NONLINEAR DYNAMICS AND STABILITY OF COMPACT OBJECTS

This thesis explores the complex dynamics, stability, and observational signatures of compact objects within General Relativity, leveraging analytical, perturbative, and numerical relativity techniques. Motivated by theoretical challenges to the classical black hole paradigm, the dark matter puzzle, and the advent of gravitational-wave astronomy, we investigate fundamental questions at the intersection of strong gravity, field theory, and astrophysics. We first examine the stability and potential for energy extraction in horizonless geometries.

By analyzing truncated Kerr spacetimes, we precisely determine the threshold for the ergoregion instability, finding it coincides with the equatorial ergosurface for large multipoles, while finding no evidence for linear instabilities driven solely by light rings on relevant timescales. Furthermore, we uncover potent energy extraction mechanisms beyond standard superradiance, demonstrating significant energy amplification via blueshift instabilities in dynamic bouncing geometries and a “blueshift-like” energy exchange between scattering states in time-periodic solitons like Q-balls.

Second, we use fully nonlinear simulations to study how black holes interact with boson stars, which are localized, self-gravitating configurations of a bosonic dark-matter field and are therefore natural targets in searches for dark compact objects. Simulating a black hole piercing both mini-boson stars and solitonic boson stars reveals the dominant role of tidal capture, often leading to the near-total accretion of the boson star, even for disparate scales.

A consistent outcome is the formation of quasi-bound scalar field remnants—“gravitational atoms”—around the final black hole, linking interaction dynamics to fundamental scalar field properties in strong gravity and potentially constraining bosonic dark matter models. Third, we study novel observational probes using gravitational waves and related phenomena. We characterize the late-time decay of gravitational perturbations, identifying source-dominated tails generated by matter or nonlinearities that can dominate over the standard inverse-power-law decay, impacting our understanding of late-time signals.

We also demonstrate that dynamical gravitational lensing during black hole ringdown encodes quasinormal mode oscillations in the light deflection angle, presenting a new multi-messenger avenue to probe strong-field dynamics. These interconnected studies refine our understanding of compact object stability, reveal complex dynamics in black hole-boson star interactions, and identify new gravitational-wave and multimessenger signatures, offering pathways to test General Relativity, probe dark matter candidates, and guide future observational strategies in the era of precision gravitational-wave astronomy