Effective stress-energy tensors, self-force, and broken symmetry

TL;DR

This paper investigates how the inhomogeneous S-type component of the self-field affects the motion and multipole moments of extended scalar charges in curved spacetimes, expanding understanding of self-force and symmetry breaking effects.

Contribution

It introduces a detailed analysis of the S field's influence on stress-energy multipole moments and derives mathematical results related to generalized Killing fields in curved spacetimes.

Findings

S field causes effective shifts in multipole moments.

Homogeneous R field largely determines self-force and self-torque.

Explicit calculation of quadrupole moment shift for scalar charge.

Abstract

Deriving the motion of a compact mass or charge can be complicated by the presence of large self-fields. Simplifications are known to arise when these fields are split into two parts in the so-called Detweiler-Whiting decomposition. One component satisfies vacuum field equations, while the other does not. The force and torque exerted by the (often ignored) inhomogeneous "S-type" portion is analyzed here for extended scalar charges in curved spacetimes. If the geometry is sufficiently smooth, it is found to introduce effective shifts in all multipole moments of the body's stress-energy tensor. This greatly expands the validity of statements that the homogeneous R field determines the self-force and self-torque up to renormalization effects. The forces and torques exerted by the S field directly measure the degree to which a spacetime fails to admit Killing vectors inside the body. A number of mathematical results related to the use of generalized Killing fields are therefore derived, and may be of wider interest. As an example of their application, the effective shift in the quadrupole moment of a charge's stress-energy tensor is explicitly computed to lowest nontrivial order.