Black holes with global monopoles in 4D noncommutative Einstein–Gauss–Bonnet gravity

In this work, we construct an exact spherically symmetric black hole solution with a global monopole in the context of four-dimensional noncommutative Einstein–Gauss–Bonnet gravity. We modeled the space–time noncommutativity via a Lorentzian-smeared mass distribution. Then we study the horizon structure and find that this black hole can have two configurations: one degenerate horizon or no horizon, depending on the black hole parameters. We also analyze thermodynamics and thermal stability by computing the Hawking temperature, entropy and heat capacity. Our analysis reveals that the Hawking temperature and entropy acquire corrections from the noncommutative parameter [Formula: see text], the energy scale of symmetry breaking [Formula: see text], and the Gauss–Bonnet coupling constant [Formula: see text]. The heat capacity exhibits divergences that signal second-order phase transitions. Thereafter, we study the black hole shadow employing the null geodesics and the Hamiltonian–Jacobi equation. Our results show that the shadow decreases with increasing [Formula: see text] or [Formula: see text] and increases with increasing [Formula: see text]. Finally, we analyze quasinormal modes or scalar perturbations, we compute them via the 6th-order WKB method, and compare them to the shadow radius methods in the eikonal limit.