Dynamical Tidal response of compact stars -- An EFT approach

TL;DR

This paper develops a systematic EFT framework to compute dynamical tidal Love numbers for non-rotating compact stars, including neutron stars with dark matter, by matching scattering amplitudes with black hole perturbation theory results.

Contribution

It introduces a new EFT-based method to calculate static and dynamical tidal Love numbers to any order, extending previous approaches and including effects of surface reflectivity and dark matter.

Findings

Computed Next-to-Next-to-Leading Order tidal Love number for neutron stars.

Derived the RG equation for the tidal Love number.

Matched EFT results with black hole perturbation theory.

Abstract

We apply the point particle EFT approach to a compact star to systematically compute dynamical tidal love numbers for various non-rotating compact objects, extending the treatment of {arXiv:2307.10391[hep-th], arXiv:2407.08327 [gr-qc]}. We calculate the scattering amplitude in Black Hole Perturbation Theory(BPHT) for \textit{arbitrary} non-rotating compact stars using the Mano-Suzuki-Takasugi(MST) method with non zero surface reflectivity and match it with that obtained from point particle EFT order by order in the low frequency expansion. This sets up a systematic framework for extracting the static and dynamical tidal love numbers(TLNs) to any order in the multipole expansion. In this paper, we employ the technique to compute the Next-to-Next-to Leading Order TLN upto a universal constant and its Renormalization Group equation for non-viscous Neutron stars and Neutron stars admixed with Bosonic or Fermionic dark matter.