  We identify a novel physical mechanism that may be responsible for energy
release in $\gamma$-ray bursts. Radial perturbations in the neutron core,
induced by its collision with collapsing outer layers during the early stages
of supernova explosions, can trigger a gravitational shock, which can readily
eject a small but significant fraction of the collapsing material at
ultra-relativistic speeds. The development of such shocks is a strong-field
effect arising in near-critical collapse in General Relativity and has been
observed in numerical simulations in various contexts, including in particular
radially perturbed neutron star collapse, albeit for a tiny range of initial
conditions. Therefore, this effect can be easily missed in numerical
simulations if the relevant parameter space is not exhaustively investigated.
In the proposed picture, the observed rarity of $\gamma$-ray bursts would be
explained if the relevant conditions for this mechanism appear in only about
one in every $10^4-10^5$ core collapse supernovae. We also mention the
possibility that near-critical collapse could play a role in powering the
central engines of Active Galactic Nuclei.
