Does a core collapse supernova emit detectable gravitational waves? I've read that LIGO will be the first thing to detect a "nearby" core collapse supernova, because the neutrino pulse travels slower than light, and the light is  trapped inside the star for several hours before it is free to propagate in a vacuum.
However, can a core collapse supernova emit detectable gravitational waves? I'm not up to tackling the GR equations involved, but ...
If it's spherically symmetrical, then it has no preferred direction. A gravitational wave stretches space in one direction while compressing it in the perpendicular one. So emission of such is not compatible with perfect spherical source symmetry. Am I right?
A star is rotating, which gives it a defined axis. Does that make a difference? It still doesn't seem able to define any perpendicular "stretch" and "shrink" directions, if it has perfect radial symmetry. Again, am I right?
If I'm not wrong, this leaves the fact that no real star collapse will actually be perfectly symmetrical. If so, are the expected deviations from radial symmetry during the collapse sufficient to make a core collapse supernova detectable by LIGO, and at what estimated distance? Does it make any difference whether the core ends up as a neutron star or a black hole?
 A: If the collapse is spherically or axially symmetric, no gravitational radiation is emitted. If the collapse is less symmetric than that, emission of gravitational waves will occur.
The more chaotic the collapse is, the greater the energy of gravitational radiation emitted.
One would expect gravitational wave to be emitted in realistic collapses.
Theoretical calculations are providing potential wave forms and LIGO and other gravitational wave detectors are searching for such events. None have yet been detected to my knowledge.
A: What you are enquiring about is discussed in quite an accessible way by Steve Carlip, in an article titled:
Aberration and the Speed of Gravity
Part of the discussion is an overview of the conditions under which gravitational waves will be emitted.
Comparison with electromagnetics: if you have two macroscopic objects, one charged positively, and one charged negatively, then the Coulomb attraction will allow them to orbit their common center of mass, but they will emit electromagnetic waves, causing the two objects to spiral inward quite rapidly.
Gravitational wave propagation does not fall in the category of transversal waves. The propagation is described as propagation of a quadrupole wave.
The nature of the gravitational wave itself is different, and the nature of how the gravitational wave is generated is different. Generation of gravitational waves occurs at a higher order, and that accounts for the fact that gravitationally bound systems such as solar systems are stable on the time scale of the lifetime of the Universe.

So yeah, a spherical symmetrical collapse event will not generate a gravitational wave.
I'm not sure what the expectation is in the case of a pulsar kick. (Pulsar kick as mentioned by PM_2Ring in the comment section.)
In the case of the Coulomb force such an event of longitudinal acceleration will result in emission of electromagnetic waves, but generation of gravitational waves is different.
