We show how a diffeomorphism invariance of the quantum Hall systems, together with topological consideration, put strong constraints on the physics that goes beyond the Chern-Simons action. We show how the Hall conductivity at finite wavenumbers is constrained. We also derive new sum rules that govern the spectrum of low-energy excitations in a fractional quantum Hall system. We show how these sum rules can be saturated by a single quasiparticle which can be interpreted as a massive emergent graviton. We identify this massive graviton with the magneto-roton and discuss consequences for experiments.