Everything about Quadrupole totally explained
A
quadrupole is one of a sequence of configurations of — for example — electric charge or current, or gravitational mass that can exist in ideal form, but it's usually just part of a
multipole expansion of a more complex structure reflecting various orders of complexity.
Mathematical definition
The traceless
quadrupole moment tensor of a system of charges (or masses, for example) is defined as
»
where
M is the mass of each hole, and
is the unit vector in the
x-direction. As the system orbits, the
x-vector will rotate, which means that it'll have a nonzero second time derivative. Thus, the system will radiate gravitational waves. Energy lost in this way was indirectly detected in the
Hulse-Taylor binary.
Just as electric charge and current multipoles contribute to the electromagnetic field, mass and mass-current multipoles contribute to the gravitational field in General Relativity, because GR also includes "
gravitomagnetic" effects. Changing mass-current multipoles can also give off gravitational radiation. However, contributions from the current multipoles will typically be much smaller than that of the mass quadrupole.
Further Information
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