We investigate and solve in the context of General Relativity the apparentparadox which appears when bodies floating in a background fluid are set inrelativistic motion. Suppose some macroscopic body, say, a submarine designedto lie just in equilibrium when it rests (totally) immersed in a certainbackground fluid. The puzzle arises when different observers are asked todescribe what is expected to happen when the submarine is given some highvelocity parallel to the direction of the fluid surface. On the one hand,according to observers at rest with the fluid, the submarine would contractand, 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 fluidelements would reach the opposite conclusion. The general relativisticextension of the Arquimedes law for moving bodies shows that the submarinesinks.
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