  We investigate and solve in the context of General Relativity the apparent
paradox which appears when bodies floating in a background fluid are set in
relativistic motion. Suppose some macroscopic body, say, a submarine designed
to lie just in equilibrium when it rests (totally) immersed in a certain
background fluid. The puzzle arises when different observers are asked to
describe what is expected to happen when the submarine is given some high
velocity parallel to the direction of the fluid surface. On the one hand,
according to observers at rest with the fluid, the submarine would contract
and, thus, sink as a consequence of the density increase. On the other hand,
mariners at rest with the submarine using an analogous reasoning for the fluid
elements would reach the opposite conclusion. The general relativistic
extension of the Arquimedes law for moving bodies shows that the submarine
sinks.
