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Figure 1:
The embedding of Minkowski space into the Einstein cylinder ![]() |
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Figure 2:
The conformal diagram of Minkowski space. |
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Figure 3:
Spacelike hypersurfaces in the conformal picture. |
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Figure 4:
Waveforms in physical space-time. |
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Figure 5:
Waveforms in conformal space-time. |
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Figure 6:
The physical scenario: The figure describes the geometry of an isolated system. Initial data are prescribed on the blue parts, i.e. on a hyperboloidal hypersurface and the part of ![]() ![]() ![]() |
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Figure 7:
The geometry of the asymptotic characteristic initial value problem: Characteristic data are given on the blue parts, i.e. an ingoing null surface and the part of ![]() |
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Figure 8:
The geometry near space-like infinity: The “point” ![]() ![]() ![]() ![]() ![]() ![]() |
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Figure 9:
The geometry of the standard Cauchy approach. The green lines are surfaces of constant time. The blue line indicates the outer boundary. |
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Figure 10:
The geometry of Cauchy-Characteristic matching. The blue line indicates the interface between the (inner) Cauchy part and the (outer) characteristic part. |
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Figure 11:
The geometry of the conformal approach. The green lines indicate the foliation of the conformal manifold by hyperboloidal hypersurfaces. |
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Figure 12:
An axi-symmetric solution of the Yamabe equation with ![]() ![]() ![]() |
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Figure 13:
The difference between two solutions of the Yamabe equation obtained with different boundary conditions outside. Only the values less than ![]() |
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Figure 14:
Upper corner of a space-time with singularity (thick line). The dashed line is ![]() |
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Figure 15:
Decay of the radiation at null-infinity. |
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Figure 16:
The radiation field ![]() |
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Figure 17:
The numerically generated ‘Kruskal diagram’ for the Schwarzschild solution. |
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Figure 18:
The rescaled Weyl tensor in a flat space-time obtained from flat initial data and random boundary data in the unphysical region. |
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