Would a Cavorite-like material violate any conservation laws? This post addresses a similar question, but rather than using gravitons as a means of propulsion, my question addresses the blocking of gravitational fields using a hypothetical passive material such as Cavorite, first envisioned by H.G. Wells in his novel The First Men in the Moon and whether the existence of any such exotic material would violate any known conservation laws. Another post, closer to my question here does address 'gravitational shielding' however focuses on violation of the equivalence principle. My interest regards shielding but with a focus on violation of conservation laws.
In We;;'s classic novel, Cavorite had the ability to shield gravitational forces if placed between two masses and the character in the novel, Cavor used this idea to shield a spacecraft from the earth below while exposing the upper part of the craft, unshielded by the Cavorite to the pull of the Moon's gravity. The result being that the craft would accelerate towards the moon. Then at the appropriate moment Cavor reversed the direction of the shield to decelerate and bring the craft to the moon's surface with some reasonable final velocity that would not kill the astronauts (and a chicken!)
So if the manufacture of Cavorite were somehow possible it could reduce or eliminate the need for [expensive] launch vehicles.
But to my main question - does such a hypothetical material violate any of the conservation laws such as energy or momentum? Cavorite seems to be a ruse for 'free' energy, on the same footing as perpetual motion machines. 
And if the idea does violate conservation laws, then does it completely destroy any feasibility of a Cavorite-like material? Or are there loopholes that can be considered?
 A: Gravitational shielding, such as what that fictional material would do, is only possible by having negative mass and violating the positive energy condition/theorem. Other arguments against gravitational shielding have already been done in PSE, one recently. This answer addresses one of the probably only remaining possibility, such as the negative mass. 
The shielding issue or 'cancelling gravity' topic has been brought up and addressed in many ways in PSE. There are some good answers such as in Is it theoretically possible to shield gravitational fields or waves?
and in Gravitational shielding and equivalence principle where it answers why it violates the principle of equivalence, unless there was negative mass involved. 
The following is a reference on that the Equivalence principle has been measured up to a pretty good accuracy. See https://en.m.wikipedia.org/wiki/Gravitational_shielding. 
So it seems the only possibility is negative mass. There are many hard to believe effects that then could take place such as runaway acceleration (two opposite sign masses push-pull each other acccelerating each other in the same direction,  more than simply perpetual motion), can cause closed timelike curves (CTCs, meaning causality is broken), has been claimed as possible exotic matter that could stabilize a wormhole with negative mass cosmic strings, and a number of other exotic properties.
Also, negative mass is associated with negative kinetic energy and faster than light travel. 
No, so conservation laws are not necessarily broken, energy (with there being positive and negative energy) and momentum conservation can be made to hold, with negative energy quantities. But a lot of other strange effects can then occur. The wiki article describes and references these and more. See 
https://en.m.wikipedia.org/wiki/Negative_mass
A: I think the second law of thermodynamics and/or conservation of energy is violated by air above a cavorite disk.
Being weightless, the air above the cavorite will tend to relax to equal pressure and density independent of height.  This will set up a "convection" like circulation with the air to either side, which does have a pressure gradient, and as far as I can see you can extract energy.
What happens to the temperature here? If it stays constant you violate conservation of energy, if it drops you violate second law of thermodynamics.
This works inside a sealed volume, so I don't see any chance to recover via air leaking off to infinitely or whatever.
