mimetic black holes in einstein-scalar-gauss-bonnet gravity

In this paper, we try to extend the intriguing concept of mimetic black holes to the realm of the gauss-bonnet gravity. mimetic black holes are a fascinating theoretical construct that mimic the exterior gravitational field of known black holes even without possessing an event horizon in some specific conditions. by incorporating the gauss-bonnet theory, we aim to investigate how the dynamics and properties of mimetic black holes are altered in this modified gravitational framework. in this particular setting, we explore the existence of black hole solutions with nontrivial scalar hair while being influenced by the mimetic scalar field in the einstein scalar-gauss-bonnet (esgb) theory. these solutions are characterized by their regularity and offer new insights into the dynamics of black holes in this theory. we proceed by conducting an analytical study in the near horizon asymptotic regime when an event horizon cab be existed. our analysis reveals that in this setup a black hole event horizon with a nontrivial hair can be formed, regardless of the sign of the lagrange multipliers λ, depending on the particular selection of the coupling between the scalar field and the gauss-bonnet term. notably, this black hole horizon remains regular, emphasizing the robustness of the black hole solutions in this setup.