Self-force via Green functions and worldline integration

Understand

A compact object moving in curved spacetime interacts with its own gravitational field.

• This leads to both dissipative and conservative corrections to the motion, which can be interpreted as a self-force acting on the object.
• The original formalism describing this self-force relied heavily on the Green function of the linear differential operator that governs gravitational perturbations.
• However, because the global calculation of Green functions in non-trivial black hole spacetimes has been an open problem until recently, alternative methods were established to calculate self-force effects using sophisticated regularization techniques that avoid the computation of the global Green function.