Black-hole threshold solutions in stiff fluid collapse

Abstract

Numerical studies of the gravitational collapse of a stiff (P = ρ) fluid have found the now-familiar critical phenomena, namely scaling of the black-hole mass with a critical exponent and continuous self-similarity at the threshold of black-hole formation. Using the equivalence of an irrotational stiff fluid to a massless scalar field, we construct the critical solution as a scalar field solution by making a self-similarity ansatz. We find evidence that this solution has exactly one growing perturbation mode; both the mode and the critical exponent, γ ≃ 0.94, derived from its eigenvalue agree with those measured in perfect fluid collapse simulations. We explain why this solution is seen as a critical solution in stiff fluid collapse but not in scalar field collapse, and conversely why the scalar field critical solution is not seen in stiff fluid collapse, even though the two systems are locally equivalent.