Black-hole evaporation for cosmological observers

This work investigates the evaporation of black holes immersed in a de Sitter environment, using the Vaidya-de Sitter spacetime. The role of cosmological observers is highlighted in the development and Hayward thermodynamics for non-stationary geometries is employed in the description of the compact objects. The results of the proposed dynamical model are compared with the usual description based on stationary geometries, with specific results for primordial black holes (PBHs). The timescale of evaporation is shown to depend significantly on the choice of cosmological observer and can differ substantially from predictions based on stationary models at late times. Deviations are also shown with respect to the standard assertion that there is a fixed initial mass just below $10^{15} \, \text{g} \sim 10^{-18} M_\odot$ for the PBHs which are completing their evaporation process at the present epoch.