Regularization of static self-forces

Understand

Various regularization methods have been used to compute the self-force acting on a static particle in a static, curved spacetime.

• Many of these are based on Hadamard's two-point function in three dimensions.
• On the other hand, the regularization method that enjoys the best justification is that of Detweiler and Whiting, which is based on a four-dimensional Green's function.
• We establish the connection between these methods and find that they are all equivalent, in the sense that they all lead to the same static self-force.