List of Figures

View Image Figure 1:
In flat spacetime, the retarded potential at x depends on the particle’s state of motion at the retarded point z(u) on the world line; the advanced potential depends on the state of motion at the advanced point z(v).
View Image Figure 2:
In curved spacetime, the retarded potential at x depends on the particle’s history before the retarded time u; the advanced potential depends on the particle’s history after the advanced time v.
View Image Figure 3:
In curved spacetime, the singular potential at x depends on the particle’s history during the interval u < t < v; for the radiative potential the relevant interval is - oo < t < v.
View Image Figure 4:
Retarded coordinates of a point x relative to a world line g. The retarded time u selects a particular null cone, the unit vector a a _O_ =_ x^ /r selects a particular generator of this null cone, and the retarded distance r selects a particular point on this generator.
View Image Figure 5:
The base point ' x, the field point x, and the geodesic b that links them. The geodesic is described by parametric relations zm(c), and tm = dzm/dc is its tangent vector.
View Image Figure 6:
Fermi normal coordinates of a point x relative to a world line g. The time coordinate t selects a particular point on the word line, and the disk represents the set of spacelike geodesics that intersect g orthogonally at z(t). The unit vector wa =_ ^xa/s selects a particular geodesic among this set, and the spatial distance s selects a particular point on this geodesic.
View Image Figure 7:
Retarded coordinates of a point x relative to a world line g. The retarded time u selects a particular null cone, the unit vector a a _O_ =_ x^ /r selects a particular generator of this null cone, and the retarded distance r selects a particular point on this generator. This figure is identical to Figure 4.
View Image Figure 8:
The retarded, simultaneous, and advanced points on a world line g. The retarded point ' x =_ z(u) is linked to x by a future-directed null geodesic. The simultaneous point x =_ z(t) is linked to x by a spacelike geodesic that intersects g orthogonally. The advanced point x'' =_ z(v) is linked to x by a past-directed null geodesic.
View Image Figure 9:
The region within the dashed boundary represents the normal convex neighbourhood of the point x. The world line g enters the neighbourhood at proper time t< and exits at proper time t>. Also shown are the retarded point z(u) and the advanced point z(v).
View Image Figure 10:
A black hole, represented by the black disk, is immersed in a background spacetime. The internal zone extends from r = 0 to r = ri« R, while the external zone extends from r = re » m to r = oo. When m « R there exists a buffer zone that extends from r = re to r = ri. In the buffer zone m/r and r/R are both small.