George Matsas[2] has analysed this paradox in the scope of general relativity and also pointed out that these relativistic buoyancy effects could be important in some questions regarding the thermodynamics of black holes.
A comprehensive explanation of Supplee's paradox through both the special and the general theory of relativity was presented by Ricardo Soares Vieira.
[3] To simplify the analysis, it is customary to neglect drag and viscosity, and even to assume that the fluid has constant density.
Supplee[1] himself concluded that the paradox can be resolved with a more careful analysis of the gravitational buoyancy forces acting on the bullet.
Considering the reasonable (but not justified) assumption that the gravitational force depends on the kinetic energy content of the bodies, Supplee showed that the bullet sinks in the frame at rest with the fluid with the acceleration
In particular, he modelled the situation using a Rindler chart, where a submarine is accelerated from the rest to a given velocity v. Matsas concluded that the paradox can be resolved by noting that in the frame of the fluid, the shape of the bullet is altered, and derived the same result which had been obtained by Supplee.
Matsas has applied a similar analysis to shed light on certain questions involving the thermodynamics of black holes.
In the first case, he showed that gravitomagnetic effects should be taken into account in order to describe the forces acting in a moving submarine underwater.