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 is the spatial part of the trace reversed perturbation of the metric, i.e. the gravitational wave. is the gravitational constant, the speed of light in vacuum, and is the mass quadrupole moment.[1]
It is useful to express the gravitational wave strain in the transverse traceless gauge, which is given by a similar formula where 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).[2]
See also
- Multipole radiation
- Birkhoff's theorem (relativity)
- PSR J0737−3039
References
- v
- t
- e
- Theory of relativity
- 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
- Thought experiments
- Unsuccessful investigations
- Wave–particle duality
- Gravitational wave
- Tea leaf paradox
- Annus mirabilis papers (1905)
- "Investigations on the Theory of Brownian Movement" (1905)
- Relativity: The Special and the General Theory (1916)
- The Meaning of Relativity (1922)
- The World as I See It (1934)
- The Evolution of Physics (1938)
- "Why Socialism?" (1949)
- Russell–Einstein Manifesto (1955)
culture
- Die Grundlagen der Einsteinschen Relativitäts-Theorie (1922 documentary)
- The Einstein Theory of Relativity (1923 documentary)
- Relics: Einstein's Brain (1994 documentary)
- Insignificance (1985 film)
- Young Einstein (1988 film)
- Picasso at the Lapin Agile (1993 play)
- I.Q. (1994 film)
- Einstein's Gift (2003 play)
- Einstein and Eddington (2008 TV film)
- Genius (2017 series)
- Oppenheimer (2023 film)
Einstein
- Albert Einstein: Creator and Rebel
- Einstein and Religion
- Einstein for Beginners
- Einstein: His Life and Universe
- Einstein's Cosmos
- I Am Albert Einstein
- Introducing Relativity
- Subtle is the Lord
- Mileva Marić (first wife)
- Elsa Einstein (second wife; cousin)
- Lieserl Einstein (daughter)
- Hans Albert Einstein (son)
- Pauline Koch (mother)
- Hermann Einstein (father)
- Maja Einstein (sister)
- Eduard Einstein (son)
- Robert Einstein (cousin)
- Bernhard Caesar Einstein (grandson)
- Evelyn Einstein (granddaughter)
- Thomas Martin Einstein (great-grandson)
- Siegbert Einstein (distant cousin)
- Category