Initial data for a black string and a Kaluza-Klein bubble: Space-dependent compactification radius

TL;DR

This paper develops initial data for simulating black strings and KK bubbles with space-dependent compactification radii, facilitating future numerical studies of their nonlinear dynamics in Kaluza-Klein spacetime.

Contribution

It introduces analytic and numerical methods to generate initial data for black strings and KK bubbles with varying compactification radii, including configurations with multiple objects at different positions.

Findings

Analytic initial data with SO(3) symmetry for black strings and KK bubbles.

Generalization of Brill-Lindquist initial data to multiple black strings.

Numerical method for initial data with separated black string and KK bubble.

Abstract

As the first step to explore the nonlinear dynamics of an extra dimension in the Kaluza-Klein (KK) spacetime with black objects through numerical relativity, we generate time-symmetric initial data of a black string and/or a KK bubble with space-dependent compactification radius. The initial data developed in this paper are classified into three types. First, we present analytic initial data with SO(3) symmetry whose three-dimensional section is spherically symmetric. These initial data include a black string without a KK bubble, a black string trapping a KK bubble, and a naked KK bubble. Second, we present analytic initial data for multiple black strings with varying compactification radius, which is a natural generalization of the Brill-Lindquist initial data for four-dimensional general relativity. Finally, we develop a numerical method for generating the initial data with a black string and a KK bubble located at different positions, which would be useful in simulating what happens when an expanding KK bubble meets black objects in dynamical context.