The gravitational mass carried by sound waves

We show that the commonly accepted statement that sound waves do not transport mass is only true at linear order. Using effective field theory techniques, we confirm the result found in [1] for zero-temperature superfluids, and extend it to the case of solids and ordinary fluids. We show that, in fact, sound waves do carry mass---in particular, gravitational mass. This implies that a sound wave not only is affected by gravity but also generates a tiny gravitational field, an aspect not appreciated thus far. Our findings are valid for non-relativistic media as well, and could have intriguing experimental implications.