Black hole with confining electric potential in scalar-tensor description of regularized 4-dimensional Einstein-Gauss-Bonnet gravity

In this paper, we analytically present an exact confining charged black hole solution to the scalar-tensor description of regularized 4-dimensional Einstein-Gauss-Bonnet gravity (4DEGBG) coupled to non-linear gauge theory containing $\sqrt{-F^{2}}$ term. Part of the importance of using a non-trivial $4D$ theory of Gauss-Bonnet gravity is that it is proven the absence of the Ostrogradsky instability was formulated in [D. Glavan and C. Lin, Phys. Rev. Lett. 124, 081301 (2020)] and then regularized 4DEGBG theory was obtained in [Hennigar et al. JHEP 07, 027 (2020)] and [Fernandes et al. Phys. Rev. D 102, no.2, 024025 (2020)] as well as this theory gains many attention because of its important finding for black hole physics. We therefore also study some properties of this solution such as temperature, specific heat, shadow and quasinormal modes. Our results here show that a confining charge $f$ gives a significant contribution to the shadow of the black hole as well as quasinormal modes frequencies.