Scattered wave functions and worldline instantons for particle production in curved spacetime

Abstract: We study the production of spin-$1/2$ particle-antiparticle pairs in curved spacetimes with nontrivial dependence on more than one coordinate. To this end, we develop two complementary approaches. First, we extend the scattered-wave-function (SWF) method, originally introduced for pair production in electromagnetic backgrounds, to curved spacetime backgrounds. Second, we complete the development of an open-worldline-instanton method by deriving the pre-exponential factor of the pair-production probability. We apply both methods to several two-dimensional metrics and find good agreement between the resulting probabilities. While the SWF approach provides numerically exact results and is particularly efficient for the examples considered here, the instanton approach offers favorable scaling to higher-dimensional backgrounds and more extreme parameter regimes. These methods provide new tools for studying pair production in multidimensional gravitational backgrounds beyond the reach of many existing approaches.