Gravitational waves are ripples in spacetime that propagate as waves and are generated by accelerating masses.Gravitational waves are oscillations of the geometry of spacetime, propagating at the speed of light. They are generated by accelerated motions of massive bodies with broken spherical symmetry: binary systems, supernova explosions. The wave has a quadrupole nature: it alternately compresses and stretches distances in perpendicular directions, corresponding to two polarizations — 'plus' and 'cross'. At the moment of black hole merger, the radiation can briefly surpass in power the combined luminosity of all stars in the observable Universe.
The idea of gravitational waves was first proposed by Henri Poincaré (1905), but the rigorous prediction was made by Albert Einstein (1916, 1918) based on the linearized equations of GR. For a long time, the existence of waves was disputed, even by Einstein himself. Experimental searches began with the pioneer detectors of Joseph Weber in the 1960s. Only in 2015 did the LIGO collaboration (founders Rainer Weiss, Kip Thorne) detect the direct merger of black holes.
From Einstein's equations G_μν = (8πG/c⁴) T_μν, by linearization one obtains the wave equation for perturbations □h_μν = 0 in vacuum. An interferometric detector (LIGO, Virgo) measures the path difference of beams in the arms caused by the change in distance under the wave's influence: for h ~ 10⁻²¹, the displacement is 10⁻¹⁸ m for a 4 km arm.
Detectors like LIGO pick up these oscillations, revealing previously invisible mergers of black holes and neutron stars, and in the future — gravitational-wave astronomy for studying the dark eras of the cosmos.
The signal of the first detection (GW150914) lasted only 0.2 seconds, but during that time three solar masses were converted into gravitational waves — equivalent to billions of billions of atomic bombs.
| h_0 | variable | gravitational wave strain amplitude — strain |
| ε | variable | ellipticity — ellipticity |
| I_zz | variable | moment of inertia about rotation axis — moment of inertia kilogram metre squared |
| f_GW | variable | gravitational wave frequency — frequency hertz |
| d | variable | distance to source — distance metre |
| G | constant | Newton's constant of universal gravitation — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared |
| c | constant | Speed of light in vacuum — speed of light = 299792458 metre per second |
| h | variable | gravitational wave strain amplitude — gravitational wave amplitude |
| M | variable | chirp mass of the binary system — chirp mass kilogram |
| f | variable | gravitational wave frequency — frequency hertz |
| d | variable | luminosity distance to the source — distance metre |
| G | constant | Newtonian constant of gravitation — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared |
| c | constant | speed of light in vacuum — speed of light = 299792458 metre per second |
| ξ^μ | variable | deviation vector between two nearby geodesics — geodesic deviation vector metre |
| τ | variable | proper time along the geodesic — proper time second |
| u^ν | variable | four-velocity of the geodesic — four velocity |
| u^ρ | variable | four-velocity of the geodesic (repeated index) — four velocity |
| ξ^σ | variable | deviation vector (repeated index) — geodesic deviation vector metre |
| D^2/dτ^2 | operator | second covariant derivative along the geodesic — covariant second derivative |
| v | variable | orbital speed — velocity metre per second |
| M | variable | central mass — mass kilogram |
| r | variable | orbital radius — radius metre |
| G | constant | Universal constant of gravitation, determining the strength of gravitational force. — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared |
| Δf | variable | Change in clock frequency — frequency change hertz |
| f | variable | Clock frequency at reference height — frequency hertz |
| g | variable | Local gravitational acceleration — gravitational acceleration metre per second squared |
| Δh | variable | Height difference — height difference metre |
| c | constant | Speed of light in vacuum — speed of light = 299792458 metre per second |











