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arXiv · 2606.15381

EMRI Dephasing from a Torsion-Inspired Near-Zone Kerr Deformation: Motivated by Spin-Polarized Dark Matter

Jingxu Wu·Liangyu Luo·Daniil Stepanenko·Jie Shi
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Abstract

Extreme-mass-ratio inspirals (EMRIs) are sensitive probes of weak conservative perturbations in the strong-field region of massive black holes. We study a phenomenological EMRI model motivated by Einstein--Cartan gravity in which a spin-polarized dark-matter spike is described by a Weyssenhoff fluid. After torsion is eliminated algebraically, the local spin contribution contains a repulsive exterior source $U_{tt}^{\rm spin}\propto-\sigma_0^2/r^3$. Solving the corresponding static linearized field equation, however, does not produce a global $1/r^3$ metric perturbation; the response contains a mass renormalization, a logarithmic $r^{-1}$ tail, and an $M/r^2$ term. We therefore introduce $g_{\mu\nu}^{\rm eff}=g_{\mu\nu}^{\rm Kerr}+\alpha h_{\mu\nu}^{\rm eff}$ only as a local near-zone matching ansatz, not as a complete rotating Einstein--Cartan black-hole solution. Within this torsion-inspired deformation we compute circular equatorial inspirals and analytic-kludge waveforms. The fiducial model can produce large phase shifts in an idealized adiabatic calculation, but the forecast is optimistic and does not include a full LISA/Taiji response, Teukolsky/self-force fluxes, eccentricity, inclination, or high-dimensional parameter degeneracies. The results should be read as constraints on an effective near-zone operator rather than as a prediction of minimally coupled Einstein--Cartan dark matter.

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Jingxu Wu, Liangyu Luo, Daniil Stepanenko, Jie Shi. 2026-06-13. EMRI Dephasing from a Torsion-Inspired Near-Zone Kerr Deformation: Motivated by Spin-Polarized Dark Matter. https://arxiv.org/abs/2606.15381

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