Abstract
The leading order finite size effects due to spin, namely that of the cubic and quartic in spin interactions, are derived for the first time for generic compact binaries via the effective field theory for gravitating spinning objects. These corrections enter at the third and a half and fourth post-Newtonian orders, respectively, for rapidly rotating compact objects. Hence, we complete the leading order finite size effects with spin up to the fourth post-Newtonian accuracy. We arrive at this by augmenting the point particle effective action with new higher dimensional nonminimal coupling worldline operators, involving higher-order derivatives of the gravitational field, and introducing new Wilson coefficients, corresponding to constants, which describe the octupole and hexadecapole deformations of the object due to spin. These Wilson coefficients are fixed to unity in the black hole case. The nonminimal coupling worldline operators enter the action with the electric and magnetic components of the Weyl tensor of even and odd parity, coupled to even and odd worldline spin tensors, respectively. Moreover, the non relativistic gravitational field decomposition, which we employ, demonstrates a coupling hierarchy of the gravito-magnetic vector and the Newtonian scalar, to the odd and even in spin operators, respectively, which extends that of minimal coupling. This observation is useful for the construction of the Feynman diagrams, and provides an instructive analogy between the leading order spin-orbit and cubic in spin interactions, and between the leading order quadratic and quartic in spin interactions.
Highlights
JHEP06(2015)059 at the 2PN order, and for rapidly rotating compact objects at the 3.5PN and 4PN orders, respectively
We complete the leading order finite size effects with spin up to the fourth post-Newtonian accuracy. We arrive at this by augmenting the point particle effective action with new higher dimensional nonminimal coupling worldline operators, involving higher-order derivatives of the gravitational field, and introducing new Wilson coefficients, corresponding to constants, which describe the octupole and hexadecapole deformations of the object due to spin. These Wilson coefficients are fixed to unity in the black hole case
In this work we derived for the first time the complete LO cubic and quartic in spin interaction potentials for generic compact binaries via the effective field theory for gravitating spinning objects [18]
Summary
We present the effective action, that removes the scale of the compact objects in the EFT approach, and augment the point particle action, as required in order to take into account finite size effects with spins. The spin-squared operator presented in eq (2.14) is equivalent to that in [12], as the building blocks of the spin-induced nonminimal couplings, considered in the body-fixed frame, are traceless and orthogonal to the 4-velocity [18] Considering this addition to the point particle action in eq (2.6) and eq (2.1), the LO quadrupole-monopole interaction, that is the LO spin-squared interaction, is derived, using the following Feynman rules we present, required to the order that we are considering in this work. Again we have omitted terms, which only contribute beyond LO Note that here it is again the Newtonian scalar, which is the leading one in the hierarchy of coupling in the electric component of the Weyl tensor in the worldline quartic spin operator
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