Gravitational Waves
Gravitational waves are ripples in the fabric of spacetime generated by accelerating massive objects, predicted by Einstein's general theory of relativity in 1916 and directly detected for the first time by the LIGO collaboration on September 14, 2015 (event GW150914). These distortions propagate at the speed of light as transverse waves, alternately stretching and squeezing spacetime in perpendicular directions. The detection of gravitational waves opened an entirely new observational window on the universe, allowing astronomers to study events such as merging black holes and neutron stars that are otherwise invisible to electromagnetic telescopes.
Key Formula
h = (4G / c⁴r) × Ï (second time derivative of quadrupole moment)
LaTeX: h = \frac{4G}{c^4 r} \ddot{I}
| Symbol | Meaning | Unit |
|---|---|---|
| h | Gravitational wave strain (dimensionless amplitude) | dimensionless |
| G | Gravitational constant (6.674 × 10⁻¹¹ N·m²/kg²) | N·m²/kg² |
| c | Speed of light | m/s |
| r | Distance from source to detector | meter (m) |
| Ï | Second time derivative of mass quadrupole moment | kg·m²/s² |
Worked Example
Problem
GW150914 had a peak strain of h ≈ 10⁻²¹. LIGO's arms are L = 4 km long. What was the maximum change in arm length?
Solution
Step 1: The strain h is defined as h = ΔL / L, where ΔL is the change in length and L is the arm length. Step 2: Rearrange to find ΔL = h × L. Step 3: Substitute values: ΔL = (10⁻²¹) × (4 × 10³ m) = 4 × 10⁻¹⁸ m. Step 4: For comparison, a proton has a diameter of about 10⁻¹⁵ m. So the arm length change was about 1/1000 the diameter of a proton.
Answer
ΔL = 4 × 10⁻¹⁸ m — roughly 1/1000th of a proton's diameter, an extraordinary measurement achievement
Notable Gravitational Wave Detection Events
| Event | Date | Source | Distance | Peak Strain h |
|---|---|---|---|---|
| GW150914 | Sep 14, 2015 | Binary black hole merger (29+36 M☉) | 410 Mpc | 10⁻²¹ |
| GW170817 | Aug 17, 2017 | Binary neutron star merger | 40 Mpc | 10⁻²² |
| GW190814 | Aug 14, 2019 | BH + mystery compact object (23+2.6 M☉) | 241 Mpc | ~10⁻²² |
| GW200105 | Jan 5, 2020 | BH + neutron star (8.9+1.9 M☉) | 280 Mpc | ~10⁻²³ |
| GW190521 | May 21, 2019 | Intermediate-mass BH formation (85+66 M☉) | 5.3 Gpc | ~10⁻²³ |
Interactive Tools
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Related Terms
General Relativity
General relativity is Albert Einstein's geometric theory of gravitation, published in 1915, which describes gravity not as a force but as the curvature of spacetime caused by mass and energy. Massive objects warp the fabric of spacetime, and other objects follow curved paths (geodesics) through this warped spacetime, which we perceive as gravitational attraction. The theory has been confirmed by numerous observations including gravitational lensing, gravitational redshift, the precession of Mercury's orbit, and the detection of gravitational waves.
Black Hole
A black hole is a region of spacetime where gravity is so extreme that nothing — not even light or other electromagnetic radiation — can escape once past the event horizon, the point of no return. Black holes form when massive stars collapse at the end of their lives (stellar black holes), or may grow supermassive through accretion and mergers in galactic centres. The boundary of a black hole is described by the Schwarzschild radius (for non-rotating black holes), and their properties are encapsulated by the "no-hair theorem": a black hole is fully described by only three parameters — mass, charge, and spin.
Spacetime
Spacetime is the four-dimensional continuum that combines the three dimensions of space (x, y, z) with the one dimension of time (t) into a single mathematical framework, first described by Hermann Minkowski in 1908 based on Einstein's special relativity. In this framework, events are described by four coordinates, and the separation between events is measured by the spacetime interval, which remains invariant under Lorentz transformations. In general relativity, spacetime is not flat but can be curved by mass and energy, and this curvature is what we experience as gravity.
From Latin "gravitas" (weight, heaviness) and Latin "unda" (wave). Einstein predicted gravitational radiation in 1916 from his field equations. The existence of gravitational waves was indirectly confirmed by Hulse and Taylor's pulsar timing observations (Nobel Prize 1993), and directly detected by LIGO in 2015 (Nobel Prize 2017 to Weiss, Barish, and Thorne).