Conformal anomaly and gravitational pair production

We conjecture that the time-reversal-even component of the pair production rate $\Gamma$ of particles in background fields in conformal 3+1 dimensional field theories is given by the anomalous trace $\langle T^\mu_{\ \mu}\rangle$ of the energy-momentum tensor: $\Gamma = (\pi/2) \langle T^\mu_{\ \mu} \rangle \Theta( \langle T^\mu_{\ \mu}\rangle)$, where $\Theta(x)$ is the Heaviside step function. We show that this relation, written in mostly-plus metric, correctly describes the one-loop Schwinger pair creation of massless particles both in scalar and spinor versions of quantum electrodynamics. It also accurately points to the Savvidi instability of the gluonic vacuum towards the formation of the chromomagnetic condensate. The conjectured formula also reproduces (presumably, non-Hawking) radiation generated by static gravitational fields in the absence of an event horizon via a new evaporation mechanism suggested in [Phys. Rev. Lett. 130, 221502 (2023)]. A concurrent mechanism of the particle production due to the axial anomaly is briefly discussed and critical remarks on the state-dependence are also given.