Topological modes in relativistic hydrodynamics

We show that gapless modes in relativistic hydrodynamics could become topologically nontrivial by weakly breaking the conservation of energy momentum tensor in a specific way. This system has topological semimetal-like crossing nodes in the spectrum of hydrodynamic modes that require the protection of a special combination of translational and boost symmetries in two spatial directions. We confirm the nontrivial topology from the existence of an undetermined Berry phase. These energy momentum nonconservation terms could naturally be produced by an external gravitational field that comes from a reference frame change from the original inertial frame, i.e., by fictitious forces in a noninertial reference frame. This noninertial frame is the rest frame of an accelerating observer moving along a trajectory of a helix. This suggests that topologically trivial modes could become nontrivial by being observed in a special noninertial reference frame, and this fact could be verified in laboratories, in principle. Finally, we propose a holographic realization of this system.