Petrov classification of analogue spacetimes

Abstract

In an effort to invariantly characterize the conformal curvature structure of analogue spacetimes built from a nonrelativistic fluid background, we determine the Petrov type of a variety of laboratory geometries. Starting from the simplest examples, we increase the complexity of the background, and thereby determine how the laboratory fluid symmetry affects the corresponding Petrov type in the analogue spacetime realm of the sound waves. We find that for more complex flows isolated hypersurfaces develop, which are of a Petrov type differing from that of the surrounding fluid. {Finally, we demonstrate that within the incompressible background approximation, as well as for all compressible quasi-one-dimensional flows, the only possible Petrov types are the algebraically general type I and the algebraically special types O and D.

arXiv comment11 pages, 2 figures; added section with general considerations on possible Petrov types of Painlevé-Gullstrand geometries, to appear in Classical and Quantum Gravity

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