Relativistic fluid flows around cosmic strings

The motion of a relativistic perfect fluid in the spacetime of a static, cylindrically symmetric, cosmic string is studied. The fluid equations are solved to first order in μ, the mass per unit length of the string (μ≅10/sup -6/ for typical grand unified theories), for subsonic flow of a relativistic fluid with arbitrary equation of state past a cosmic string. As the adiabatic sound speed (partialp/partialrho)/sub s//sup 1/2/ is approached, a shock forms, orthogonal to the flow and containing the string. The formalism developed by Taub for treating shocks in relativistic perfect fluids is applied to supersonic flow past a cosmic string. The shock equations are then solved for weak shocks in a fluid with an arbitrary equation of state, and also in the (extreme) strong-shock limit for an arbitrary equation of state which approaches an ideal gas in its high-temperature limit. We find that strongly shocked fluid forms a dense, thin sheet behind the string, as expected. The density contrast across the shock remains small until the four-velocity of the string is at least of order μ/sup -1/ times the sound four-velocity