Fuzzy black hole models in f ( G ) Gravity

Abstract

In this manuscript, we explore the concept of dark matter black holes, inspired by the Einasto density profile in the background of $f(\mathcal{G})$ gravity, where $\mathcal{G}$ is a Gauss-Bonnet invariant. This work extends the scope beyond the noncommutative tiny black hole structure which incorporates dark matter as a constituent forming the black hole. Our investigation demonstrates the feasibility of constructing black hole solutions for various Einasto index values, $f(\mathcal{G})$ gravity parameters, and parameters of mass function adopting anisotropic fluid configuration to characterize the matter sector. Specifically, by adopting an equation of state in which the radial pressure equals the negative of the energy density, we derive black hole solutions exhibiting a horizon structure with the central singularity replaced by a regular de Sitter core akin to the Reissner-Nordstr"{o}m black holes. Furthermore, we explore an alternative scenario where the equation of state is nonlocal, resulting in the construction of self-gravitating fuzzy dark matter droplets together with the dark source $f(\mathcal{G})$ corrections.