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Generalized Carter constant for quadrupolar test bodies in Kerr spacetime
by Geoffrey Compère, Adrien Druart, Justin Vines
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Geoffrey Compère · Adrien Druart |
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| Preprint Link: | https://arxiv.org/abs/2302.14549v2 (pdf) |
| Date accepted: | 2023-11-10 |
| Date submitted: | 2023-10-27 10:56 |
| Submitted by: | Druart, Adrien |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
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.
Author comments upon resubmission
First, we would like to thank the referees for their very encouraging comments on our manuscript.
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Regarding $Q^{\text{lin}}$, we meant that it was identical to R\”udiger’s invariant $Q^R$ but we omitted to state it. We have now simplified the notation and defined $Q^{\text{lin}}$ directly in Eqs. (49) and (50) and then explained that it is equal to R\”udiger’s $Q_R$, see arguments around Eq. (53).
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Regarding $\mathcal A$, we agree with the comments of the referee. We added further comments on the significance of $\mathcal Q$ after Eq. (79).
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Thanks to the referee for pointing out to a sign mistake. It has now been corrected. Please see the updated Eqs. (93), (94), (95). We also corrected a factor in Eqs. (100) and (101).
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Regarding the existence of conserved quantities with higher multipolar content, we are totally in line with the referee. We added one further paragraph on these prospects in the conclusions following the suggestion of the referee.
Published as SciPost Phys. 15, 226 (2023)
Reports on this Submission
Report #1 by Scott Hughes (Referee 1) on 2023-11-1 (Invited Report)
Report
I am fully happy with the authors' responses to my report. I confess I have not read through the revised manuscript as thoroughly as I did for my initial report, but I read it closely enough to examine the changes they made.
I am happy to recommend acceptance with no further changes.