Cosmologically coupled black holes (CCBHs), whose masses evolve in response to the cosmological expansion, have recently attracted significant theoretical and observational interest. Existing studies have treated CCBHs as purely classical objects, neglecting the effect of Hawking radiation (HR), which competes with the cosmological coupling (CC) mechanism. We take a first step toward studying evaporating CCBHs, adopting a quasiadiabatic approximation in which the HR rate is evaluated at the instantaneous CCBH mass, and modeling the CC mechanism through the phenomenological scaling of the mass with the scale factor, $M\propto a^k$. We show that, depending on the coupling strength $k$, even late-time CC activation can significantly delay Hawking evaporation, or lead to asymptotic CC-dominated mass growth, with important implications. We set limits on the abundance of primordial CCBHs from $\gamma$-ray observations, finding limits which are weaker than their uncoupled counterparts, as CCBHs are kept farther from the endpoint of evaporation for a longer time. Unlike standard primordial black holes, the CCBH formation and present-day masses no longer approximately coincide, even for formation masses $M_{\mathrm{form}}\gtrsim {10}^{15}\mathrm{g}$. Therefore, the same population of primordial CCBHs may be subject to evaporation limits through its past emission history, as well as to other limits (such as microlensing) through its present-day mass.

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• Classical black holes