Relativistic tidal properties of neutron stars
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 gravitoelectrictype coefficient Gμ_{ℓ}=[length]^{2ℓ+1} measuring the ℓthorder mass multipolar moment GM_{a1…aℓ} induced in a star by an external ℓthorder gravitoelectric tidal field G_{a1…aℓ}; (ii) a gravitomagnetictype coefficient Gσ_{ℓ}=[length]^{2ℓ+1} measuring the ℓth spin multipole moment GS_{a1…aℓ} induced in a star by an external ℓthorder gravitomagnetic tidal field H_{a1…aℓ}; and (iii) a dimensionless “shape” Love number h_{ℓ} measuring the distortion of the shape of the surface of a star by an external ℓthorder gravitoelectric tidal field. All the dimensionless tidal coefficients Gμ_{ℓ}/R^{2ℓ+1}, Gσ_{ℓ}/R^{2ℓ+1}, and h_{ℓ} (where R is the radius of the star) are found to have a strong sensitivity to the value of the star’s “compactness” c≡GM/(c_{0}^{2}R) (where we indicate by c_{0} the speed of light). In particular, Gμ_{ℓ}/R^{2ℓ+1}̃k_{ℓ} is found to strongly decrease, as c increases, down to a zero value as c is formally extended to the “black hole (BH) limit” c^{BH}=1/2. The shape Love number h_{ℓ} is also found to significantly decrease as c increases, though it does not vanish in the formal limit c→c^{BH}, but is rather found to agree with the recently determined shape Love numbers of black holes. The formal vanishing of μ_{ℓ} and σ_{ℓ} as c→c^{BH} is a consequence of the nohair properties of black holes. This vanishing 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.
 Publication:

Physical Review D
 Pub Date:
 October 2009
 DOI:
 10.1103/PhysRevD.80.084035
 arXiv:
 arXiv:0906.0096
 Bibcode:
 2009PhRvD..80h4035D
 Keywords:

 04.25.Nx;
 04.40.Dg;
 95.30.Sf;
 PostNewtonian approximation;
 perturbation theory;
 related approximations;
 Relativistic stars: structure stability and oscillations;
 Relativity and gravitation;
 General Relativity and Quantum Cosmology
 EPrint:
 21 pages, 10 figures. Matches the published version