Gravitational Wave

Full definition

Imagine spacetime as a vast, perfectly tensioned elastic sheet. Every mass dimples a well there, deeper the heavier the mass. Now wiggle a mass abruptly — spin two masses around each other at high speed — and the two wells begin to oscillate. The oscillations don't stay local: they propagate through the sheet as ripples travelling outward. These ripples in spacetime are gravitational waves.

At a location crossed by a gravitational wave, distances between objects alternately compress and stretch along two perpendicular directions. The typical amplitude detected by LIGO — when a black-hole merger occurs a billion light-years away — is of order h ~ 10⁻²¹. That means a 1 km distance varies by 10⁻²¹ × 10³ m = 10⁻¹⁸ m. A thousandth of a proton diameter. LIGO measures that. Strictly speaking, it is probably the most precise measurement ever made in the history of physics.

Einstein published the prediction in a seminal 1916 paper, then returned in 1918 with the quadrupole formula giving emitted power. By 1936 he wavered and proposed with Rosen that these waves were mathematical artefacts — a mistake quickly corrected. Joseph Weber attempted the first direct detections in the 1960s-1970s with aluminium resonant bars; he announced several signals without confirmation. Binary pulsars provided the first indirect proof: pulsar PSR B1913+16 (Hulse and Taylor, 1974) loses orbital energy at precisely the rate predicted by Einstein's formula. 1993 Nobel Prize.

Direct proof had to wait until September 14, 2015 at 09:50 UTC, when the two LIGO interferometers (Hanford and Livingston, 3,000 km apart) simultaneously recorded a characteristic 0.2-second chirp: the signature of two black holes merging 1.3 billion light-years away. The public announcement on February 11, 2016 sent tremors through the community. 2017 Nobel Prize in Physics to Rainer Weiss, Barry Barish and Kip Thorne.

Numbers and sources

Einstein's quadrupole formula gives the power radiated by a rotating massive system:

P ≈ (G / 5c⁵) · ⟨d³Q/dt³⟩²

where Q is the system's quadrupole moment. For a tight binary, this simplifies to:

P ≈ (32/5) · (G⁴/c⁵) · (M₁M₂)²(M₁+M₂) / r⁵

The 1/r⁵ falloff is decisive: radiation becomes titanic when the two bodies close in before merger. For GW150914 (merger of 36 and 29 M☉ black holes), peak power reached ~3.6 × 10⁴⁹ W — about 50 times the luminous power of the entire observable Universe for 0.2 seconds. Mass-equivalent radiated: 3 M☉, converted entirely into gravitational waves.

Catalogued sources.

• Stellar black-hole mergers: the majority (>80 events in GWTC-3, 2021). Masses 5-100 M☉. Frequencies 30-300 Hz.

• Neutron-star mergers: rare (2 confirmed: GW170817 in 2017, GW190425 in 2019). Longer signal (60-120 seconds). GW170817 coupled to an electromagnetic counterpart (kilonova AT2017gfo) launched the multi-messenger era.

• Mixed black-hole + neutron-star mergers: first two confirmed cases in 2021 (GW200105, GW200115).

• Core-collapse supernovae: not yet detected, weak expected signal (only for a galactic supernova).

• Rotating pulsars: continuous radiation, not detected (limits on deformations < 10⁻⁸).

• Stochastic background: possible evidence reported by NANOGrav (2023) in the nanohertz range, attributed to supermassive black-hole binaries across the Universe.

Speed and polarization. GW170817 plus its gamma-ray counterpart (1.7-second delay over 130 million light-years) constrain the speed of gravitational waves to c to |Δc/c| < 10⁻¹⁵. This single result ruled out the majority of alternative modified-gravity models at once.

Types and frequency regimes

Gravitational waves span a phenomenal spectrum, from 10⁻¹⁸ Hz (cosmological horizon) to 10⁴ Hz (compact binaries). Each range demands a different detector.

High frequency (10-10,000 Hz) — LIGO, Virgo, KAGRA. Ground-based kilometre-scale laser interferometers. Sources: stellar black-hole and neutron-star mergers. Sensitive to 100 Mpc-1 Gpc. First detection: GW150914 (September 2015).

Mid-frequency (10⁻⁴-1 Hz) — LISA (ESA). 2.5-million-km triangular interferometer, three satellites orbiting the Sun. Launch planned 2035-2037. Sources: supermassive black-hole mergers (10⁵-10⁸ M☉), EMRIs (compact objects inspiralling into a supermassive black hole), galactic compact binaries.

