> Just as light can be bent and magnified when it passes through the gravitational fields of galaxies and other massive objects, gravitational waves should be warped in the same way, too.
I'm gonna need a refresher course on that.
I'm gonna need a refresher course on that.
So, imagine you have a massive celestial body floating out in space, with a large gravitational field. Its gravitational field is always propagating. Now, take that celestial body, and make it completely and instantaneously disappear. There's now a gravitational differential between the now-gone body, and its previously propagated gravity field. You should be able to detect that if you're close, say through tidal differences.
Very similar happens with black holes colliding, except the gravity differential comes from the two black holes oscillating near each other, close to the speed of light.
Edit: this obviously isn't exactly how this works, since it makes a lot of assumptions, such as the ability to instantaneously remove something. So, don't think of this as how "things actually work", but as a model to help build your intuition.
That doesn't mean there's anything wrong with the model. It's just GIGO.
Of course, it's not actually disappearing, just moving, but the original point was about detecting sharp changes in the gravitational waves. A quick Google search tells me that gravitational wave red shifting is a thing, and I imagine that with blackholes it's a very important phenomenon and area of study. And I would guess that there can also be interesting second-order effects that such a blackhole's movements have on the propagation of gravitational and electromagnetic waves from other objects.
Yes.
> with blackholes it's a very important phenomenon
Black holes can lense gravitational radiation emitted by background systems.
Most background systems we are likely to detect soon will involve black holes. But these are black holes in some sort of mutual orbit, rather than black holes simply moving across some system of celestial coordinates.
For black holes that are moving linearly at near the speed of light, the black hole's effect on the metric elongates like a pencil, with the field weak outside and growing strong towards the centre of the "lead" or graphite. This is similar to Lorentz-contracting the near region around the black hole, and one can generalize a bit and say that as the boost between an observer and any object increases, the object thins. In the ultra-ultrarelativistic limit, the object and all the strengthening-towards-infinity field values around it become infinitely thin.
As one's speed relative to a black hole gets very close to c, the black hole becomes quite easy to model as an exceptionally high-energy massless particle.
You get this effect when your small space capsule whizzes by our galaxy's central black hole at speeds near that of light too, and your small momentary perturbation basically affects the black hole not at all. Because Lorentz contraction is reciprocal, whizzing a black hole -- even a large one -- at ultrarelativistic speeds past the International Space Station is going to have very little effect on it.
We model this with the https://en.wikipedia.org/wiki/Aichelburg%E2%80%93Sexl_ultrab... metric of General Relativity and usually some gauge fixing and small perturbations.
Tossing a large black hole past the ISS at low speeds compared to light will really mess up the neighbourhood of the solar system, but your space capsule can pretty safely manage a slow-compared-to-light hyperbolic orbit around a large black hole without much problem (ignoring any accretion disc and twin "paradox" issues).
If the sun instantaneously vanished, we would see it disappear at the same instant as its gravitational effect stops, 8 minutes after the actual event occurred. For those 8 minutes while the light and gravitational information are in transit, the Earth will continue to revolve around a visible (though now nonexistant) sun.
In the same way as if the sun suddenly jerked ten million miles to the south, we would see it move at the same instant as its gravitational force vector changed, 8 minutes after the actual event occurred, but that's harder to keep in your head.
See also: https://physics.stackexchange.com/questions/100893/is-einste...
These are usually probed by adding test masses of some sort, letting them evolve along available trajectories. Some such test masses are pointlike, neutral, and nearly massless; others are some sort of classical or quantum field. In most cases, the goal is to keep T^{\mu\nu} negligible.
One can alternatively be lead by the stress-energy tensor, and may be tempted to call T^{\mu\nu} the matter tensor in that case. One typically chooses some vacuum background -- Minkowski space, usually, but any background can be used -- and then uses perturbation theory to capture how the chosen matter alters that background curvature. This is very common in cosmology.
> Except for the cosmological constant, but that's different
No, it's not different; one has flexibility to move the cosmological constant into the RHS for calculational convenience without having to change its interpretation as part of the background curvature: https://en.wikipedia.org/wiki/Lambdavacuum_solution
Source: Bachelor at GTR
Since light and gravitational waves both propagate through spacetime, both will try to go straight but will get bent since they're traveling through curved spacetime.
It's sort of analogous to how your path gets bent as you try to walk straight along the earth, making you walk in a really big circle. Except that in General Relativity, time is getting bent too and trajectories aren't through space, but spacetime.
Slightly technically: the "curvature of spacetime" in your question is the metric tensor field ("the metric") which fills the whole of spacetime. Yes, when we have a binary like above, the metric is dynamical. We can deliberately fix a background metric chosen for calculational or conceptual ease, and capture much of the metric dynamics as small perturbations on the background.
In this picture, we usually get gravitational waves by imposing a coordinate time on a relevant part of the spacetime, and then finding which small perturbations obey an appropriate time-dependent massless wave equation.
More physically, what this picture is saying is that in the case of a single binary, if an observer stays at one spatial location and from time to time checks its accelerometers, and they will point to the retarded positions of the objects in the binary. If you put a gravitational lense between the binary and the observer, one is free to encode the lense as a perturbation, or one can add it into the background. (The former is more popular for reasons I'll explain further below.)
