Love tensor of a slowly rotating body

Abstract: A rotating body immersed in a gravitomagnetic tidal field is subjected to a Lorentz-like force $v \times B$, where $v$ is the rotational velocity, and $B$ is the gravitomagnetic field, which is produced by mass currents associated with the companion’s orbital motion. The body’s response to this force can be described in terms of a tidal polarizability. In this talk I describe a post-Newtonian theory of this tidal polarizability, which takes the form of a Love tensor, a four-index object that relates the body's current quadrupole moment $S_{jk}$ to the gravitomagnetic tidal moment $B_{jk}$. The tensorial nature of this quantity has to do with the fact that each $e^{i m \phi}$ piece of the tidal force gives rise to an m-specific velocity perturbation, and therefore to a tidal polarizability that depends on m. The collection of these m-specific Love numbers makes up the Love tensor.

cosmology and nongalactic astrophysicsother condensed matterquantum gasesstrongly correlated electronssuperconductivitygeneral relativity and quantum cosmologyHEP - theory

Audience: researchers in the topic

Carnegie Mellon theoretical physics