[sjastro]

Good grief these questions are becoming harder.

Originally Posted by Nesti

Assuming there are many EQUALLY massed objects in a localised region of space:

Q1. Does the speed of any gravity wave vary with the topology, given that there are now many variations in metric values within the [composite] field?

Not likely. The gravitational wave may lose energy but not speed, when it interacts with matter that has caused the variation in topology.
This is analogous to the interaction of electromagnetic waves with matter. The waves may be scattered or absorbed but the resultant wave is still travelling at c with reduced energy and longer wavelength.

Q2. Is there a distortion in the propagation because of the composite field?

I assume you mean if there there is a change to the wave's metric.

Consider two massive bodies revolving around a center of mass. The strength of the field will change (as will the metric) as the orbit of each body decays and there is a non zero quadrupole moment.

Now consider the same two bodies but one body is simply moving past the other. Even though the fields may overlap there is no change to the field strength or the metric as there is now a dipole moment and zero quadrupole moment.

A gravitational wave moving through may overlap with the neighbouring field but there will be no change to the metric as the field strength of the wave or the neighbourhood has not changed.

Yes, I realise the discussion has come full-circle, but if a photon must follow a geodesic derived from a composition of many fields, then any single gravity wave must also be distorted otherwise its propagation would be more direct than the light's geodesic (which is actually the straightest path anyway).

If gravity waves always propagate at c, and if the masses within our composite field are all equal to each-other, then all waves properties must be equal also (shape etc). So we should have interference patterns appearing (exaggerated metric values) in the composite field...these regions of interference should hold either a reduction in the expression of curvature, or a hightened expression of curvature...the same as we see in all other types of fields. If we do not see this, then metric values hold no relation to the physical reality we observe only a mathematical 'similarity'. We could just as easily say the light mediates the gravitational field for itself, creating its own geodesic path based upon other sources of light.

Even if the masses are rotating around each other in decaying orbits to form a varying metric, a passing gravitational wave does not contribute to the quadrupole symmetry. It will not be influenced by the space time geometry and will still travel at c.

Regards

Steven