Numerical solutions reveal that the threshold of black hole formation in charged Vlasov matter shifts from stationary horizonless shells to extremal black holes past a critical charge-to-mass ratio of unity.
Scaling of curvature in sub-critical gravitational collapse
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abstract
We perform numerical simulations of the gravitational collapse of a spherically symmetric scalar field. For those data that just barely do not form black holes we find the maximum curvature at the position of the central observer. We find a scaling relation between this maximum curvature and distance from the critical solution. The scaling relation is analogous to that found by Choptuik for black hole mass for those data that do collapse to form black holes. We also find a periodic wiggle in the scaling exponent.
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Gravitational collapse in the vicinity of the extremal black hole critical point
Numerical solutions reveal that the threshold of black hole formation in charged Vlasov matter shifts from stationary horizonless shells to extremal black holes past a critical charge-to-mass ratio of unity.
- Critical collapse of vacuum spacetimes: Nakamura wave initial data