Image 1 Caption: Low frequency gravitational waves (frequency of order 30 nHz ≅ 1 cycle/year) can be observed via pulsar timing arrays (PTAs) which consist of a set of pulsars plus radio telescopes. Nature gives us the pulsars and we build radio telescopes.
Shown in Image 1 is Lovell Telescope (a radio telescope), Jodrell Bank Observatory, Lower Withington, Cheshire, England, United Kingdom.
The Lovell Telescope is being used by as part of two pulsar timing array collaborations: the European Pulsar Timing Array (EPTA) and the International Pulsar Timing Array (IPTA).
Features:
The millisecond pulsars emit extremely regular radio pulses with periods of <∼ 10 ms
Gravitational waves from extragalactic sources displace the millisecond pulsars relative to Earth by small amounts, and thus change the time between pulses due to the change in light travel time due to the finite vacuum light speed c = 2.99792458*10**8 m/s (exact by definition) ≅ 3*10**8 m/s = 3*10**5 km/s ≅ 1 ft/ns.
By studying the changes in light travel time for a PTA, we can determine the magnitude of the displacement caused by the gravitational waves and the frequency of the gravitational waves.
Gravitational waves as can be seen in the animation are quadrupole waves (in lowest order to be exact). As infinite plane wave gravitational waves pass through, space is expanded and contracted alternatively in two perpendicular directions. To extend the picture, every line of test particles aligned with one direction would expand and contract alternating with the expansion and contraction in the other direction of every line of test particles aligned with the that other direction.
For ideal test particles, the gravitational waves lose/gain NO energy passing through. However, if the test particles interact with each other, then energy might be (lost to)/(gained from) some form in the system of the test particles. In most actual astrophysical cases, one would expect large gravitational waves propagating through the observable universe to lose energy in expanding non-elastic systems. However, systems of mutually gravitating stars, planets, etc. are probably to 1st order elastic systems. So such large gravitational waves probably do NOT lose much energy by interacting with local astronomical objects as they propagate. This makes the large gravitational waves very useful observables for the nature of their sources. Note, the energy available to deposit in any location must go down as the gravitational waves expand from their sources.
Another remarkable emarkable feature about gravitational waves is that they do NOT necessarily obey the conservation of energy principle. There is NO absolute proof that the gravitational potential energy they remove from their source will be deposited elsewhere: it might be less or more in total. There is a proof that gravitational waves do obey conservation of energy principle in a sense in an important special case (see Roger Penrose, The Road to Reality, 2004, p. 467--468).
The last feature brings up an issue also related to the first feature. Gravitational potential energy is NOT actually an energy of the gravitational field in an ordinary sense. Note the gravitational field is our classical limit way of thinking of the curvature of spacetime which is how gravity is manifested in general relativity. So the gravitational field is NOT a field in the sense of the electromagnetic field which has an associated energy density: i.e., there is so much energy here, so much energy there. If gravitational field had an energy density, then the gravitational field would become self-gravitating which would be extremely paradoxical since it is NOT self-gravitating in the classical limit. Also, the simplest approach to gravitational field energy density leads to it having negative mass which is really hard to make sense of. General relativity avoids the paradox by coding energy stored in the structures of spacetime (e.g., gravitational waves) nonlocally, and so it does NOT appear in the energy-momentum tensor T_ij of the Einstein field equations NOR anywhere explicitly. You can put energy into the structures of spacetime and get it out, but while in those structures it is NOT exactly known where it is. It can be approximately known (see Roger Penrose, The Road to Reality, 2004, p. 465).
In 2021 Arzoumanian et al. (2021) writing for the NANOGrav collaboration reported that they had a signals that were plausibly extrasolar and therefore could be gravitational waves of the gravitational wave background (GWB; stochastic background). However, it is possible that signal is some kind of noise and/or a systematic error. Signal did NOT conform to
(see Adam Mann, Galaxy-Size Gravitational-Wave Detector Hints at Exotic Physics, SciAm, 2021feb03).
Note that Lieu et al. (2022) find that low frequency gravitational waves probably CANNOT propagate for more than ∼ 1 Gpc through the intergalactic medium (IGM). This greatly limits the detectability of sources of low frequency gravitational waves. In particular, primordial gravitational waves may be undetectable---a vast disappointment.
Images:
Local file: local link: gravitational_waves_low_frequency.html.
Image link: Wikimedia Commons:
File:Lovell Telescope 5.jpg.
Image link:
NANOGrav:
An Acoustical Analogue of a Galactic-scale Gravitational-Wave Detector.
Image link: Wikimedia Commons:File:Gravitational-wave detector sensitivities and astrophysical gravitational-wave sources.png.
Image link: Wikimedia Commons:
File:GravitationalWave PlusPolarization.gif.
File: Relativity file:
gravitational_waves_low_frequency.html.