Toward the CompactHedron: Bounds on Neutron Stars from Microscopic Principles
Abstract
We investigate the implications of causality and positivity for the tidal Love numbers of gravitating objects. We 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 and its derivatives. For simplicity, we focus on the quadrupolar gravito-electric sector, which provides the leading contribution to tidal deformability. We 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. These bounds delineate an allowed region in the parameter space of the effective theory and apply to any localized object. In particular, we study their application to neutron stars. We compute the dynamical Love numbers through fourth order in the frequency expansion for a representative set of polytropic and tabulated neutron-star equations of state and show that, in the low-compactness regime, the bounds translate into constraints on the first oscillation mode of the star. Importantly, these constraints are conceptually independent of the stability and thermodynamic conditions commonly imposed in the literature. While our focus is primarily on conservative systems, we also discuss how the bounds are modified in the presence of dissipation. Our results lay the ground for a systematic framework to derive bounds on compact objects from fundamental principles.
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BibTeX
@misc{apostolidis2026toward,
title = {{Toward the CompactHedron: Bounds on Neutron Stars from Microscopic Principles}},
author = {Thomas Apostolidis and Alessandro Longo and Borna Salehian and Luca Santoni},
howpublished = {HAL},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.36025},
eprint = {2609.36025},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05781879v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Toward the CompactHedron: Bounds on Neutron Stars from Microscopic Principles
AU - Thomas Apostolidis
AU - Alessandro Longo
AU - Borna Salehian
AU - Luca Santoni
PY - 2026
DA - 2026/09/28
PB - HAL
DO - 10.48550/arxiv.2609.36025
UR - https://hal.science/hal-05781879v1
AB - We investigate the implications of causality and positivity for the tidal Love numbers of gravitating objects. We 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 and its derivatives. For simplicity, we focus on the quadrupolar gravito-electric sector, which provides the leading contribution to tidal deformability. We 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. These bounds delineate an allowed region in the parameter space of the effective theory and apply to any localized object. In particular, we study their application to neutron stars. We compute the dynamical Love numbers through fourth order in the frequency expansion for a representative set of polytropic and tabulated neutron-star equations of state and show that, in the low-compactness regime, the bounds translate into constraints on the first oscillation mode of the star. Importantly, these constraints are conceptually independent of the stability and thermodynamic conditions commonly imposed in the literature. While our focus is primarily on conservative systems, we also discuss how the bounds are modified in the presence of dissipation. Our results lay the ground for a systematic framework to derive bounds on compact objects from fundamental principles.
ER -