Abstract
Relativistic superfluids are of interest in extreme astrophysical or cosmological situations. Some of their properties, ultrabaricity in particular, are studied by means of exact solutions of Einstein’s equations. Those found are almost invariably characterized by equations of state of the typeP = αϱ + const with 0 ≤ α ≤ 1 and ϱ proportional to the square of the number density. They are therefore neither ultrabaric (P > ϱ nor superluminal (vS > 1). Exceptions are, however, represented by the generalized interior Schwarzschild solution, the Stephani solution and a new conformally flat solution also of the Stephani type. For these superluminality is allowed if no assumptions are introduced regarding the mechanism of propagation of sound waves. In the one with Stephani metric, transitions can occur in principle from evolutionary stages withvS > 1 to others withvS < 1, andvice versa.
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