Generalized Carter and Rüdiger constants for spinning charged probes in √Kerr backgrounds exist only for Wilson coefficients matching spin-exponentiated effective Compton amplitudes up to second order in spin.
Levi, Next to Leading Order gravitational Spin1-Spin2 coupling with Kaluza-Klein reduction, Phys
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abstract
We use the recently proposed Kaluza-Klein (KK) reduction over the time dimension, within an effective field theory (EFT) approach, to calculate the next to leading order (NLO) gravitational spin1-spin2 interaction between two spinning compact objects. It is shown here that to NLO in the spin1-spin2 interaction, the reduced KK action within the stationary approximation is sufficient to describe the gravitational interaction, and that it simplifies calculation substantially. We also find here that the gravito-magnetic vector field defined within the KK decomposition of the metric mostly dominates the mediation of the interaction. Our results coincide with those calculated in the ADM Hamiltonian formalism, and we provide another explanation for the discrepancy with the result previously derived within the EFT approach, thus demonstrating clearly the equivalence of the ADM Hamiltonian formalism and the EFT action approach.
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gr-qc 3years
2026 3representative citing papers
The NLO gravitational spin-orbit Hamiltonian for N spinning bodies is computed via PN-EFT, with only three-body diagrams new beyond the binary case, and the result matches the known ADM Hamiltonian up to canonical transformation.
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Generalized Carter & R\"udiger Constants of $\sqrt{\text{Kerr}}$
Generalized Carter and Rüdiger constants for spinning charged probes in √Kerr backgrounds exist only for Wilson coefficients matching spin-exponentiated effective Compton amplitudes up to second order in spin.
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N-body next-to-leading order gravitational spin-orbit interaction via effective field theory
The NLO gravitational spin-orbit Hamiltonian for N spinning bodies is computed via PN-EFT, with only three-body diagrams new beyond the binary case, and the result matches the known ADM Hamiltonian up to canonical transformation.
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Love numbers of black holes and compact objects
A pedagogical review of Love numbers and tidal responses for black holes and compact objects in general relativity and extensions.