The characteristics of circular motion and quasiperiodic oscillations around accelerating black hole

Tao-Tao Sui; Xin-Yang Wang

doi:10.1140/epjc/s10052-025-14857-9

2024 Impact factor 4.8

Particles and Fields

Open Access

Eur. Phys. J. C (2025) 85: 1112
https://doi.org/10.1140/epjc/s10052-025-14857-9

Regular Article - Theoretical Physics

The characteristics of circular motion and quasiperiodic oscillations around accelerating black hole

Tao-Tao Sui^a and Xin-Yang Wang

Center for Fundamental Physics, School of Mechanics and Photoelectric Physics, Anhui University of Science and Technology, 232001, Huainan, Anhui, China

^a suitaotao@aust.edu.cn

Received: 3 August 2025
Accepted: 22 September 2025
Published online: 8 October 2025

Abstract

This study explores the motion of massive test particles and associated quasi-periodic oscillations (QPOs) around an accelerating black hole. The acceleration factor A suppresses the radial effective potential $V_{eff}$ $V_{\text {eff}}$ , thereby lowering the energy $E$ ${\mathcal {E}}$ and angular momentum $L$ ${\mathcal {L}}$ required for stable circular orbits. Stability demands $\partial_{r}^{2} V_{eff} \geq 0$ $\partial _r^2 V_{\text {eff}} \ge 0$ , setting an upper bound AM $\leq 0.0161$ $\le 0.0161$ . As A increases, the innermost stable circular orbit (ISCO) radius grows, while $L ISCO$ ${\mathcal {L}}{\text {ISCO}}$ and $E ISCO$ ${\mathcal {E}}{\text {ISCO}}$ decrease. Radiative efficiency $ϵ$ $\epsilon$ rises with A, peaking at $6.9 %$ $6.9\%$ . Fundamental frequencies show that A accelerates the decay of the Keplerian $Ω_{ϕ}$ $\Omega _{\phi }$ and vertical $Ω_{θ}$ $\Omega _{\theta }$ frequencies, while suppressing the radial frequency E. The divergence between $Ω_{θ}$ $\Omega _{\theta }$ and $Ω_{ϕ}$ $\Omega _{\phi }$ increases with A, differing from spherical black hole behavior. Using the RP, ER3, ER4, and WD QPO models, the WD model predicts the highest frequencies. ER4’s resonant radius remains fixed across frequency ratios, unlike ER3. Although A suppresses twin-peak QPO frequencies, it enhances the nodal precession frequency $ν_{nod}$ $\nu _{\text {nod}}$ . Fitting observational data from GRO J1655−40 and XTE J1859+226 and applying the TOV limit, the ER4 model uniquely fits GRO J1655−40 with $(10^{3} A, M, r / M) \approx (4.31, 3.43 M_{⊙}, 8.08)$ $(10^3A, M, r/M) \approx (4.31, 3.43 M_\odot , 8.08)$ . For XTE J1859+226, three models yield $10^{3} A \approx 1.4$ $10^3A \approx 1.4$ , excluding ER3, suggesting stronger acceleration in GRO J1655−40.

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Funded by SCOAP³.

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The characteristics of circular motion and quasiperiodic oscillations around accelerating black hole

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