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’s...

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Bibliographic Details
Published inSciPost physics Vol. 15; no. 6; p. 226
Main Authors Compère, Geoffrey, Druart, Adrien, Vines, Justin
Format Journal Article
LanguageEnglish
Published SciPost 01.12.2023
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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:2542-4653
2542-4653
DOI:10.21468/SciPostPhys.15.6.226