Relativistic tidal properties of neutron stars

We study the various linear responses of neutron stars to external relativistic tidal fields. We focus on three different tidal responses, associated to three different tidal coefficients: (i) a gravito-electric-type coefficient $G{\ensuremath{\mu}}_{\ensuremath{\ell}}=[\mathrm{\text{length}}{]}^{2\ensuremath{\ell}+1}$ measuring the $\ensuremath{\ell}$th-order mass multipolar moment $G{M}_{{a}_{1}\dots{}{a}_{\ensuremath{\ell}}}$ induced in a star by an external $\ensuremath{\ell}$th-order gravito-electric tidal field ${G}_{{a}_{1}\dots{}{a}_{\ensuremath{\ell}}}$; (ii) a gravito-magnetic-type coefficient $G{\ensuremath{\sigma}}_{\ensuremath{\ell}}=[\mathrm{\text{length}}{]}^{2\ensuremath{\ell}+1}$ measuring the…