Quadrupole formula: Difference between revisions
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factor of c added: \ddot{I}_{ij}(t-r) becomes \ddot{I}_{ij}(t-r/c); needed for consistency with the factor \frac{2 G}{c^4 r} |
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In [[general relativity]], the '''quadrupole formula''' describes rate at which [[gravitational wave]]s are emitted from a system of masses based on the change of the (mass) [[quadrupole moment]]. The formula reads |
In [[general relativity]], the '''quadrupole formula''' describes rate at which [[gravitational wave]]s are emitted from a system of masses based on the change of the (mass) [[quadrupole moment]]. The formula reads |
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:<math> \bar{h}_{ij}(t,r) = \frac{2 G}{c^4 r} \ddot{I}_{ij}(t-r), </math> |
:<math> \bar{h}_{ij}(t,r) = \frac{2 G}{c^4 r} \ddot{I}_{ij}(t-r/c), </math> |
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where <math> \bar{h}_{ij}</math> is the (spatial part of) the [[trace reversed]] perturbation of the metric (i.e. the gravitational wave), and <math>I_{ij}</math> is the mass quadrupole moment.<ref>{{cite book |
where <math> \bar{h}_{ij}</math> is the (spatial part of) the [[trace reversed]] perturbation of the metric (i.e. the gravitational wave), and <math>I_{ij}</math> is the mass quadrupole moment.<ref>{{cite book |
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|title=Spacetime and Geometry |
|title=Spacetime and Geometry |
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Revision as of 19:33, 8 June 2016
In general relativity, the quadrupole formula describes 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 is the (spatial part of) the trace reversed perturbation of the metric (i.e. the gravitational wave), and is the mass quadrupole moment.[1]
The formula was first obtained by Albert Einstein in 1916. 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
- ^ Carroll, Sean M. Spacetime and Geometry. Pearson/Addison Wesley. pp. 300–307. ISBN 0805387323.
- ^ Poisson, Eric; Will, Clifford M. Gravity:Newtonian, Post-Newtonian, Relativistic. Cambridge University Press. pp. 550–563. ISBN 9781107032866.
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