Neutrino pair annihilation in curved spacetime: a fast moment method and the geometry of flavour conversion
Neutrino-antineutrino annihilation above black-hole accretion discs is shaped both by general-relativistic transport and by neutrino flavour conversion. Whether these effects can be treated independently depends on how gravity weights the different flavour populations. We investigate this interplay using backward ray tracing in Schwarzschild and Kerr spacetimes, combined with an exact angular-moment formulation of the annihilation kernel that we validate against the analytic spherical solution and published disc calculations. We first establish that flavour-conversion corrections are independent of the spacetime geometry when conversion is uniform and the initial heavy-lepton neutrino emission is negligible. For uniform conversion, this separability remains approximately valid when the flavour-dependent emitting regions overlap: compared with the same discs in flat space, moving with the same local velocities, gravity enhances the deposited energy by factors of 1.4-5, while changing the relative conversion effect by no more than 6% for most temperature profiles considered; conversion that varies across the disc raises this to 22% around a rapidly spinning hole. A qualitatively different regime emerges when heavy-lepton neutrinos originate from an inner ring separated from the electron-flavour emitting regions. Relativistic bending and energy shifts preferentially enhance annihilations involving inner-ring neutrinos, producing relativistic conversion factors up to 2.4 times the flat-space ones. In one configuration, flavour equipartition reduces the deposition by 54% in flat space but increases it by 11% in Kerr spacetime. These results identify the spatial arrangement of flavour-dependent neutrinospheres as a key determinant, in the models considered, of whether flavour conversion and relativistic transport can be treated separately.