  Accurately modeling the tidal response of neutron stars is crucial to
connecting gravitational wave observations of binaries to ultra-dense nuclear
physics. Most current models of the tidal response of relativistic stars either
assume a static response model, or use phenomenological models inspired by
Newtonian gravity. In this work, we present a general formalism for computing
the linear dynamical tidal response function of relativistic, spherically
symmetric stars. Our formalism incorporates stratification due to thermal and
chemical imbalances, allowing one to study the effects of g modes on the tidal
response function. We also describe how to incorporate sources of dissipation
due to shear and bulk viscosity. To showcase the utility of our approach, we
present several applications for polytropic stars in general relativity. We
show how our formalism can capture the dynamical tidal resonance due to the f
and g modes of inviscid stars and explore the sensitivity of the dynamical
tidal response to the compactness of the star. We also compute the dissipative
tidal deformability due to bulk and shear viscous dissipation assuming a simple
viscous profile for the bulk and shear viscosity.
