Linearised gravity and gravitational waves

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.

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.