--- title: "Linearised gravity and gravitational waves" description: "Linearised gravity describes small spacetime perturbations. Radiative disturbances travel at light speed and change transverse separations of free test masses. For an isolated slow-moving source, radi" canonical: https://lightmysky.com/learn/science/linearised-gravity-and-gravitational-waves-mt_z0tMZDGMHi source: https://lightmysky.com/learn/science/linearised-gravity-and-gravitational-waves-mt_z0tMZDGMHi.md retrieved: 2026-11-12 --- > **Agent view.** This is the Markdown twin of the page, for tools and assistants. > When to use this site, and the call that answers each job: https://lightmysky.com/agent-instructions.md > API description (OpenAPI 3.1): https://lightmysky.com/openapi.json · Authentication: https://lightmysky.com/auth.md > Pricing: https://lightmysky.com/pricing.md · Catalog: https://lightmysky.com/llms.txt · Full catalog: https://lightmysky.com/llms-full.txt > Every machine-readable file on this domain: https://lightmysky.com/.well-known/ai-catalog.json > Ask for Markdown with `Accept: text/markdown`, a `.md` address, or `?mode=agent`. # Linearised gravity and gravitational waves Linearised gravity describes small spacetime perturbations. Radiative disturbances travel at light speed and change transverse separations of free test masses. For an isolated slow-moving source, radiation begins with a changing quadrupole. Detectors measure dimensionless strain using laser interference. Subject: Science · Area: Astronomy & Astrophysics · Ages 23 to 24 Page: https://lightmysky.com/learn/science/linearised-gravity-and-gravitational-waves-mt_z0tMZDGMHi ## Ready when they can - Explains why the linearised equations resemble electromagnetic radiation with a different source - Describes what a passing wave does to a ring of freely floating test masses - Says why there is no monopole or dipole gravitational radiation ## Lesson: Ripples in the shape of space Write a weak metric perturbation as gμν=ημν+hμν, with |hμν| small. The radiative part obeys a wave equation in vacuum and travels at light speed. This resembles electromagnetic radiation, but gravitational sources are described by stress-energy rather than electric charge and current. The wave produces tidal changes in relative separations. For an isolated slow-moving source, leading gravitational radiation comes from a changing mass quadrupole: a changing directional pattern of mass. A circular binary radiates even at steady angular speed because that pattern rotates. A perfectly spherical pulsation does not radiate gravitational waves. Stellar collapse can radiate if it is not spherical. Consider a weak, linearly plus-polarized plane wave passing perpendicular to a ring of free test masses. To first order, one transverse direction stretches while the other contracts, then the changes reverse. The ring alternates between two oval shapes. This describes that polarization; other polarizations need not follow the same fixed-axis pattern. *(drawing: At leading weak-field order, conservation of mass-energy and momentum removes mass-monopole and mass-dipole radiation. Higher multipoles can also radiate.)* Strain is a fractional length change, ΔL/L, so it has no units. A 4 km arm changing by 4×10⁻¹⁸ m has a response strain of 10⁻²¹. The measured response depends on the source, its distance and the detector's orientation. A length change alone is not a strain until it is divided by the original length. LIGO splits laser light between perpendicular arms and recombines the returning beams. Phase is position in a wave cycle. Interference adds the beams' wave amplitudes; their relative optical phase affects the measured intensity. A passing wave can alter this phase through different arm responses, giving a differential signal. Comparing detectors helps distinguish an astronomical signal from local disturbances. LIGO does not record an ordinary sound wave. The first directly detected signal, GW150914, arrived on 14 September 2015; the discovery was announced in February 2016. Its changing waveform matched models of two black holes merging. This was a gravitational-wave measurement, not a photograph of the black holes. The source interpretation came from comparing the signal with relativistic models. **Recap.** Changing quadrupoles radiate even in circular binaries. Waves change transverse separations. Strain is ΔL/L, and laser interference measures a detector's differential response. *Original lesson, questions and flashcards written for this dataset.* ## Practice 8 questions on this page, each with its working shown. ## Needs first - [Curvature and the Einstein field equation](https://lightmysky.com/learn/science/curvature-and-the-einstein-field-equation-mt_1CxE6kRDt_) - [The Schwarzschild solution: orbits, redshift and the horizon](https://lightmysky.com/learn/science/the-schwarzschild-solution-orbits-redshift-and-the-horizon-mt_dNZpRDeZUE) ## Optional connections - [Radiation from an Accelerating Charge](https://lightmysky.com/learn/science/radiation-from-an-accelerating-charge-mt_Qr0rMEOYAg)