Structure of Logarithmically-Corrected Starobinsky Fuzzy Dark Matter Black Holes

This work constructs an anisotropic, Einasto-profile fuzzy dark matter (DM) black hole (BH) using a logarithmically-corrected Starobinsky gravity, $f(R)=R+βR^2+γR^2\ln(R/μ^2)$, a form motivated by one-loop quantum corrections to the gravitational action rather than by the pure quadratic term alone. We derive the generalized trace equation for this action, show that its $β$- and $γ$-dependence collapses to a single compact source term, and solve the resulting field equations perturbatively about an exact general-relativistic (GR) background for two distinct anisotropic equations of state: a de~Sitter-type branch and a non-local branch, the latter worked through to a closed tangential-pressure profile rather than left incomplete. The logarithmic correction is found to raise the extremal (zero-temperature) threshold relative to pure quadratic gravity and to increase the core tangential pressure noticeably in the non-local branch.

Source: arXiv:2610.35974v1 - http://arxiv.org/abs/2610.35974v1 PDF: https://arxiv.org/pdf/2610.35974v1 Original Link: http://arxiv.org/abs/2610.35974v1