Radial Stress and the Innermost Stable Circular Orbit of a Bardeen Black Hole in a Dark Matter Halo: A First-Order Response Criterion
Abstract
A dark matter density profile alone does not determine the spacetime around a black hole; the radial stress must be prescribed separately and governs the strong-field orbital response. We study a Bardeen black hole in a Hernquist halo through three spherical models sharing the same density, mass function, and cutoff but differing in radial stress: a halo with prDM=−ρDM, its truncated form, and a truncated Einstein cluster with prDM=0. Treating the halo as a small perturbation, we derive a first-order criterion for the leading innermost stable circular orbit shift, Cλ=Cρ+λCp. The two truncated closures shift this orbit in opposite directions for the Hernquist profile, and unexpanded calculations for five density profiles confirm the predicted signs. Checks using a Hayward background and a published Dehnen-halo result show that the criterion is not restricted to the Bardeen-Hernquist system. A continuous stress interpolation identifies a critical closure at which the leading shift vanishes. For a representative four-year extreme-mass-ratio inspiral, changing the radial stress at fixed density and cutoff produces a phase difference of several radians in a leading-order adiabatic treatment.
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BibTeX
@misc{deng2026radial,
title = {{Radial Stress and the Innermost Stable Circular Orbit of a Bardeen Black Hole in a Dark Matter Halo: A First-Order Response Criterion}},
author = {Yang Deng and Jia-Zhou Liu and Wen-Di Guo},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.16685},
eprint = {2609.16685},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.16685},
}
RIS
TY - UNPB
TI - Radial Stress and the Innermost Stable Circular Orbit of a Bardeen Black Hole in a Dark Matter Halo: A First-Order Response Criterion
AU - Yang Deng
AU - Jia-Zhou Liu
AU - Wen-Di Guo
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.16685
UR - https://arxiv.org/abs/2609.16685
AB - A dark matter density profile alone does not determine the spacetime around a black hole; the radial stress must be prescribed separately and governs the strong-field orbital response. We study a Bardeen black hole in a Hernquist halo through three spherical models sharing the same density, mass function, and cutoff but differing in radial stress: a halo with p_r^DM=−ρ_DM, its truncated form, and a truncated Einstein cluster with p_r^DM=0. Treating the halo as a small perturbation, we derive a first-order criterion for the leading innermost stable circular orbit shift, C_λ=C_ρ+λC_p. The two truncated closures shift this orbit in opposite directions for the Hernquist profile, and unexpanded calculations for five density profiles confirm the predicted signs. Checks using a Hayward background and a published Dehnen-halo result show that the criterion is not restricted to the Bardeen-Hernquist system. A continuous stress interpolation identifies a critical closure at which the leading shift vanishes. For a representative four-year extreme-mass-ratio inspiral, changing the radial stress at fixed density and cutoff produces a phase difference of several radians in a leading-order adiabatic treatment.
ER -