In this talk I will show that gapless modes in relativistic hydrodynamics could become topologically nontrivial by weakly breaking the conservation of energy momentum tensor in a specific way. These energy momentum non-conservation terms could naturally be produced by an external gravitational field that comes from a coordinate transformation from the flat spacetime. This suggests that topologically trivial modes could become topologically nontrivial by being observed in a special non-inertial reference frame. I will also introduce a possible holographic realization of this system.