Gravitational Waves
On 14 September 2015, two L-shaped instruments separated by 3,000 km detected a distortion of spacetime smaller than a proton. The signal lasted 0.2 seconds. It confirmed a prediction of general relativity that Einstein himself doubted could ever be measured.
1. What Are Gravitational Waves?
General relativity describes gravity not as a force but as the curvature of spacetime caused by mass and energy. When massive objects accelerate asymmetrically, the changing curvature propagates outward as waves at the speed of light: gravitational waves.
Unlike electromagnetic waves, gravitational waves stretch and squeeze space itself — alternately elongating space along one axis while compressing it along the perpendicular axis. This is the "plus" (h+) and "cross" (h×) polarizations.
The amplitude — called strain h — measures the fractional change in distance: h = ΔL/L. LIGO measured h ~ 10⁻²¹, meaning a 4 km arm changed by ~10⁻¹⁸ m — 1/1000th the diameter of a proton.
2. The Quadrupole Formula
Einstein's quadrupole formula gives the power radiated as gravitational waves. For a binary system with total mass M, reduced mass μ, and orbital separation a:
Characteristic strain at distance r:
h ~ (G/c⁴) · (2 · d²I/dt²) / r
where I_ij is the reduced mass quadrupole moment.
Crucially, P ∝ a⁻⁵: as the binary spirals in, it radiates more power, which shrinks the orbit further, which increases the radiation — a runaway inspiral. This is why binary neutron stars merge in finite time (Hulse-Taylor pulsar inspired the 1993 Nobel Prize).
3. How LIGO Works
LIGO (Laser Interferometer Gravitational-Wave Observatory) uses Michelson interferometry with 4 km arms to detect the differential length change caused by a passing wave.
- A 1 W laser is split into two perpendicular beams bouncing ~280 times between mirrors (power-recycled to ~100 kW).
- When recombined, the beams interfere. A gravitational wave stretches one arm and compresses the other, shifting the interference pattern.
- Mirrors (test masses) are 40 kg fused silica, suspended by quadruple pendulums to isolate seismic noise below ~10 Hz.
- Quantum noise limits sensitivity at high frequencies; thermal noise at mid-band; seismic at low frequencies.
- Two LIGO detectors (Hanford WA + Livingston LA) 3,000 km apart enable coincident detection and sky localisation. Virgo (Italy) and KAGRA (Japan) add baselines.
4. Reading the Strain Signal
A binary black hole merger signal has three phases:
- Inspiral: Slow spiral over millions of years, then faster. LIGO detects the last fraction of a second. Frequency sweeps upward — the "chirp".
- Merger: The horizons touch (~10 ms). Peak strain and frequency.
- Ringdown: The merged black hole oscillates in characteristic quasi-normal modes, rapidly damping. Allows measurement of final mass and spin.
df/dt = (96/5) · π^(8/3) · (G M_c / c³)^(5/3) · f^(11/3)
Template-matched filtering: GR predicts waveform shapes as a function of masses, spins, sky angles. LIGO cross-correlates ~10⁵ precomputed templates against the data. Detection threshold: SNR > 8 in each detector.
5. Key Detections
| Event | Date | Type | Masses (M☉) | Distance (Mpc) |
|---|---|---|---|---|
| GW150914 | 2015-09-14 | BBH | 36 + 29 → 62 | ~430 |
| GW170817 | 2017-08-17 | BNS | 1.17 + 1.36 | ~40 |
| GW190521 | 2019-05-21 | BBH | 85 + 66 → 142 | ~5.3 Gpc |
| GW200105 | 2020-01-05 | NSBH | 8.9 + 1.9 | ~280 |
As of O3 (third observing run), LIGO/Virgo/KAGRA have catalogued over 90 compact binary merger candidates. GW190521 produced an intermediate-mass black hole (~142 M☉) in the "pair-instability supernova gap" — masses that ordinary stellar evolution cannot produce, suggesting hierarchical mergers.
6. Multi-Messenger Astronomy
GW170817 was historic: the first binary neutron star merger detected in gravitational waves and electromagnetic light, opening the era of multi-messenger astronomy.
- 1.7 seconds after the merger, the Fermi satellite detected a short gamma-ray burst (GRB 170817A) — confirming the decades-old hypothesis that short GRBs come from neutron star mergers.
- Over the following weeks, optical and infrared observations of the host galaxy NGC 4993 showed a kilonova: the radioactive decay of heavy r-process elements (gold, platinum, uranium) synthesised in the merger. A single merger can produce ~10 Earth-masses of gold.
- Independent measurement of H₀: using the gravitational wave distance + redshift of the host galaxy, the "standard siren" method gave H₀ = 70 +12/-8 km/s/Mpc — a new way to measure cosmic expansion.
7. The Future — LISA & ET
Ground-based detectors hit a frequency floor ~1–10 Hz (seismic noise). Two next-generation instruments push further:
- LISA (Laser Interferometer Space Antenna, ESA, ~2035): 2.5 million km arms in space. Targets millihertz band: massive BH mergers, galactic white-dwarf binaries, extreme-mass-ratio inspirals (EMRIs).
- Einstein Telescope (planned, Europe): Underground, L-shaped, 10 km arms. Factor ~10 sensitivity improvement. Can "hear" mergers across the observable universe and probe neutron star equation of state.
- Pulsar Timing Arrays (NANOGrav, PPTA, EPTA): Use millisecond pulsars as galactic-scale GW detectors for ultra-low nanohertz frequencies. In 2023, evidence for a stochastic gravitational wave background was announced — possibly from supermassive BH binaries in the early universe.