Relativistic orbital perturbation theory in Schwarzschild space-time background

The osculating elements technique provides a powerful framework for describing the motion of celestial bodies in curved spacetime. With the upcoming LISA mission offering unprecedented opportunities to observe gravitational waves from extreme mass-ratio inspirals (EMRIs), the development of accurate and analytically tractable orbital models is essential. This dissertation presents a general-relativistic perturbation scheme for osculating elements that describes orbital motion under the influence of perturbing forces in a Schwarzschild spacetime background.
The evolution equations are formulated using Weierstrass elliptic functions, yielding a robust mathematical framework that preserves analytical continuity across different orbital regimes and overcomes limitations inherent in traditional trigonometric parametrizations. Explicit examples of physically motivated perturbing forces are provided, and linearised analytical solutions of the corresponding osculating elements evolution equations are derived.