A gravitational wave (GW) is a phenomenon of general relativity, which models gravity as curves in spacetime (curvature), specifically of waves of spacetime, propagating from disturbances. Gravitational wave astronomy is, naturally, the study of such waves. Gravitational wave strain is essentially the amplitude of the wave.
A similar-sounding term, gravity wave is entirely different: a wave on a boundary surface of a fluid using gravity (buoyancy) as its restoring force. An ocean wave is an example.
The first indirect evidence of gravitational waves was the observation of the decays of orbits of a binary system (the Hulse-Taylor Binary) decays that matched the predictions of the effects of gravitational waves. All orbits decay in such manner, but it is typically insignificant and non-detectable. Heavy objects (e.g., compact objects) in small orbits can produce waves sufficiently intense to detect directly, and a final collision between objects would be the most detectable, i.e., a gravitational wave event.
Clear detection of well-explained gravitational waves (GW detections) requires a signal that stands out from the expected background of extremely slight waves from ongoing phenomena, the gravitational wave background (GWB). For example, the expected waves of the final fall of black hole binaries as they merge would have to show above the plethora of lesser waves from black hole binaries not yet so close together or more distant. The merging of such massive objects is a runaway process: as they draw nearer, the gravitational ways they produce grow more efficient at radiating away the kinetic energy.
Among the efforts to detect gravitational waves are space mission plans, LISA and the New Gravitational Wave Observatory (NGO), ground-based Michelson interferometers such as LIGO and Virgo (which have spotted waves of black hole mergers and neutron star mergers) and KAGRA, and ground-based pulsar-timing analysis efforts, including NANOGrav, Parkes Pulsar Timing Array, International Pulsar Timing Array, and European Pulsar Timing Array. Detecting GWs in pulsar-timing histories requires considerable data (possibly a decade's worth), storage and processing.
The signal from a gravitational wave detection of a compact object merger is increasing GW frequency, and is referred to as a chirp. Detectable gravitational waves produced by impending binary SMBH mergers (resulting from galaxy mergers) time have extremely low frequencies for a long time, e.g., within the range of 10-9Hz (about a cycle per year) to 10-6Hz (about a cycle per day) and are a target of pulsar timing arrays.
The formation of GWs requires a type of asymmetry in the motion of masses: for example, a perfectly symmetric supernova (matter ejected uniformly in all directions) will not trigger waves. An orbit does, which is why the observation of a decaying orbit (involving objects massive enough to detect such a decay) was taken as evidence of GWs. The quadrupole moment of mass produces the waves, called gravitational quadrupole radiation. Albert Einstein, in his development of general relativity, derived the quadrupole formula which describes the waves produced by a reconfiguration of mass.
The waves are transverse, affecting distances across the path of the wave, and gravitation waves from orbits propagate roughly out over the plane of the orbit, decreasing in amplitude inversely with distance (i.e., like ripples in a pond; not per an inverse square law), so doubling a detector's sensitivity (so as to sense a strain half as large as before) multiplies the volume of potential sources by eight, i.e., the cube of the ratio of improvement.
The first clear gravitational wave detection was in 2015. Detections have been labeled GW followed by a six-digit date. The first six accepted detections were all detected by LIGO, some with Virgo as well after it was upgraded to similar sensitivity. The six are GW150914, GW151226, GW170104, GW170608, GW170814, and GW170817. They are grouped in time because the detectors are only up for limited periods of time, being down for maintenance and upgrades. Over time, upgrades increase the detectors' sensitivity and more should be detected. Having three detectors (LIGO's two detectors plus Virgo) allows the direction of the events to be limited to two possible regions of the celestial sphere totaling about 60 square degrees, greatly improving the chances of identifying them with other (electromagnetic radiation) signals, e.g., multi-messenger astronomy.
The first six detections provided data regarding the frequency of such events within the volume to which the detectors are sensitive. Additionally, they adjust the previous notion that neutron star mergers would be the most common source, since five out of six were black hole mergers, and the black holes merging were larger than what was expected to be detected. Subsequent operation of the detectors has now produced more than 60 candidate detections as of 2/2020.