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Kerr Black Holes in an Expanding Bubble

Marco Astorino

TL;DR

This work constructs an exact stationary solution of vacuum general relativity describing a collinear array of Kerr black holes inside an expanding bubble of nothing, generated by the Belinski-Sakharov inverse scattering method and defined by $R_{\,\mu\nu}=0$. The bubble background enables equilibrium for single and rotating binary configurations by balancing gravitational attraction, with regularisation removing Misner strings and conical defects; the solution yields physical quantities such as $M$, $J$, $A$, $T$, and $\Omega$ that satisfy the Smarr relation $M = T S + 2 \Omega J$, while highlighting subtleties of the first law in this background. Special cases include Schwarzschild in the bubble, and the rotating binary demonstrates genuine equilibrium possibilities in a nontrivial background, suggesting extensions to charged or de Sitter-like settings and deeper connections to rotating spacetimes in curved backgrounds.

Abstract

An exact and analytical solution, in four-dimensional general relativity, describing a collinear array of an arbitrary number of Kerr black holes inside an expanding bubble of nothing is built, thanks to the inverse scattering technique. Physical properties and thermodynamics of the single Kerr in the bubble are studied. No cosmic strings or struts are present. The binary black hole system displays equilibrium configurations, because the expanding bubble surrounding the black holes balances the mutual gravitational attraction of the two constituents.

Kerr Black Holes in an Expanding Bubble

TL;DR

This work constructs an exact stationary solution of vacuum general relativity describing a collinear array of Kerr black holes inside an expanding bubble of nothing, generated by the Belinski-Sakharov inverse scattering method and defined by . The bubble background enables equilibrium for single and rotating binary configurations by balancing gravitational attraction, with regularisation removing Misner strings and conical defects; the solution yields physical quantities such as , , , , and that satisfy the Smarr relation , while highlighting subtleties of the first law in this background. Special cases include Schwarzschild in the bubble, and the rotating binary demonstrates genuine equilibrium possibilities in a nontrivial background, suggesting extensions to charged or de Sitter-like settings and deeper connections to rotating spacetimes in curved backgrounds.

Abstract

An exact and analytical solution, in four-dimensional general relativity, describing a collinear array of an arbitrary number of Kerr black holes inside an expanding bubble of nothing is built, thanks to the inverse scattering technique. Physical properties and thermodynamics of the single Kerr in the bubble are studied. No cosmic strings or struts are present. The binary black hole system displays equilibrium configurations, because the expanding bubble surrounding the black holes balances the mutual gravitational attraction of the two constituents.

Paper Structure

This paper contains 10 sections, 46 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Brief review of the expanding bubble of nothing
  3. N Kerr black holes in an Expanding bubble
  4. Single Kerr-NUT in the Bubble
  5. Regularisation
  6. Charges and Thermodynamics
  7. Schwarzschild in the Bubble
  8. Rotating Binary black hole system balanced by the Bubble
  9. Conclusions
  10. Acknowledgements

Figures (2)

  • Figure 1: Isometric embedding of the Schwarzschild black hole horizon (orange) and (part of ) the bubble's horizon of nothing (violet) immersed in the three-dimensional Euclidean space; for $w_1=-4 , w_2=-1, w_3=1, w_4=4$. The geometry of the black hole is deformed by the presence of the surrounding bubble.
  • Figure 2: A pictorial illustration representing a couple of collinear black hole enclosed in a bubble. See \ref{['fig:embedding-schwarzschild']}, for a more precise image based on the actual metric solution, specifically the Schwarzschild black hole horizon in the bubble of nothing embedded in the three-dimensional Euclidean space.