Analytic approximations, perturbation theory, effective field theory methods and their applications

TL;DR

The paper surveys GR20 & Amaldi10 sessions on analytic approximations, perturbation theory, EFT methods, and approximate solutions to Einstein equations, highlighting how $3.5$PN and ongoing $4$PN analyses, NRGR EFT, and EOB frameworks are advancing gravitational-wave modeling for compact binaries. It discusses conservative and dissipative dynamics, including spin effects and finite-size corrections via tidal Love numbers, radiative multipoles and tail effects with RG structure, and self-force results for EMRIs that inform waveform templates. It notes the synergy between analytic methods and numerical relativity in producing accurate GW templates across regimes, including ultra-relativistic limits via large-$N$ EFT. It also surveys tests of gravity in modified theories (scalar-tensor, Gauss–Bonnet, Chern–Simons) and foundational issues (cosmic censorship, horizon stability, and high-energy gravity connections).

Abstract

We summarize the parallel session B4: 'Analytic approximations, perturbation theory effective field theory methods and their applications' and the joint session B2/B4: 'Approximate solutions to Einstein equations: Methods and Applications', of the GR20 & Amaldi10 conference in Warsaw, July 2013. The contributed talks reported significant advances on various areas of research in gravity.