Generalized Carter constant for quadrupolar test bodies in Kerr spacetime

We establish the existence of a deformation of the usual Carter constant which is conserved along the motion in a fixed Kerr background of a spinning test body possessing the spin-induced quadrupole coupling of a black hole. The conservation holds perturbatively up to second order in the test body&#...

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Bibliographic Details
Published inarXiv.org
Main Authors Compère, Geoffrey, Druart, Adrien, Vines, Justin
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 26.10.2023
Subjects
Black holes
Couplings
Differential equations
Neutron stars
Physics - General Relativity and Quantum Cosmology
Quadrupole interaction
Quadrupoles
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Summary:We establish the existence of a deformation of the usual Carter constant which is conserved along the motion in a fixed Kerr background of a spinning test body possessing the spin-induced quadrupole coupling of a black hole. The conservation holds perturbatively up to second order in the test body's spin. This constant of motion is obtained through the explicit resolution of the conservation constraint equations, employing covariant algebraic and differential relations amongst covariant building blocks of the Kerr background. For generic spin-induced quadrupole couplings, which describe compact objects such as neutron stars, we obtain a no-go result on the existence of such a conserved quantity.
ISSN:2331-8422
DOI:10.48550/arxiv.2302.14549