Quadrupole formula
In general relativity, the quadrupole formula describes the rate at which gravitational waves are emitted from a system of masses based on the change of the (mass) quadrupole moment. The formula reads where formula_2 is the spatial part of the trace reversed perturbation of the metric, i.e. the gravitational wave. formula_3 is the gravitational constant, formula_4 the speed of light in vacuum, and formula_5 is the mass quadrupole moment. It is useful to express the gravitational wave strain in the transverse traceless gauge, which is given by a similar formula where formula_6 is the traceless part of the  mass quadrupole moment. The total energy (luminosity) carried away by gravitational waves is The formula was first obtained by Albert Einstein in 1918. After a long history of debate on its physical correctness, observations of energy loss due to gravitational radiation in the Hulse–Taylor binary discovered in 1974 confirmed the result, with agreement up to 0.2 percent (by 2005).