Cauchy Data for Formation of Multiple Black Holes with Prescribed ADM Parameters

TL;DR

This paper presents a straightforward method to construct initial data for multiple black holes with specified physical parameters, leading to spacetimes that contain several dynamically forming black holes without trapped surfaces initially.

Contribution

It introduces a simple construction of smooth, asymptotically flat vacuum initial data modeling multiple black holes with prescribed ADM parameters and no initial trapped surfaces.

Findings

Initial data contain no trapped surfaces.

Future development contains multiple causally independent trapped regions.

Spacetimes with multiple black holes are expected from well-separated components.

Abstract

We give a simple construction of smooth, asymptotically flat vacuum initial data modeling a relativistic collapsing $N$--body system, with independently prescribed ADM energy, linear momentum, and angular momentum for each component, subject to the timelike condition $\E>|\P|$. The initial data contain no trapped surfaces, and the future development contains multiple causally independent trapped regions that dynamically form from localized subsets of the initial slice. In particular, the maximal development of data with well-separated collapsing components and relative motion is expected to yield spacetimes containing multiple black holes.