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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 radiative 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
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 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. |
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