Gravitational waves of objects with the same angular momentum So I read that gravitational waves are produced when the quadrupole moment of a system is not symmetric.
What does it actually mean for the quadrupole moment to be asymmetric? If there are two black holes with the same angular momentum accelerating towards each other in an orbital motion, does that mean the quadrupole is symmetric anyway and therefore gravitational waves won't be produced?
And a contracting/expanding sphere will not produce gravitational waves due to the symmetry of its quadrupole moment. If say the sphere is contracting and expanding at an accelerated rate, does the quadrupole moment stay symmetric?(kinda leads back to my original question about what the symmetry means)
 A: 
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.



where $h_{ij}$  is the spatial part of the trace reversed perturbation of the metric, i.e. the gravitational wave. $G$  is the gravitational constant, $c$  the speed of light in vacuum, and $I$  is the mass quadrupole moment
....


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)

Note that in the formula the quadrupole moment of the mass itself is not changing; when its space and time location changes, there is energy radiated as gravitational waves.
In this link there is discussion of moments. A completely symmetric body has the zeroth moment, when describing charge distributions it is derived to be the charge. An elliptic body has a dipole moment, the word dipole  taken from the use in electricity, where there are two opposing charge poles.  The asymmetry you misinterpret must be in the shape of the body to give a quadrupole moment.
