Center of Gravity Seminar: Chia-Hsien Shen

Title: Effective Black Hole Perturbation Theory: framework and applications

Abstract: Black holes are the most perfect macroscopic objects in our universe. Their equilibrium solutions are remarkably simple, and we have developed powerful techniques to study their perturbations through the black hole perturbation theory (BHPT). However, a systematic extension of these techniques to more general systems—such as neutron stars, exotic compact objects, or binary systems—remains challenging. In this talk, I will describe a new framework, dubbed Effective Black Hole Perturbation Theory, that systematically extends BHPT by combining it with the worldline effective field theory. As an example, I will apply this framework to waveform emission, an observable that has no direct analog in BHPT. The effective BHPT allow us to formulate and compute the Sommerfeld factor, which is the gravitational correction to waveform emission. We explicitly computed the Sommerfeld factor for scalar waveform to tenth order in the perturbative theory. Beyond perturbation theory, I will show an exact connection between the waveform and Compton scattering, as well as a nonperturbative structure in the classical renormalization group of the multipoles. The talk will be concluded by discussing prospects and challenges of this framework for higher-precision calculations for gravitational waves. Based on arXiv:2604.14112 with Chih-Hao Chang and Zihan Zhou.