Introduction to Self-Force Theory

The point particle approximation is useful when studying the motion of a point particle in a background field, but not sufficient when accuracy matters. An electron moving in an electromagnetic field has a field of its own, which affects the background field, producing a back reaction. The same is true for a massive and compact object moving in a background gravitational field, like a small black hole orbiting a larger black hole (so-called extreme mass ratio inspirals). In this course, we introduce self-force theory for the electromagnetic field and extend it further in the case of gravitational self-force. Mathematically relevant topics like regularization or effective field methods are also discussed.

16th September, 2026 ~ 6th January, 2027

Weekday	Time	Venue	Online	ID	Password
Wednesday	13:30 - 16:05	Shuimo	ZOOM 01	928 682 9093	BIMSA

Basic differential geometry, Tensor calculus, Special relativity, Einstein field equations, Schwarzschild/Kerr basics, Classical field theory, Electromagnetism

Part I — Foundations of Self-Force Theory
- Introduction: What is Self-Force?
- Radiation Reaction in Electromagnetism
- Green Functions and Field Propagation

Part II — Mathematical Framework of Self-Force
- Singular Fields and Regularization
- Self-Force in Curved Spacetime
- Mode-Sum Regularization
- Effective Source Methods

Part III — Gravitational Self-Force
- Why Gravity is Different
- Linearized Gravity and Perturbation Theory
- Gravitational Self-Force Equation
- Schwarzschild and Kerr Self-Force
- Extreme Mass-Ratio Inspirals (EMRIs)
- EMRI Waveform Modeling

Gralla et al., "A Rigorous Derivation of Electromagnetic Self-force" (2009)
Wald, "Introduction to Gravitational Self-Force" (2009)
Barack & Pound, "Self-force and radiation reaction in general relativity" (2018)
Trestini et al., "Constants of motion in gravitational self-force theory" (2026)

Advanced Undergraduate , Graduate , Postdoc , Researcher

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Alejandro Torres-Orjuela obtained his Physics Bachelor's degree from the Free University of Berlin and his Physics Master's degree, as well as his Bachelor's and Master's degrees in Mathematics from the Technical University of Berlin. Later, he moved to China to do his Ph.D. at Peking University, where he worked with Prof. Xian Chen and Prof. Pau Amaro Seoane from 2017 to 2021. After his Ph.D., Alejandro moved to the TianQin Center at Sun Yat-Sen University, where he worked for two years as a PostDoc in the Theoretical Study group led by Prof. Jianwei Mei. In 2023, Alejandro took a position as a Post-Doctoral Fellow at the University of Hong Kong, as a member of Prof. Jane Dai's group. Since November 2024, Alejandro has been an Assistant Professor in BIMSA. In his work, Alejandro studies different aspects of gravitational wave astronomy with a particular focus on the effect of the environment on gravitational wave detection. His research further includes gravitational wave sources with electromagnetic counterparts, extreme mass ratio systems, and multiband detection across the spectrum, with a particular focus on space-based detectors TianQin and LISA.