Gravitational self-force in nonvacuum spacetimes

Understand

The gravitational self-force has thus far been formulated in background spacetimes for which the metric is a solution to the Einstein field equations in vacuum.

• While this formulation is sufficient to describe the motion of a small object around a black hole, other applications require a more general formulation that allows for a nonvacuum background spacetime.
• We provide a foundation for such extensions, and carry out a concrete formulation of the gravitational self-force in two specific cases.
• In the first we consider a particle of mass $m$ and scalar charge $q$ moving in a background spacetime that contains a background scalar field.