Fractional quantum Hall (FQH) states support an emergent spin-2 quasiparticle, called the graviton, which corresponds to long-wavelength fluctuations of an internal metric in the quantum Hall fluid. In this talk, I will describe this mode and discuss the possibility of graviton modes in fractional Chern insulators, which are analogues of FQH phases without an applied magnetic field. I argue that the broken translation and rotation symmetry from the underlying lattice in these phases will generally result in many scattering channels for the graviton, giving a significantly decreased lifetime for the mode. This is reflected in numerical results, where the peak associated to the graviton mode decreases rapidly with system size compared to the Landau level case. Finally, I will consider ways in which the lifetime of this mode may be increased.

Associated arXiv preprint:2502.02640