Relativistic effective action of dynamical gravitomagnetic tides for slowly rotating neutron stars. (arXiv:2011.03508v2 [gr-qc] UPDATED)

<a href="http://arxiv.org/find/gr-qc/1/au:+Gupta_P/0/1/0/all/0/1">Pawan Kumar Gupta</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Steinhoff_J/0/1/0/all/0/1">Jan Steinhoff</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Hinderer_T/0/1/0/all/0/1">Tanja Hinderer</a>

Gravitomagnetic quasi-normal modes of neutron stars are resonantly excited by

tidal effects during a binary inspiral, leading to a potentially measurable

effect in the gravitational-wave signal. We take an important step towards

incorporating these effects in waveform models by developing a relativistic

effective action for the gravitomagnetic dynamics that clarifies a number of

subtleties. Working in the slow-rotation limit, we first consider the

post-Newtonian approximation and explicitly derive the effective action from

the equations of motion. We demonstrate that this formulation opens a novel way

to compute mode frequencies, yields insights into the relevant matter

variables, and elucidates the role of a shift symmetry of the fluid properties

under a displacement of the gravitomagnetic mode amplitudes. We then construct

a fully relativistic action based on the symmetries and a power counting

scheme. This action involves four coupling coefficients that depend on the

internal structure of the neutron star and characterize the key matter

parameters imprinted in the gravitational waves. We show that, after fixing one

of the coefficients by normalization, the other three directly involve the two

kinds of gravitomagnetic Love numbers (static and irrotational), and the mode

frequencies. We discuss several interesting features and dynamical consequences

of this action, and analyze the frequency-domain response function (the

frequency-dependent ratio between the induced flux quadrupole and the external

gravitomagnetic field), and a corresponding Love operator representing the

time-domain response. Our results provide the foundation for deriving precision

predictions of gravitomagnetic effects, and the nuclear physics they encode,

for gravitational-wave astronomy.

Gravitomagnetic quasi-normal modes of neutron stars are resonantly excited by

tidal effects during a binary inspiral, leading to a potentially measurable

effect in the gravitational-wave signal. We take an important step towards

incorporating these effects in waveform models by developing a relativistic

effective action for the gravitomagnetic dynamics that clarifies a number of

subtleties. Working in the slow-rotation limit, we first consider the

post-Newtonian approximation and explicitly derive the effective action from

the equations of motion. We demonstrate that this formulation opens a novel way

to compute mode frequencies, yields insights into the relevant matter

variables, and elucidates the role of a shift symmetry of the fluid properties

under a displacement of the gravitomagnetic mode amplitudes. We then construct

a fully relativistic action based on the symmetries and a power counting

scheme. This action involves four coupling coefficients that depend on the

internal structure of the neutron star and characterize the key matter

parameters imprinted in the gravitational waves. We show that, after fixing one

of the coefficients by normalization, the other three directly involve the two

kinds of gravitomagnetic Love numbers (static and irrotational), and the mode

frequencies. We discuss several interesting features and dynamical consequences

of this action, and analyze the frequency-domain response function (the

frequency-dependent ratio between the induced flux quadrupole and the external

gravitomagnetic field), and a corresponding Love operator representing the

time-domain response. Our results provide the foundation for deriving precision

predictions of gravitomagnetic effects, and the nuclear physics they encode,

for gravitational-wave astronomy.

http://arxiv.org/icons/sfx.gif