Formation of multiple Black Holes from Cauchy data

Abstract

We construct a family of asymptotically flat Cauchy initial data for the Einstein vacuum equations that contain no trapped surfaces, yet whose future development admits multiple causally independent trapped surfaces. Assuming the weak cosmic censorship conjecture, this implies the formation of multiple black holes in finite time. The initial data are obtained by surgically modifying a vacuum geometrostatic manifold equipped with the Brill-Lindquist metric: the data agree exactly with the Brill-Lindquist metric outside a collection of balls centered at its multiple poles, and each ball is replaced by a constant-time slice of a well-prepared dynamical spacetime. The construction is based on Christodoulou's short-pulse framework, a stability analysis in the finite future of the short-pulse region, the geometry of geometrostatic manifolds with small mass and large separation, and the obstruction-free annular gluing method developed by Mao-Oh-Tao. The absence of trapped surfaces in the initial data is verified via a standard mean curvature comparison argument.