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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.18790 |
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| _version_ | 1866917449688940544 |
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| author | de Firmian, Christopher Vines, Justin |
| author_facet | de Firmian, Christopher Vines, Justin |
| contents | We consider the motion of a charged spinning test/probe particle -- governed by the Mathisson-Papapetrou-Dixon equations with generic, adiabatic, and conservative spin- and field-induced multipole moments -- in a background $\sqrt{\text{Kerr}}$ field on flat spacetime: the electromagnetic field of a charged spinning ring-disk singularity obtained from the $G\to 0$ limit of the Kerr-Newman solution for a charged spinning black hole. We investigate the existence of two extra hidden constants of motion, analogous to the Carter constant (for geodesic motion in a Kerr spacetime, or for its spinning-probe generalization) and Rüdiger's linear-in-spin constant for a spinning probe in a Kerr background. We find that these two constants exist only when the Wilson coefficients parameterizing the probe's multipole structure take the particular values corresponding to spin-exponentiation of the effective Compton amplitudes through second order in spin. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_18790 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Generalized Carter & Rüdiger Constants of $\sqrt{\text{Kerr}}$ de Firmian, Christopher Vines, Justin General Relativity and Quantum Cosmology We consider the motion of a charged spinning test/probe particle -- governed by the Mathisson-Papapetrou-Dixon equations with generic, adiabatic, and conservative spin- and field-induced multipole moments -- in a background $\sqrt{\text{Kerr}}$ field on flat spacetime: the electromagnetic field of a charged spinning ring-disk singularity obtained from the $G\to 0$ limit of the Kerr-Newman solution for a charged spinning black hole. We investigate the existence of two extra hidden constants of motion, analogous to the Carter constant (for geodesic motion in a Kerr spacetime, or for its spinning-probe generalization) and Rüdiger's linear-in-spin constant for a spinning probe in a Kerr background. We find that these two constants exist only when the Wilson coefficients parameterizing the probe's multipole structure take the particular values corresponding to spin-exponentiation of the effective Compton amplitudes through second order in spin. |
| title | Generalized Carter & Rüdiger Constants of $\sqrt{\text{Kerr}}$ |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2602.18790 |