#Curved space graph free

The mathematical tools required to derive the equations of motion of a point scalar charge, a point electric charge, and a point mass in a specified background spacetime are developed here from scratch.

#Curved space graph free

Because this field satisfies a homogeneous wave equation, it can be thought of as a free field that interacts with the particle it is this interaction that gives rise to the self-force. What remains after subtraction is a regular field that is fully responsible for the self-force. But it is possible to isolate the field’s singular part and show that it exerts no force on the particle - its only effect is to contribute to the particle’s inertia. The field’s action on the particle is difficult to calculate because of its singular nature: the field diverges at the position of the particle. The work done by the self-force matches the energy radiated away by the particle. The self-force contains both conservative and dissipative terms, and the latter are responsible for the radiation reaction. In the near zone the field acts on the particle and gives rise to a self-force that prevents the particle from moving on a geodesic of the background spacetime. In each of the three cases the particle produces a field that behaves as outgoing radiation in the wave zone, and therefore removes energy from the particle. This review is concerned with the motion of a point scalar charge, a point electric charge, and a point mass in a specified background spacetime.