How does non-metricity affect particle creation and evaporation in bumblebee gravity?

Abstract: In this work, we analyze the impact of non-metricity on particle creation and the evaporation process of black holes within the framework of bumblebee gravity. In general lines, we compare black holes in the metric formalism [1] and the metric-affine approach [2]. Initially, we focus on bosonic particle modes to investigate Hawking radiation. Using the Klein-Gordon equation, we compute the Bogoliubov coefficients and derive the Hawking temperature. Subsequently, we examine Hawking radiation as a tunneling process, resolving divergent integrals through the residue method. The analysis is then extended to fermionic particle modes, also within the tunneling framework. Particle creation densities are calculated for both bosonic and fermionic cases. Additionally, greybody bounds are estimated for bosonic and fermionic particles. Furthermore, we explore the evaporation process, considering the final state of the black holes and we also investigate the correlation between the greybody factors and the quasinormal modes. Finally, constraints on the Lorentz-violating parameters $\ell$ (for the metric case) and $X$ (for the metric-affine case) are established using recent astrophysical data on black hole lifetimes. In a general panorama, non-metricity (except for the tensor perturbations) in bumblebee gravity raises particle density for bosons while reducing it for fermions, increases greybody factors (for both bosons and fermions), amplifies the emission rate, and accelerates the evaporation process.