  Based on previous work that topologically nontrivial gapless modes in
relativistic hydrodynamics could be found by weakly breaking the energy
momentum conservation, in this paper, we study the holographic system which
produces the same hydrodynamic modes. In the hydrodynamic system, one
possibility to obtain the energy momentum non-conservation is to couple the
system to external gravitational fields, i.e. to observe the system in a
special non-inertial frame. Similar to what happens in the hydrodynamic system,
a non-inertial frame version of holography indeed produces the same
topologically nontrivial gapless hydrodynamic modes. We also generalize the
study of topological modes in relativistic hydrodynamics to the case with one
extra U(1) current and find that more complicated topological phase diagrams
could exist when we consider more possibilities of the mass terms. We also
discuss the possible underlying mechanism for this topological change in the
spectrum when being observed in a non-inertial reference frame.
