Department of Physics and Astronomy, Bowdoin College, Brunswick, Maine 04011, USA.
Mathematical Sciences, University of Southampton, Southampton SO17 1BJ, United Kingdom.
Phys Rev Lett. 2019 Oct 25;123(17):171103. doi: 10.1103/PhysRevLett.123.171103.
We numerically investigate the threshold of black-hole formation in the gravitational collapse of electromagnetic waves in axisymmetry. We find approximate power-law scaling ρ_{max}∼(η_{*}-η)^{-2γ} of the maximum density in the time evolution of near-subcritical data with γ≃0.145, where η is the amplitude of the initial data. We directly observe approximate discrete self-similarity in near-critical time evolutions with a log-scale echoing period of Δ≃0.55. The critical solution is approximately the same for two families of initial data, providing some evidence of universality. Neither the discrete self-similarity nor the universality, however, are exact. We speculate that the absence of an exactly discrete self-similarity might be caused by the interplay of electromagnetic and gravitational wave degrees of freedom, or by the presence of higher-order angular multipoles, or both, and discuss implications of our findings for the critical collapse of vacuum gravitational waves.
我们在轴对称引力波塌缩中数值研究了黑洞形成的阈值。我们发现，在接近次临界数据的时间演化中，最大密度ρ_{max}∼(η_{*}-η)^{-2γ}近似呈幂律分布，其中γ≃0.145，η是初始数据的幅度。我们直接观察到在接近临界的时间演化中近似离散自相似性，对数标度回波周期Δ≃0.55。对于两个初始数据集家族，临界解大致相同，这为普遍性提供了一些证据。然而，离散自相似性和普遍性都不是精确的。我们推测，离散自相似性的缺失可能是由电磁和引力波自由度的相互作用引起的，也可能是由更高阶角多极矩的存在引起的，或者两者兼而有之，并讨论了我们的发现对真空引力波临界塌缩的影响。
