nLab gravitational wave





physics, mathematical physics, philosophy of physics

Surveys, textbooks and lecture notes

theory (physics), model (physics)

experiment, measurement, computable physics



The physical theory of Einstein-gravity (“general relativity”) predicts, via Einstein's equations of motion, that vacuum spacetime may show a kind of oscillations of the field of gravity roughly analogous to electromagnetic waves in electromagnetism. (Both kinds of waves are oscillation of the field itself and do not depend on some “medium” such as a water wave does.) In fact, since the force of gravity is reflected in the pseudo-Riemannian geometry of spacetime, a gravitational wave is a kind of periodic distortion of spacetime geometry itself.

Experimental observation

At the end of the 20th century, there had accumulated excellent but indirect evidence for gravitational waves from the observation of binary pulsars (Hulse-Taylor 75). Their observed rotational motion loses energy precisely to the extent that general relativity predicts is being radiated away by gravitational waves.

On 11 Febrary 2016 was the announcement of the first direct detection by the LIGO collaboration, using laser interferometry, of a gravitational wave signal coming from the in-spiral and merge of a pair of black holes (LIGO 2016). The signal was a chirp at 35-250 Hz (converted to audio in this looped recording), detected as coming from the sky over the southern hemisphere on 14 September 2015.

Further direct detections of gravitational wave events followed. The event GW170817 LIGO-Virgo17 showed gravitational waves from merging neutron stars coincident with the corresponding electromagnetic radiation.



The first article that correctly derived gravitational waves from the Einstein equations is

  • Albert Einstein, Über Gravitationswellen, Sitzungsberichte der Königlich Preußischen Akademie der Wissenschaften Berlin (1918), 154-167

In particular this correctly stated that gravitational waves require a quadrupole moment as a source (e.g. a rotating binary star system) and not just a dipole moment (e.g. an oscillating charge) as for electromagnetic waves (the graviton has spin 2, the photon has spin 1…), thereby correcting a mistake to this effect in the earlier article

  • Albert Einstein, Näherungsweise Integration der Feldgleichungen der Gravitation, Sitzung der physikalisch-mathematischen Klasse vom 22. Juni 1916 (web)

The reality of gravitational wave solutions however kept being a cause of concern for many years (Einstein himself was concerned that the linearization approximation used in their derivation might have been too coarse), for a brief account of the early history see

A modern walk through the derivation of gravitational waves from linearization of Einstein's equations may be found for instance on pages 5-24 of

See also

Review in view of modern gravitational wave detection (see below):

Discussion in view of quantum gravity:

Theoretical predictions

Discussion of theoretical predictions for events that have a chance to yield detectable gravitational wave signals includes:

  • Thibault Damour, Gravitational Waves from Coalescing Binary Black Holes: Theoretical and Experimental Challenges, talk in Munich, 2010 (web, youtube)

In particular, the computation of the signal from the coalescence of two inspiralling black hole binaries is due to

Review of the theoretical predictions and their experimental verification is given in

Discussion using the string theoretic KLT relation/double copy-approach for computing higher order corrections to gravitational wave-signatures of relativistic binary mergers for use with LIGO:

  • Zvi Bern, Clifford Cheung, Radu Roiban, Chia-Hsien Shen, Mikhail P. Solon, Mao Zeng, Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order, Phys. Rev. Lett. 122, 201603 (2019) (arXiv:1901.04424)

Discussion in relation to the soft graviton theorem:

Experimental observation

Indirect detection of gravitational waves based on energy loss of a binary pulsar system is due to

  • Hulse, Taylor, Discovery of a pulsar in a binary system, The astrophysical journal, 195:L51-53, 1975 (web)

The first proposal of the LIGO-type experiment for the detection of gravitational waves is due to

  • M. Gertsenshtein, I. Postivoit, On the detection of low frequency gravitational waves, Soviet Physics JETP, volume 16, number 2, 1963 (pdf)

Direct detection of gravitational waves by the LIGO experiment is reported in

  • B. P. Abbott et al. (LIGO Scientific Collaboration and Virgo Collaboration), Observation of Gravitational Waves from a Binary Black Hole Merger, Phys. Rev. Lett. 116, 061102, 11 February 2016, doi:10.1103/PhysRevLett.116.061102

  • B. P. Abbott et al. (LIGO Scientific Collaboration and Virgo Collaboration), GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral Phys. Rev. Lett. 119, 161101, 2017 (doi:10.1103/PhysRevLett.119.161101)


  • Salvatore Vitale, The first five years of gravitational-wave astrophysics (arXiv:2011.03563)

Last revised on June 8, 2023 at 05:54:20. See the history of this page for a list of all contributions to it.