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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 . |
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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 . |
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Figure 3:
In curved spacetime, the singular potential at depends on the particle’s history during
the interval ; for the regular potential the relevant interval is . |
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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. |
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Figure 5:
The base point , the field point , and the geodesic segment that links them.
The geodesic is described by parametric relations and is its tangent vector. |
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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. |
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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. |
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Figure 8:
The retarded, simultaneous, and advanced points on a world line . The retarded point
is linked to by a future-directed null geodesic. The simultaneous point
is linked to by a spacelike geodesic that intersects orthogonally. The advanced point
is linked to by a past-directed null geodesic. |
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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 . |
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Figure 10:
A small body, represented by the black disk, is immersed in a background spacetime. The
internal zone is defined by , while the external zone is defined by . Since ,
there exists a buffer region defined by . In the buffer region and are both
small. |
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Figure 11:
The spacetime region is bounded by the union of the spacelike surface , the
timelike tube , and the null surface . |