Abstract
This dissertation studies the response of compact objects in general relativity and beyond through three connected themes: stellar pulsations with generalized matter models, tidal Love numbers in gravitational and vector-tensor theories, and effective field theory descriptions of classical gravitational dynamics. The broader motivation is to improve the theoretical interpretation of neutron-star observables relevant to gravitational-wave astronomy, multimessenger astrophysics, and strong-field tests of gravity.
First, we develop relativistic pulsation formalisms for neutron stars with generalized matter sectors. We present a formulation of the nonradial stellar pulsation problem for anisotropic stars and then construct a more systematic covariant framework using relativistic viscoelasticity. These results extend the standard perfect-fluid treatment and provide a foundation for studying how anisotropy, elasticity, viscosity, and relaxation effects modify the quasinormal spectrum and damping of compact stars.
Second, we investigate tidal response in theories with additional vector structure. In Hořava--Lifshitz gravity, where the theory is renormalizable and ultraviolet complete, we study universal relations involving Love numbers for neutron stars and identify a new shift Love number associated with the coupling between the metric and the preferred vector sector. In Einstein--Maxwell theory, we formulate gauge-invariant definitions of vector-tensor Love numbers for charged neutron stars and magnetars. Using perturbation theory together with worldline effective field theory, we show in analytic low-compactness expansions that effective field theory matching is essential for separating genuine response coefficients from gauge- or coordinate-dependent contributions.
Finally, we study the eikonal limit of quantum field theory and its relation to worldline effective field theory. We show how classical contributions to two-body scattering emerge from selected Feynman diagrams in the ℏ→0 limit and demonstrate the correspondence between the eikonal expansion of second-quantized field theory and diagrammatics in the worldline formalism.
Together, these results clarify how response coefficients, mode structure, and classical observables are modified by generalized models and how they can be systematically extracted within effective field theory approaches to compact objects.
