  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 non-conservation 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 non-inertial reference frame. This non-inertial 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 non-inertial reference frame, and this fact could be
verified in laboratories, in principle. Finally, we propose a holographic
realization of this system.
