How does nonmetricity shape quantum emission from rotating bumblebee black holes?

Abstract

We investigate how nonmetricity affects particle creation and evaporation in rotating bumblebee black holes by comparing metric and metric-affine solutions. We normalize the stationary Killing vectors at spatial infinity before defining physical frequencies, angular velocities, and temperatures. This procedure changes the static comparison and gives the leading calibration $\ell=3X/4$. In the metric solution, $\ell$ shifts the horizons, stationary limit surfaces, and extremal boundary, increases the normalized horizon angular velocity, and suppresses the Hawking temperature. Nevertheless, the surface gravity remains uniform and the scalar wave equation separable. We derive the tunneling factors, quantum occupation numbers, radial potential, and an analytical lower bound for the axisymmetric greybody factor. In the metric-affine geometry, nonmetricity preserves the Kerr coordinate locations of the horizons and stationary limit surfaces, but changes the physical horizon area, normalized angular velocity, and meridional sector. The component $g_{r\theta}$ couples angular channels, whereas the local surface gravity depends on latitude when $aX\neq0$. Consequently, the generic rotating configuration admits neither a single global Hawking temperature nor an independent channel-by-channel emission spectrum. In the static limit, under the same Stefan-Boltzmann prescription, both Lorentz-violating geometries have lower luminosities and longer lifetimes, with the metric-affine black hole radiating less and evaporating more slowly. A local slow-rotation expansion preserves this tendency but does not establish a global rotating evaporation hierarchy. Existing weak-field constraints limit fractional corrections to static quantum-emission observables to below $1.3\times10^{-11}$.