Cauchy data for multiple collapsing boson stars

TL;DR

The paper constructs asymptotically flat Cauchy initial data for the Einstein-Maxwell-Klein-Gordon system describing N well-separated charged boson stars, arranged so that their futures contain N causally independent trapped surfaces. The authors develop a six-part strategy combining a short-pulse mechanism, a stability-enabled transition region, a multi-centered charged Brill-Lindquist exterior, and a localized Klein-Gordon star region, culminating in an electrovacuum gluing that preserves charges. This extends previous vacuum N-body collapse results to a matter-coupled setting, providing a rigorous, fully geometric realization of dynamical multi-body boson-star collapse with controlled interaction. The construction yields initial data free of trapped surfaces that evolve to form multiple disjoint trapped surfaces in finite time, highlighting the rich and intricate dynamics of EMKG systems in general relativity and contributing to the broader understanding of N-body gravitational interactions in nonlinear field theories.

Abstract

We construct Cauchy initial data for the Einstein-Maxwell-Klein-Gordon (EMKG) system, which evolves in finite time into spacetimes containing multiple trapped surfaces. From a physical perspective, this corresponds to preparing multiple well-separated boson stars, each of which collapses to form a spacelike black hole region. In particular, this extends the result of the second and third named authors on the formation of multiple trapped surfaces in vacuum to the EMKG system.

Figures (5)

• Figure 1: Geometric illustration of $(\Sigma,g,k,E,B,\psi,\phi,A,\Phi)$ from Theorem \ref{['maintheoremintro']} for $N=3$. From the center outward: Euclidean disk; short-pulse annulus (red); barrier annulus (blue); star shell (green); near-star annulus; Brill-Lindquist exterior. We refer the union of the Euclidean disk, short-pulse annulus, barrier annulus and star shell to be the star region.
• Figure 2: Short-pulse cone. The red region is called the short-pulse region and the orange circle denotes the trapped surface $S_{-\frac{\delta a}{4},\delta}$.
• Figure 3: The red region marks the short-pulse domain, and the blue region indicates the transition zone. The hypersurface $\Sigma$ represents the target constant-time slice.
• Figure 4: The initial conditions in Theorem \ref{['thmtrapped']} lead to trapped surface ($S_{-\frac{\delta a}{4},\delta}$) formation in the future of the $H_{u_0}$ and $\underline{H}_0$.
• Figure 5: constant-time slice $(\Sigma_{\delta,a},g_{\delta,a},k_{\delta,a},E_{\delta,a},B_{\delta,a})$.

Theorems & Definitions (106)

• Theorem 1.1: Informal version
• Definition 2.1
• Proposition 2.2: EMKG constraint equations
• proof
• Corollary 2.3: EM constraint equations
• Remark 2.4
• Definition 2.5
• Definition 2.6
• Definition 2.7
• Proposition 2.8