Figure 1:
In flat spacetime, the retarded potential at depends on the particle’s state of motion at the retarded point on the world line; the advanced potential depends on the state of motion at the advanced point . 

Figure 2:
In curved spacetime, the retarded potential at depends on the particle’s history before the retarded time ; the advanced potential depends on the particle’s history after the advanced time . 

Figure 3:
In curved spacetime, the singular potential at depends on the particle’s history during the interval ; for the radiative potential the relevant interval is . 

Figure 4:
Retarded coordinates of a point relative to a world line . The retarded time selects a particular null cone, the unit vector selects a particular generator of this null cone, and the retarded distance selects a particular point on this generator. 

Figure 5:
The base point , the field point , and the geodesic that links them. The geodesic is described by parametric relations , and is its tangent vector. 

Figure 6:
Fermi normal coordinates of a point relative to a world line . The time coordinate selects a particular point on the word line, and the disk represents the set of spacelike geodesics that intersect orthogonally at . The unit vector selects a particular geodesic among this set, and the spatial distance selects a particular point on this geodesic. 

Figure 7:
Retarded coordinates of a point relative to a world line . The retarded time selects a particular null cone, the unit vector selects a particular generator of this null cone, and the retarded distance selects a particular point on this generator. This figure is identical to Figure 4. 

Figure 8:
The retarded, simultaneous, and advanced points on a world line . The retarded point is linked to by a futuredirected null geodesic. The simultaneous point is linked to by a spacelike geodesic that intersects orthogonally. The advanced point is linked to by a pastdirected null geodesic. 

Figure 9:
The region within the dashed boundary represents the normal convex neighbourhood of the point . The world line enters the neighbourhood at proper time and exits at proper time . Also shown are the retarded point and the advanced point . 

Figure 10:
A black hole, represented by the black disk, is immersed in a background spacetime. The internal zone extends from to , while the external zone extends from to . When there exists a buffer zone that extends from to . In the buffer zone and are both small. 
http://www.livingreviews.org/lrr20046 
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