The vacuum-core vortex in relativistic perfect fluids

The governing equations in non-relativistic (conventional) compressible fluid flows are derived as a low-energy limit in relativistic flows. This suggests that exact solutions obtained in non-relativistic fluid dynamics possess their relativistic counterparts. As an example of such solutions, we consider a stationary potential flow and examine the relativistic effect on a vacuum-core (hollow-core) vortex solution in compressible fluid flows. The vacuum-core vortex solution is an exact solution in stationary potential flows, which is also true in relativistic flows. We construct the vacuum-core vortex solution in relativistic fluid flows and discuss the differences and similarities between non-relativistic and relativistic flows. We show that the vacuum-core radius in relativistic flows is larger than the one in non-relativistic flows for a fixed polytropic exponent and depends on the transonic speed (local sound speed) in the flow field. We also calculate various physical quantities such as density, pressure, and sound speed as functions of radius r from the center of the core and compare them with those in non-relativistic flows.