Аннотация
Cosmic voids—the immense, sparsely populated regions that lie between galaxies—emerge as key players in the life cycle of black holes. In this work, we investigate their influence within the framework of four-dimensional Einstein-Gauss-Bonnet gravity, an extension of general relativity that introduces higher-order curvature terms. Our results indicate that both the void depth, characterized by δ c , and the Gauss-Bonnet coupling α , strongly shape the horizon structure of black holes, in some cases even suppressing their formation in highly underdense regions. We further study the characteristic oscillations, or quasinormal modes, triggered by perturbations of these black holes, showing that the combined effects of cosmic underdensities and curvature corrections imprint distinctive patterns that could be probed through future gravitational-wave signals. The thermodynamic sector reveals equally striking consequences: temperature, entropy, and stability are all reshaped by the surrounding voids, with the possibility of stable extremal remnants emerging. Finally, by examining the energy emission rate—closely tied to the apparent shadow—we demonstrate that evaporation proceeds at markedly different rates depending on δ c and α . This interplay between environment and modified gravity opens new avenues for understanding black hole evolution and provides concrete signatures that upcoming astrophysical observations may be able to test.