**Authors**: Thbiault Damour, Alessandro Nagar

**Date**: 30 May 2009

**Abstract**: 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\mu_\ell=[length]ˆ{2\ell+1} measuring the \ellˆ{th}-order mass multipolar moment GM_{a_1… a_\ell} induced in a star by an external \ellˆ{th}-order gravito-electric tidal field G_{a_1… a_\ell}; (ii) a gravito-magnetic-type coefficient G\sigma_\ell=[length]ˆ{2\ell+1} measuring the \ellˆ{th} spin multipole moment G S_{a_1… a_\ell} induced in a star by an external \ellˆ{th}-order gravito-magnetic tidal field H_{a_1… a_\ell}; and (iii) a dimensionless ‘shape’ Love number h_\ell measuring the distorsion of the shape of the surface of a star by an external \ellˆ{th}-order gravito-electric tidal field. All the dimensionless tidal coefficients G\mu_\ell/Rˆ{2\ell+1}, G\sigma_\l/Rˆ{2\ell+1} and h_\ell (where R is the radius of the star) are found to have a strong sensitivity to the value of the star's ‘compactness’ c\equiv GM/(c_0ˆ2 R) (where we indicate by c_0 the speed of light). In particular, G\mu_\l/Rˆ{2\l+1}\sim k_\ell is found to strongly decrease, as c increases, down to a zero value as c is formally extended to the ‘black-hole limit’ cˆ{BH}=½. The shape Love number h_\ell is also found to significantly decrease as c increases, though it does not vanish in the formal limit c\to cˆ{BH}. The formal vanishing of \mu_\ell and \sigma_\ell as c\to cˆ{BH} is a consequence of the no-hair properties of black holes; this suggests, but in no way proves, that the effective action describing the gravitational interactions of black holes may not need to be augmented by nonminimal worldline couplings.

0906.0096
(/preprints)

2009-06-07, 09:59
**[edit]**

© M. Vallisneri 2012 — last modified on 2010/01/29

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