Tidal Love Numbers of Neutron Stars

For a variety of fully relativistic polytropic neutron star models we calculate the star’s tidal Love number k2. Most realistic equations of state for neutron stars can be approximated as a polytrope with an effective index n ≈ 0.5 − 1.0. The equilibrium stellar model is obtained by numerical integration of the Tolman-Oppenheimer-Volkhov equations. We calculate the linear l = 2 static perturbations to the Schwarzschild spacetime following the method of Thorne and Campolattaro. Combining the perturbed Einstein equations into a single second order differential equation for the perturbation to the metric coefficient gtt, and matching the exterior solution to the asymptotic expansion of the metric in the star’s…