infinitesimal" criterion. Such a thing is called a "Killing horizon". But in your scenario, the true event horizon would not be given this way.

See the website in my sig for links to on-line resources and citations of relevant books. In particular, the monograph by Hawking and Ellis, The Large Scale Structure of Space-Time, contains a classic discussion of how the horizon behaves during merger of two black holes, and the monograph by Frolov and Novikov, Black Hole Physics, contains an introduction to such topics as quasinormal modes, which govern how a hole responds to small perturbations. But you might want to start with the excellent survey articles in Black Holes and Relativistic Stars, ed. by Robert Wald. See section 4.7.3 of the article by Rees for recoil, see the article by Teukolsky for numerical simulation of mergers, and see the article by Kip Thorne for the radiation predicted in merger scenarios.

HTH
 P: 70 Thank you very much for your answers! I will have to read more about this subject to get a better grasp of the specifics, but as I understand from Chris' answer the asymmetry seems to be 'solved' by gravity waves, carrying away the asymmetric component of the gravitational field.
 Sci Advisor P: 2,341 Yes, that's about right. Now you have a new mystery to chew on: why haven't "kicked" holes been observed?
 P: 87 I was reading something last week about off-centre galactic nuclei and quasars that were outside the main body of a galaxy. I'm at work so I can't find it, but maybe this is relevant: http://www.citebase.org/fulltext?for...o-ph%2F0208215 I was also reading about "seat belts" in New Scientist, again I'm not sure if it's relevant: http://space.newscientist.com/articl...ack-holes.html On the subject of stellar black holes rather than supermassive black holes, is anybody aware of any apparent puzzles or unexpected results re the mass of black hole candidate objects?
P: 2,341
 Quote by Voltage I was reading something last week about off-centre galactic nuclei and quasars that were outside the main body of a galaxy. I'm at work so I can't find it, but maybe this is relevant: http://www.citebase.org/fulltext?for...o-ph%2F0208215
Yes, the kick effect is mentioned in the abstract.

 Quote by Voltage I was also reading about "seat belts" in New Scientist, again I'm not sure if it's relevant: http://space.newscientist.com/articl...ack-holes.html
Yes, that's what we are talking about. But "seat belts" is a terribly misleading term. It had been known previously that if the spin axis of the holes are aligned, the recoil effect is weak. These researchers are claiming that during the infall, the spins become aligned. So they are saying not "we found a seat belt" (a restraining force counteracting a sharp kick) but "we found that no seat belts are needed" (since no kick). If true that would go a long ways toward explaining the mystery, but its early days yet.

 Quote by Voltage On the subject of stellar black holes rather than supermassive black holes, is anybody aware of any apparent puzzles or unexpected results re the mass of black hole candidate objects?
Could you be more specific?
 P: 87 If we have a binary system that looks like this: o O where the o is a candidate black hole and the O is a star of some typical type and mass, one would observe each object orbiting the other, and would be able to work out approximate masses and orbits. Does anybody know if there's have been any unusual observations or inferences? For example is the calculated mass of o much larger than that of a typical star, and is there a distribution of o masses that doesn't fit the distribution of stellar masses. Alternatively does anybody know of any candidate stellar black holes that follow an atypical galactic orbit?
P: 2,043
 Quote by Chris Hillman In principle, the event horizon would generally be well defined but it is always defined in "teleological" fashion. That is, knowing the locus of the event horizon requires roughly speaking knowledge of the entire future history.
Not always, for instance in closed universes it would not be. Strickly spreaking black holes cannot even exist in such universes.
 Sci Advisor P: 2,341 Sorry, Voltage, nothing comes to mind, possibly because "atypical/unusual" "stellar mass distribution" is still too vague for me. All I can suggest is that you repost your question in the moderated newsgroup sci.astro.research.
 P: 87 Many thanks Chris. Will do.

 Related Discussions Classical Physics 2 Introductory Physics Homework 9 Special & General Relativity 4 Brain Teasers 4 General Physics 23