Not yet reviewed by Pith; the record is open.

Our understanding of the core-collapse supernova explosion mechanism is incomplete. While the favoured scenario is delayed revival of the stalled shock by neutrino heating, it is difficult to reliably compute explosion outcomes and energies, which depend sensitively on the complex radiation hydrodynamics of the post-shock region. The dynamics of the (non-)explosion depend sensitively on how energy is transported from inside and near the proto-neutron star (PNS) to material just behind the supernova shock. Although most of the PNS energy is lost in the form of neutrinos, hydrodynamic and hydromagnetic waves can also carry energy from the PNS to the shock. We show that gravity waves excited by core PNS convection can couple with outgoing acoustic waves that present an appreciable source of energy and pressure in the post-shock region. Using one-dimensional simulations, we estimate the gravity wave energy flux excited by PNS convection and the fraction of this energy transmitted upward to the post-shock region as acoustic waves. We find wave energy fluxes near $10^{51}\,\mathrm{erg}\,\mathrm{s}^{-1}$ are likely to persist for $\sim1\,\mathrm{s}$ post-bounce. The wave pressure on the shock may exceed $10\%$ of the thermal pressure, potentially contributing to shock revival and, subsequently, a successful and energetic explosion. We also discuss how future simulations can better capture the effects of waves, and more accurately quantify wave heating rates.