Structure of Logarithmically-Corrected Starobinsky Fuzzy Dark Matter Black Holes
Abstract
This work constructs an anisotropic, Einasto-profile fuzzy dark matter (DM) black hole (BH) using a logarithmically-corrected Starobinsky gravity, f(R)=R+βR2+γR2ln(R/μ2), 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.
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BibTeX
@misc{ilyas2026structure,
title = {{Structure of Logarithmically-Corrected Starobinsky Fuzzy Dark Matter Black Holes}},
author = {M. Ilyas and Fatima Bint-e-Munir and Rana Zaman Ahmad and M. Shahan},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.35974},
eprint = {2610.35974},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.35974},
}
RIS
TY - UNPB
TI - Structure of Logarithmically-Corrected Starobinsky Fuzzy Dark Matter Black Holes
AU - M. Ilyas
AU - Fatima Bint-e-Munir
AU - Rana Zaman Ahmad
AU - M. Shahan
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.35974
UR - https://arxiv.org/abs/2610.35974
AB - 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^2ln(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.
ER -