Thermodynamics, thermodynamic geometry, and the shadow of a Bardeen black hole surrounded by a Kiselev fluid: the role of regularity, asymptotics, and observational self-consistency
Abstract
We reconsider the Bardeen black hole surrounded by a Kiselev fluid, obtained by adding a Kiselev term to the Ayon-Beato-Garcia-Bardeen metric. Contrary to claims in the literature, the solution is regular at the origin only for c=0: for c≠0 curvature invariants diverge as r→0, and the spacetime is asymptotically de Sitter-like rather than flat, with a cosmological horizon rc for 0<c<cN(q). We map the full (q,c) domain of horizon structures in closed form, locating the extremal and Nariai-type boundaries and their cusp. Using the Ma-Zhao prescription for the mass-dependent nonlinear-electrodynamics source, we derive the corrected entropy and verify the extended first law and Smarr relation to machine precision by computer-algebra differentiation, not through the entropy's own definition. The heat capacity shows a single Davies-type divergence, located as a closed-form quartic and expanded analytically in c. In thermodynamic geometry, the Quevedo-metric curvature has a spurious second singularity generated by the entropy's integration constant and the non-uniqueness of its conformal factor; we isolate this artefact and show only the Davies-point divergence is physical. The Ruppeiner curvature, identically zero for pure Bardeen, becomes non-zero once c≠0. For the shadow, we compute the critical impact parameter bc(q,c,w) and show the nominal bound c≲10−2/M from the EHT image of Sagittarius A* is not self-consistent: the same c places the cosmological horizon nine orders of magnitude closer than Earth's distance to Sgr A*, and the bound is fourteen orders of magnitude larger than H0/c, the true cosmological dark-energy scale. We reinterpret the EHT constraint as bounding c only near the horizon, not as an astrophysical or cosmological bound on the quintessence parameter.
Related
- On Black Holes Surrounded by Radiation II: Thermodynamics
- Geodesics and thermodynamics of a κ-deformed anti-de Sitter black hole surrounded by a quintessence field
- Thermodynamic volumes of extended black hole thermodynamics with auxiliary gauge fields
- Thermodynamic Volumes of Extended Black Hole Thermodynamics with Auxiliary Gauge Fields
- Global equilibrium at order 𝒪(ℏ2): pseudo-gauge ambiguity, Maxwell relations, and thermodynamic consistency
BibTeX
@misc{quyet2026thermodynamics,
title = {{Thermodynamics, thermodynamic geometry, and the shadow of a Bardeen black hole surrounded by a Kiselev fluid: the role of regularity, asymptotics, and observational self-consistency}},
author = {Hoang Van Quyet},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.03801},
eprint = {2610.03801},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.03801},
}
RIS
TY - UNPB
TI - Thermodynamics, thermodynamic geometry, and the shadow of a Bardeen black hole surrounded by a Kiselev fluid: the role of regularity, asymptotics, and observational self-consistency
AU - Hoang Van Quyet
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.03801
UR - https://arxiv.org/abs/2610.03801
AB - We reconsider the Bardeen black hole surrounded by a Kiselev fluid, obtained by adding a Kiselev term to the Ayon-Beato-Garcia-Bardeen metric. Contrary to claims in the literature, the solution is regular at the origin only for c=0: for c≠0 curvature invariants diverge as r→0, and the spacetime is asymptotically de Sitter-like rather than flat, with a cosmological horizon r_c for 0<c<c_N(q). We map the full (q,c) domain of horizon structures in closed form, locating the extremal and Nariai-type boundaries and their cusp. Using the Ma-Zhao prescription for the mass-dependent nonlinear-electrodynamics source, we derive the corrected entropy and verify the extended first law and Smarr relation to machine precision by computer-algebra differentiation, not through the entropy's own definition. The heat capacity shows a single Davies-type divergence, located as a closed-form quartic and expanded analytically in c. In thermodynamic geometry, the Quevedo-metric curvature has a spurious second singularity generated by the entropy's integration constant and the non-uniqueness of its conformal factor; we isolate this artefact and show only the Davies-point divergence is physical. The Ruppeiner curvature, identically zero for pure Bardeen, becomes non-zero once c≠0. For the shadow, we compute the critical impact parameter b_c(q,c,w) and show the nominal bound c≲10^−2/M from the EHT image of Sagittarius A* is not self-consistent: the same c places the cosmological horizon nine orders of magnitude closer than Earth's distance to Sgr A*, and the bound is fourteen orders of magnitude larger than H_0/c, the true cosmological dark-energy scale. We reinterpret the EHT constraint as bounding c only near the horizon, not as an astrophysical or cosmological bound on the quintessence parameter.
ER -