Alternatively, it might help to think of gravitation as a gauge theory, wherein one can only measure potential differences between two points in spacetime rather than some absolute potential.
Let's start by defining a background wherein the potential is everywhere identical and calling that the vacuum expectation value (vev). If our background has some static spherical mass on it, we can measure a potential difference between fairly-close-to-the-mass and far-from-the-mass[1]. The potential difference is not time-dependent.
As we add any such mass we may update our vev a little, but at enormous distances from all the masses, it's only a very little, so we can largely take a value much closer to our set of masses.
But when we add in more than one mass, we lose time-independence.
If the initial conditions are picked so the masses do not orbit or twist around each other, our masses will obey Raychaudhuri's focusing theorem, and we can reason using shell theorem or Birkhoff's theorem, and expect no gravitational waves detectable outside the collapsing system. On the other hand, if we let our masses fall into orbits, we get gravitational waves.
In the focusing-only case we end up seeing vev - potential_near increasing during the collapse, where near is at a large finite radial distance (in Schwarzschild coordinates) from the collapsing mass, and we measure vev at radial infinity. In the orbiting case, vev - potential_near has a long term tendency to increase, but will vary slightly depending on the orientation of the measurement points to the binary.
A large mass -- like a galaxy cluster -- far from the source is just a region where the potential departs from vev. Helpfully, when the lense mass is that large and the GW frequency is high (e.g. near the end of a binary inspiral, or quantitatively greater than ~ 1 Hz), we can draw a direct formal analogy with electromagnetism: the geometrical optics approximation [2]. Following gravitational wave analogy with https://en.wikipedia.org/wiki/Geometrical_optics we map the difference in potential from the vev to a difference in index of refraction and let the GW plane wave refract. It's useful to remember here that GWs are modelled in a linearization of the Einstein Field Theory and so treating galaxy clusters as linear media or galaxies as nested shells of linear media is a reasonable approach. Unfortunately, in general wave optical solutions are only obtainable numerically.
Using the full GR, you have a metric with pretty much no symmetries and good luck with the calculations. Your starting point for extragalactic GW sources would be a "swiss cheese" like Einsten-Straus 1931 with multiple vacuoles and then combine that with a pp-wave, probably perturbatively, ideas which have been explored in the literature although usually in cosmological/primordial GW contexts [3]. (Compare with a more formal statement of the approach in previous paragraphs, e.g. in §1.2 at http://aether.lbl.gov/www/classes/p139/homework/hw12.pdf )
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[1] If we are sufficiently close to Newton, by splitting spacetime according to a slow-moving-compared-to-light observer not very close to any compact massive objects then we can can use : https://en.wikipedia.org/wiki/Gauss%27s_law_for_gravity#Pois...
[2] Thorne, K. S. 1987, in Three Hundred Years of Gravitation, ed. S. W. Hawking & W. Israel (Cambridge: Cambridge Univ. Press), p. 361, and Isaacson [1967] https://doi.org/10.1103/PhysRev.166.1263 (PDF version https://drum.lib.umd.edu/bitstream/handle/1903/17447/Isaacso... )
[3] for some pointers, see the Introduction section of https://arxiv.org/abs/1307.4371
Oh yes, me too. I learnt that gravitation bends space-time and that's why light rays seem to be bent. If gravitation is just waves too, then how does that work and who bends the gravitational waves. This gets even more puzzling if we assume gravitation is mediated by particles[1]. On the other hand if gravitation is just wave and not particle it would be completely unlike the other fundamental interactions including those mediated by photons, aka light.
[1] LIGO detected gravitational waves but we don't know if gravitation particles (gravitons) exist. Detection of gravitons might not be practically possible.
I think your confusion comes from your thinking that the same word ("wave") is always used for the same effect. In your few sentences the "wave" is the word which is used for completely different effects and scales:
For the gravitational waves that we measure we don't have to worry about some single "gravitation particle". The gravitational wave detectors don't have to care "if gravitation particles (gravitons) exist" as that's on completely another scales, you can imagine these (measured) waves as being created by such an immense number of "gravitons" that these are surely not seen.
If you want some analogy: you know that for people to think easier about the spacetime curvature due to the gravitation one says imagine a 2D membrane with a ball on it (representing a star or a black hole or some other big object) curving the membrane. Now what are the events LIGO detects: imagine two balls, rotating one around another, resulting in the ripples on the membrane, just like two fast boats circling produce interesting waves on the surface of the lake. LIGO detects such ripples.
So the curvatures due to the masses always exist, but the huge masses moving around produce the ripples in the spacetime (it's just the shape of the curvature that changed in the different time points). That is not "gravitation is just waves too" that's: we see the ripples independently of the existence or non-existence of the gravitons on the quantum level.
To go back to the "boats on the lake" example, you detect the waves of the whole lake surface, and on that level to observe these waves it's irrelevant to you that the water is made of molecules, that the molecules are made of the atoms, that the atoms are made of the particles, and that there are the experiments that demonstrate the quantum nature ("wave"-like nature) of the said particles.
The difference in the orders of magnitudes between the waves LIGO detects and quantum "wave"-like particles is immense, so big that there aren't any simple examples I can imagine.