If by "anti-gravity" you mean a force that opposes the earth gravity effect on a body, usually designated as weight, that force is called "lift" if it's created by aerodynamic means.
If by "anti-gravity" you mean a method to shield the effect of earth's gravity on a body, you will be unsuccessful because what we call "gravity" does not exist, according to Einstein, "gravity" is a curvature of space-time continuum.
It also could be, as Dr. Raymer says, because it annoys the unicorns.
Dr. Dusan, I agree that the second opinion applies to interplanetary/interstellar travel. The first opinion can also be obtained by other means to produce an opposing force without using the air medium. And such kind of propulsion is the focus.
Dr. James, I'm trying to understand the unicorn-troubling matter of methods of repelling. I would like to know why can't an anti-gravity force be achieved, within the laws of physics? What is obstructing it's feasibility?
AFAIK, no principle *forbids* a negative mass (gosh: there's a whole wikipedia page on the topic:
https://en.wikipedia.org/wiki/Negative_mass)
But it's somewhat troubling in that there are no suggestions (from, say, high energy physics) of particles with negative mass - so the absence of evidence is pretty significant.
A light-hearted article on the problems of negative mass is here:
I can only assume that you are going after the topic of anti-gravity propulsion because you have addressed and solved many of issues that arise in superluminal travel. Admiral Raymer is correct in his mention of annoyance of unicorns. Another problem facing anti-gravity propulsion is that the anti-graviton remains very ellusive.
Gravity is an acceleration force and has only ever been identified in additive form, no serious form of 'anti-gravity' has ben observed. However it is quite common to oppose gravity, usually by means of the application of 'thrust', meaning the application of energy in some means to directly oppose the gravitational vector.
As the impact of gravity on energy in normal circumstances is slight to non existent, this would suggest that high energy physics is the natural area of research for you.
Bad tempered unicorns really should learn how to contribute, in the same way that dragons have.
The second order term in the linearized solution (in the weak field limit) of General Relativity requires only a non-trivial shift of the center of mass of an object. Interestingly enough, this condition is satisfied when the dynamic center of mass shift of a rotating hemisphere is considered. Special relativistic mass increase effect indeed makes the dynamic center of the mass of the rotating hemisphere to shift close to the flat side.
So the gravitational dipole moment does exist and it is defined by mass times the dynamic shift of the center of mass.
Confirmation of the validity of this approach can be seen from the fact that it derives Lense-Thirring force close to the center of mass.
The full spectrum of this dipole gravity field can shown to be the cause of the Jets from the rotating black hole at the galactic center.
Details of this investigation has been presented in my book "Physics of the New Millennium, Birth of the New Paradigm".
There is a lot more presentation than the theory of dipole gravity in the book.
You really don't want to miss it. If you are in the field of gravitation and dark matter problem, it will definitely save your time.