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 by Nicolis and Penco [Phys. Rev. B 97, 134516 (2018)PRBMDO2469-995010.1103/PhysRevB.97.134516] 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 nonrelativistic media as well, and could have intriguing experimental implications.

Wess-Zumino terms for relativistic fluids, superfluids, solids, and supersolids.

We use the coset construction of low-energy effective actions to systematically derive Wess-Zumino (WZ) terms for fluid and isotropic solid systems in two, three, and four spacetime dimensions. We recover the known WZ term for fluids in two dimensions as well as the very recently found WZ term for fluids in three dimensions. We find two new WZ terms for supersolids that have not previously appeared in the literature. In addition, by relaxing certain assumptions about the symmetry group of fluids we find a number of new WZ terms for fluids with and without charge, in all dimensions. We find no WZ terms for solids and superfluids.

Implications of relativity on nonrelativistic Goldstone theorems: gapped excitations at finite charge density.

We adapt the Goldstone theorem to study spontaneous symmetry breaking in relativistic theories at finite charge density. It is customary to treat systems at finite density via nonrelativistic Hamiltonians. Here, we highlight the importance of the underlying relativistic dynamics. This leads to seemingly new results whenever the charge in question is spontaneously broken and does not commute with other broken charges. We find that that the latter interpolate gapped excitations. In contrast, all existing versions of the Goldstone theorem predict the existence of gapless modes. We derive exact nonperturbative expressions for their gaps, in terms of the chemical potential and of the symmetry algebra.

No-hair theorem for the Galileon.

We consider a Galileon field coupled to gravity. The standard no-hair theorems do not apply because of the Galileon's peculiar derivative interactions. We prove that, nonetheless, static spherically symmetric black holes cannot sustain nontrivial Galileon profiles. Our theorem holds for trivial boundary conditions and for cosmological ones, and regardless of whether there are nonminimal couplings between the Galileon and gravity of the covariant Galileon type.

Proposal for an observational test of the Vainshtein mechanism.

Modified gravity theories capable of genuine self-acceleration typically invoke a Galileon scalar which mediates a long-range force but is screened by the Vainshtein mechanism on small scales. In such theories, nonrelativistic stars carry the full scalar charge (proportional to their mass), while black holes carry none. Thus, for a galaxy free falling in some external gravitational field, its central massive black hole is expected to lag behind the stars. To look for this effect, and to distinguish it from other astrophysical effects, one can correlate the gravitational pull from the surrounding structure with the offset between the stellar center and the black hole. The expected offset depends on the central density of the galaxy and ranges up to ∼0.1 kpc for small galaxies. The observed offset in M87 cannot be explained by this effect unless the scalar force is significantly stronger than gravity. We also discuss the systematic offset of compact objects from the galactic plane as another possible signature.

Equivalence principle for scalar forces.

The equivalence of inertial and gravitational masses is a defining feature of general relativity. Here, we clarify the status of the equivalence principle for interactions mediated by a universally coupled scalar, motivated partly by recent attempts to modify gravity at cosmological distances. Although a universal scalar-matter coupling is not mandatory, once postulated, it is stable against classical and quantum renormalizations in the matter sector. The coupling strength itself is subject to renormalization, of course. The scalar equivalence principle is violated only for objects for which either the graviton self-interaction or the scalar self-interaction is important--the first applies to black holes, while the second type of violation is avoided if the scalar is Galilean symmetric.