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arXiv · 2501.11642

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

Hirotaka Yoshino
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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.

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Hirotaka Yoshino. 2025-01-20. Initial data for a black string and a Kaluza-Klein bubble: Space-dependent compactification radius. https://doi.org/10.1103/physrevd.111.084048

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