Quadrupole formula

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

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

where ${\bar {h}}_{{ij}}$ is the (spatial part of) the trace reversed perturbation of the metric (i.e. the gravitational wave), and $I_{{ij}}$ 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.

Albert Einstein
Physics	Special relativity General relativity Mass–energy equivalence (E=MC²) Brownian motion Photoelectric effect Einstein coefficients Einstein solid Equivalence principle Einstein field equations Einstein radius Einstein relation (kinetic theory) Cosmological constant Bose–Einstein condensate Bose–Einstein statistics Bose–Einstein correlations Einstein–Cartan theory Einstein–Infeld–Hoffmann equations Einstein–de Haas effect EPR paradox Bohr–Einstein debates Teleparallelism Unsuccessful investigations
Works	Annus Mirabilis papers (1905) "Investigations on the Theory of Brownian Movement" (1905) Relativity: The Special and the General Theory (1916) The World as I See It (1934) "Why Socialism?" (1949) Russell–Einstein Manifesto (1955)
Family	Pauline Koch (mother) Hermann Einstein (father) Maja Einstein (sister) Mileva Marić (first wife) Elsa Einstein (second wife) Lieserl Einstein (daughter) Hans Albert Einstein (son) Eduard Einstein (son) Bernhard Caesar Einstein (grandson) Evelyn Einstein (granddaughter) Thomas Martin Einstein (great-grandson)
Einstein Prizes	Albert Einstein Award Albert Einstein Medal Albert Einstein Peace Prize Albert Einstein World Award of Science Einstein Prize (APS) Einstein Prize for Laser Science
Related	Political views Religious views Albert Einstein House Einstein refrigerator Brain In popular culture Einsteinium Awards and honors List of things named after Albert Einstein Einstein Papers Project Die Grundlagen der Einsteinschen Relativitäts-Theorie (1922 documentary) The Einstein Theory of Relativity (1923 documentary) Relics: Einstein's Brain Genius (2017 series)

Relativity

Special
relativity

Background	Principle of relativity Special relativity
Foundations	Frame of reference Speed of light Hyperbolic orthogonality Rapidity Maxwell's equations
Formulation	Galilean relativity Galilean transformation Lorentz transformation
Consequences	Time dilation Relativistic mass Mass–energy equivalence Length contraction Relativity of simultaneity Relativistic Doppler effect Thomas precession Relativistic disks
Spacetime	Light cone World line Spacetime diagram Biquaternions Minkowski space

General
relativity

Background	Introduction Mathematical formulation
Fundamental concepts	Special relativity Equivalence principle World line Riemannian geometry Minkowski diagram Penrose diagram
Phenomena	Black hole Event horizon Frame-dragging Geodetic effect Lenses Singularity Waves Ladder paradox Twin paradox Two-body problem
Equations	ADM formalism BSSN formalism Einstein field equations Geodesic equation Friedmann equations Linearized gravity Post-Newtonian formalism Raychaudhuri equation Hamilton–Jacobi–Einstein equation Ernst equation
Advanced theories	Brans–Dicke theory Kaluza–Klein Mach's principle Quantum gravity
Solutions	Schwarzschild (interior) Reissner–Nordström Gödel Kerr Kerr–Newman Kasner Taub–NUT Milne Robertson–Walker pp-wave van Stockum dust Weyl−Lewis−Papapetrou

Scientists

Einstein field equations:

G_{\mu \nu }+\Lambda g_{\mu \nu }={8\pi G \over c^{4}}T_{\mu \nu }

and their analytical solution by Ernst equation:

\displaystyle \Re (u)(u_{rr}+u_{r}/r+u_{zz})=(u_{r})^{2}+(u_{z})^{2}.

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