It's true that kev did not write out the full metric, but given that he was assuming an orbit where for any infinitesimal segment you'd have [tex]d\phi = 0[/tex], those extra terms would disappear anyway so this wouldn't affect his final results. And kev never claimed
he was starting from the full metric, he said in post #8
that he was "Starting with this equation given by pervect", and pervect had already eliminated terms that went to zero.
What about it? That would appear to be an equation for Schwarzschild coordinate velocity (as opposed to kev's 'local velocity') for an object in circular orbit with varying [tex]\theta[/tex] coordinate, as with the type of orbit I described--again, do you agree that the type of orbit I described is a physically valid one? If you agree there would be a valid physical orbit with that type of coordinate description (with [tex]\phi[/tex] having one constant value for half the orbit and a different constant value for the other half), do you disagree that the above equation would be the correct coordinate velocity for an object in this orbit?
I think you don't understand what special pleading
is, the fact that I and others respond to each of your various arguments with counterarguments, resulting in you continually abandoning your previous arguments in favor of new arguments you have invented on the spot, does not qualify as "special pleading". Yes or no, do you acknowledge that the arguments you made against kev's derivation prior
to the new argument you've made in the posts here
kev's formula is not intended to be a "general" one for arbitrary motion, it deals specifically with the case of an object in circular orbit. And since the OP was asking about whether total time dilation was a sum of gravitational and velocity-based time dilation, I thought it would be interesting to point out that for this specific case, total time dilation was actually a product of the two (whereas your more general formula does not relate in any obvious way to the formulas for gravitational and velocity-based time dilation)
Do you deny that the general formula would reduce to the specific formulas found by pervect/kev in the specific case they were considering, namely an infinitesimal section of a circular orbit where the radial coordinate and one of the two angular coordinates are constant?
If a general formula reduces to a more specific formula under the specific conditions assumed in the derivation of the specific formula, I'd say that both are right.