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Figure 1:
This figure shows a cross-section of a coordinate shape (the thick curve) which is not a Strahlkörper about the local coordinate origin shown (the large dot). The dashed line shows a ray from the local coordinate origin, which intersects the surface in more than one point. |
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Figure 2:
This figure shows part of a simulation of the spherically symmetric collapse of a model stellar core (a ![]() |
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Figure 3:
This figure shows a number of light cones and future-pointing outgoing null geodesics in a neighborhood of the event horizon in Schwarzschild spacetime, plotted in ingoing Eddington–Finkelstein coordinates ![]() ![]() ![]() ![]() ![]() ![]() |
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Figure 4:
This figure shows a view of the numerically-computed event horizon in a single slice, together with the locus of the event horizon’s generators that have not yet joined the event horizon in this slice, for a head-on binary black hole collision. Notice how the event horizon is non-differentiable at the cusp where the new generators join it. Figure reprinted with permission from [103]. © 1996 by the American Physical Society. |
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Figure 5:
This figure shows a perspective view of the numerically-computed event horizon, together with some of its generators, for the head-on binary black hole collision discussed in detail by Matzner et al. [108]. Figure courtesy of Edward Seidel. |
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Figure 6:
This figure shows the cross-section of the numerically-computed event horizon in each of five different slices, for the head-on collision of two extremal Kastor–Traschen black holes. Figure reprinted with permission from [46]. © 2003 by the American Physical Society. |
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Figure 7:
This figure shows two views of the numerically-computed event horizon’s cross-section in the orbital plane for a spiraling binary black hole collision. The two orbital-plane dimensions are shown horizontally; time runs upwards. The initial data was constructed to have an approximate helical Killing vector, corresponding to black holes in approximately circular orbits (the ![]() ![]() |
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Figure 8:
This figure shows the polar and equatorial radii of the event horizon (solid lines) and apparent horizon (dashed lines) in a numerical simulation of the collapse of a rapidly rotating neutron star to form a Kerr black hole. The dotted line shows the equatorial radius of the stellar surface. These results are from the D4 simulation of Baiotti et al. [21]. Notice how the event horizon grows from zero size while the apparent horizon first appears at a finite size and grows in a spacelike manner. Notice also that both surfaces are flattened due to the rotation. Figure reprinted with permission from [21]. © 2005 by the American Physical Society. |
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Figure 9:
This figure shows the apparent horizons (actually MOTSs) for a spherically symmetric numerical evolution of a black hole accreting a narrow shell of scalar field, the 800.pqw1 evolution of Thornburg [155]. Part (a) of this figure shows ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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Figure 10:
This figure shows the numerically-computed apparent horizons (actually MOTSs) at two times in a head-on binary black hole collision. The black holes are colliding along the ![]() |
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Figure 11:
This figure shows the irreducible masses ( ![]() ![]() ![]() |
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Figure 12:
This figure shows the expansion ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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Figure 13:
This figure shows the expansion ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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Figure 14:
This figure shows the pretracking surfaces at various times in a spiraling binary black hole collision, projected into the black holes’ orbital plane. (The apparent slow drift of the black holes in a clockwise direction is an artifact of the corotating coordinate system; the black holes are actually orbiting much faster, in a counterclockwise direction.) Notice how, even well before the common apparent horizon first appears ( ![]() ![]() |
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