Angular Momenta in $4+1$ Vacuum Critical Collapse

Abstract

We investigate the critical collapse of gravitational waves that carry angular momenta. Working in five-dimensional vacuum Einstein gravity under an SU$(2)\times {\mathbb{Z}}_4$ symmetry ansatz, we numerically evolve several families of initial data near the threshold of black-hole formation. Near-critical data approaches the discretely self-similar Bizoń-Chmaj-Schmidt solution, which is irrotational. We find that the near-threshold mass scaling has a universal critical exponent, but the angular-momentum scaling has one of two critical exponents, depending on the family of initial data. The angular-momentum critical exponents are therefore not universal under this symmetry ansatz. Our results agree with predictions from perturbation theory about the critical solution.

arXiv comment12 pages, 2 figures