On the motion of compact objects in relativistic viscous fluids

Abstract We present a world-line effective field theory of compact objects moving relativistically through a viscous fluid. The theory is valid when velocity gradients are small compared to the inverse size of the object. Working within the EFT eliminates the need to solve a boundary value problem by turning all interactions between the fluid and the object into a source term in the action. We use the EFT to derive the relativistic equations of motion for a compact object immersed in a viscous fluid in a curved background, when the relative velocity of the object and the fluid is small compared to the speed of light.