Potential flows in general relativity: Some exact solutions

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Abstract
We present analytic solutions for the steady-state, subsonic flow of gas around various relativistic obstacles. The gas obeys a P=ρ adiabatic equation of state and the flow velocity can be arbitrarily close to the speed of light. The obstacles include spheres, shells, cylinders, wedges, and black holes. Some time-dependent solutions in curved spacetime are also described. The solutions may provide physical insight into more general flows and serve as benchmarks for testing multidimensional hydrodynamic codes in general relativity. They also have astrophysical applications to fluid flow past compact objects, star clusters, and cosmic strings.