Nanohertz (10⁻⁹ Hz) — Pulsar Timing Arrays. Millisecond-pulsar networks as natural clocks, monitored by NANOGrav (USA), EPTA (Europe), PPTA (Australia), IPTA (global). In June 2023, NANOGrav announced 3-4 σ evidence of a nanohertz stochastic background — likely the cumulative population of supermassive black-hole binaries.

Ultra-low frequency (10⁻¹⁶-10⁻¹⁸ Hz) — CMB B-mode polarization. Signature of primordial gravitational waves from cosmic inflation. No detection yet, limit r < 0.036 (BICEP/Keck 2021). Priority target of LiteBIRD (JAXA, 2029).

Typical amplitude h. Around 10⁻²¹ for a stellar merger at z ≈ 0.1. LISA will detect down to h ~ 10⁻²³. Future detectors Einstein Telescope (Europe, ~2035) and Cosmic Explorer (USA, ~2035) will target h ~ 10⁻²⁴ and 10,000 mergers per year.

How do we detect them?

Three main technologies, one per frequency range.

Ground-based laser interferometry (LIGO, Virgo, KAGRA). A laser splits into two perpendicular beams travelling down 4 km arms (LIGO), 3 km (Virgo), or 3 km underground (KAGRA), then recombines at a photodetector. Suspended, ultra-isolated mirrors are touched by the gravitational wave, which compresses one arm while stretching the other. The interference reveals fractional arm-length variations as small as 10⁻²¹. LIGO inaugurated in 2002; Advanced LIGO upgrade in 2015 (enabling GW150914). The O4 run (May 2023 - 2024) doubled the detection rate: one event every 2-3 days.

Pulsar Timing Arrays. Millisecond pulsars are fiercely stable clocks (precision ~10⁻¹⁵). A nanohertz gravitational wave crossing the pulsar-Earth network modifies pulse arrival times with a precise angular pattern (Hellings-Downs curve). With 15 years of data on 68 pulsars, NANOGrav announced preliminary detection at ~3.5 σ in June 2023.

Space interferometry (LISA). Three satellites in a 2.5-million-km triangle, exchanging laser beams. Orbit the Sun trailing ~20° behind Earth. ESA launch planned ~2035-2037. Sensitive to supermassive black-hole mergers up to z ~ 20 — essentially all detectable. Also sensitive to a primordial cosmological background.

Multi-messenger. Event GW170817 (August 17, 2017) opened the era: neutron-star merger detected by LIGO/Virgo, then gamma-ray burst 1.7 s later by Fermi, then optical kilonova AT2017gfo in NGC 4993 identified 11 hours later by Swope (Chile). More than 70 observatories followed up. This cascade measured H₀ by standard siren, verified heavy-metal production (gold, platinum) in kilonovae, and constrained the speed of gravitational waves to c.

Not to be confused with

Several confusions deserve to be cleared up.

Gravity waves. In English, 'gravity waves' (without 'al') denote surface waves in a fluid under gravity — ocean waves, atmospheric ripples. Unrelated. 'Gravitational waves' (with 'al') are the spacetime waves. The linguistic trap is easy and worth avoiding.

Static gravitational force. The Newtonian attraction between two masses at rest is not a wave — it is a static field. A gravitational wave appears only when a mass accelerates (more precisely when the system's quadrupole moment varies). A symmetrically rotating object emits no waves.

Graviton. Hypothetical particle of quantum gravity, the quantum of a gravitational wave — analogue of the photon for light. No individual detection foreseeable in the short term (absurdly small cross-sections). Gravitational waves, on the other hand, are classical phenomena perfectly described by general relativity without needing quantization.

Gravitational lensing. Static effect, tied to spacetime curvature by a mass at rest. Both phenomena stem from general relativity but operate differently: the lens bends light; the wave carries energy through the vacuum.

Electromagnetic waves. Gravitational and EM waves both propagate at c, both carry energy, both are emitted by accelerated masses/charges. But EM waves are dipolar (standard linear polarizations) and emitted by electric charges, whereas gravitational waves are quadrupolar (2 tensor modes + and ×) and emitted by any mass in asymmetric acceleration.

Gravitational radiation vs. gravitational wave. The two terms are synonyms in scientific literature. By analogy: 'electromagnetic radiation' and 'electromagnetic wave' describe the same phenomenon, depending on whether the energy or wave aspect is emphasised.