Toward the CompactHedron: Bounds on Neutron Stars from Microscopic Principles
Abstract: Much is still unknown about neutron stars, including their equation of state, which describes the matter in their interior. Next-generation gravitational-wave detectors can help shed light on this question by measuring the so-called Love numbers, which encode the tidal response of a compact object to an external perturbation. In this talk, I will investigate the implications of causality and positivity for the tidal Love numbers of gravitating objects. I will work within the framework of point-particle effective field theory, where the Love numbers correspond to the Wilson coefficients of operators constructed from the curvature tensor. I will show that requiring the tidal response to be retarded and to decay at high frequencies, together with the assumption of passivity, leads to nontrivial bounds on the Love numbers. I will then outline the computation of dynamical Love numbers through fourth order in the frequency expansion, using dimensional regularization, for a representative set of neutron-star equations of state, and show that, in the low-compactness regime, the bounds translate into constraints on the fundamental oscillation mode of the star. While the focus is primarily on conservative systems, I will also discuss how the bounds are modified in the presence of dissipation. These results lay the groundwork for a systematic framework to derive bounds on compact objects from fundamental principles.