Linear stability analysis in inhomogeneous equilibrium configurations

Understand

We propose a novel method to find local plane-wave solutions of the linearized equations of motion of relativistic hydrodynamics in inhomogeneous equilibrium configurations, i.e., when a fluid in equilibrium is rigidly moving with nonzero thermal vorticity.

• Our method is based on extending the conserved currents to the tangent bundle, using a type of Wigner transformation.
• The Wigner-transformed conserved currents can then be Fourier-transformed into the cotangent bundle to obtain the dispersion relations for the space-time dependent eigenfrequencies.
• We show that the connection between the stability of hydrodynamics and the evolution of plane waves is not as straightforward as in the homogeneous case, namely, it is restricted to the equilibrium-preserving directions in the cotangent bundle.