For a slowly moving isolated source, the leading gravitational-wave luminosity iswhere is the trace-free mass quadrupole moment.
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The quadrupole formula is used in the context of electrostatics and gravitation to describe the potential created by a distribution of charges or mass that can be approximated as a quadrupole moment. It is particularly useful in situations where the charge or mass distribution is more complex than a simple dipole or monopole, and it becomes relevant in fields like molecular physics and astrophysics.