How fast does gravity propagate? The standard answer, "at the speed of light, " is correct for gravitational waves but misses something important. Within linearized general relativity on a flat background (and analogously in the ADM initial-value formulation of the exact theory), the gravitational field decomposes into a constraint sector and a radiative sector. The constraint sector fixes the Newtonian-like binding potential at each moment on a chosen spacelike hypersurface. The radiative sector describes transverse-traceless gravitational waves, which carry energy on the light cone. We show that these two sectors can be cleanly decomposed in the linearized setting using a "velocity gauge, " built in direct analogy with a well-known construction in electromagnetism 4. In this framework, the apparent propagation speed of the gauge-variant binding potential ᵥ is a freely chosen gauge parameter (not a physical quantity), while gravitational waves always travel at c and all measurable quantities (tidal forces, geodesic deviation) remain the same regardless of the choice. The standard post-Newtonian (PN) approximation independently corroborates this picture: through 3PN order, conservative dynamics is built from instantaneous potentials, with wave-like propagation entering only at 2. 5PN (radiation reaction) and 4PN (hereditary tails) 5. The well-known absence of gravitational aberration in orbiting bodies is reinterpreted as a property of the constraint sector, not a measurement of wave speed. The 2017 neutron-star merger observation (GW170817) measured the speed of gravitational waves; it did not and could not measure the "speed" of gauge-variant binding potentials, because constraint equations are not radiative propagation laws. We work strictly within general relativity and introduce no new physics.
Louis McGinty (Thu,) studied this question.