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

${\displaystyle {\bar {h}}_{ij}(t,r)={\frac {2G}{c^{4}r}}{\ddot {I}}_{ij}(t-r/c),}$

where ${\displaystyle {\bar {h}}_{ij}}$: the spatial part of the trace reversed perturbation of the metric, i.e. the gravitational wave, and ${\displaystyle I_{ij}}$ is the mass quadrupole moment.[1]

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).[2]

References

1. Carroll, Sean M. (2004). Spacetime and Geometry. Pearson/Addison Wesley. pp. 300–307. ISBN 978-0805387322.
2. Poisson, Eric; Will, Clifford M. (2014-05-29). Gravity:Newtonian, Post-Newtonian, Relativistic. Cambridge University Press. pp. 550–563. ISBN 9781107032866.