PROBING THE NATURE OF COMPACT OBJECTS: SCATTERING, TIDES AND QUASINORMAL MODES

Abstract

The LIGO-VIRGO-KAGRA (LVK) collaboration has detected 90 confirmed gravitational-wave (GW) events and nearly 200 confident triggers across four observational runs. Coalescing black-hole (BH) and neutron-star (NS) binaries are primary GW sources, offering the unique possibility to probe the nature of compact objects and gravitational dynamics. This dissertation investigates how the intrinsic properties of compact objects affect their dynamics and GW emission, using worldline effective field theories (WEFTs) and BH perturbation theory (BHPT), with emphasis on selected scattering processes in General Relativity (GR).

Scattering of two BHs in the post-Minkowskian (PM) regime has proven valuable for extracting binary dynamics from gauge-invariant scattering observables. As a simpler analog, we study electromagnetic (EM) scattering of two charged particles in the post-Lorentzian (PL) expansion. We compute scattering observables to 3PL order and map them

to their bound-orbit counterparts, deriving new boundary-to-bound (B2B) relations. We verified these mappings for gravity at first post-Newtonian (PN) order.

Another key setup involves GWs scattering off compact objects i.e., gravitational Compton/Raman scattering. We compute the classical Compton amplitude at linear order in the mass of the scattering body, and to third order in spin, for generic parity-invariant compact objects, using a WEFT with spin-induced multipole couplings, finding agreement with expectations from amplitude-based methods in the Kerr BH case, while presenting new results for generic objects.

We extract the low-frequency tidal response of Kerr BHs by matching the tidal contribution to the Raman amplitude computed in BHPT to its WEFT counterpart, thereby constraining key tidal coefficients such as Love numbers and dissipation numbers. We then use the dissipation numbers to compute horizon-flux-induced mass and angular-momentum loss in Kerr-BH binaries, resolving longstanding discrepancies with the test-body limit and obtaining waveform corrections up to 4PN order. Additionally, we recover the vanishing of BH Love numbers and identify a nonlinear mixing of tidal and non-tidal effects, resulting in a scale-dependent tidal response via classical renormalization group flow.

We also extend this approach to NSs, and extract electric, quadrupolar, Love and dissipation numbers from the Raman amplitude as a function of the boundary conditions for the metric perturbations at the stellar surface, that are determined by numerically solving the metric- and matter-perturbation equations inside the NS. This allows us to roughly quantify the impact of tidal heating on the GW phase during the inspiral across different equations of state.

Finally, we study the interplay between quasinormal modes (QNMs) and reflectivity for generic compact objects modeled in the membrane paradigm --- a phenomenological framework that encodes interior structure via a fictitious surface fluid. We extend the phenomenological framework to linear order in spin, we analyze how membrane parameters influence the QNM spectrum and reflectivity.