Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Black diring and infinite nonuniqueness

Hideo Iguchi, Takashi Mishima

TL;DR

The paper investigates five-dimensional vacuum gravity with $S^1$-rotating black rings and demonstrates that concentric di-ring configurations can be generated via a solution-generating technique based on the Weyl-Papapetrou formalism and rod-structure analysis. By applying a solitonic transformation to a carefully chosen seed, the authors construct the black di-ring, fix regularity and periodicity conditions to eliminate conical singularities, and extract physical quantities from the asymptotic Ernst potential. A key result is the existence of infinite nonuniqueness: there are continuous families of di-rings with the same mass $m$ and angular momentum $J$, including a path that connects the fat and thin single black rings. The work highlights di-rings as a mechanism to explore the landscape of 5D black objects and suggests further extensions to multi-angular-momentum solutions and connections to configurations like black Saturn.

Abstract

We show that the $S^1$-rotating black rings can be superposed by the solution generating technique. We analyze the black diring solution for the simplest case of multiple rings. There exists an equilibrium black diring where the conical singularities are cured by the suitable choice of physical parameters. Also there are infinite numbers of black dirings with the same mass and angular momentum. These dirings can have two different continuous limits of single black rings. Therefore we can transform the fat black ring to the thin ring with the same mass and angular momentum by way of the diring solutions.

Black diring and infinite nonuniqueness

TL;DR

The paper investigates five-dimensional vacuum gravity with -rotating black rings and demonstrates that concentric di-ring configurations can be generated via a solution-generating technique based on the Weyl-Papapetrou formalism and rod-structure analysis. By applying a solitonic transformation to a carefully chosen seed, the authors construct the black di-ring, fix regularity and periodicity conditions to eliminate conical singularities, and extract physical quantities from the asymptotic Ernst potential. A key result is the existence of infinite nonuniqueness: there are continuous families of di-rings with the same mass and angular momentum , including a path that connects the fat and thin single black rings. The work highlights di-rings as a mechanism to explore the landscape of 5D black objects and suggests further extensions to multi-angular-momentum solutions and connections to configurations like black Saturn.

Abstract

We show that the -rotating black rings can be superposed by the solution generating technique. We analyze the black diring solution for the simplest case of multiple rings. There exists an equilibrium black diring where the conical singularities are cured by the suitable choice of physical parameters. Also there are infinite numbers of black dirings with the same mass and angular momentum. These dirings can have two different continuous limits of single black rings. Therefore we can transform the fat black ring to the thin ring with the same mass and angular momentum by way of the diring solutions.

Paper Structure

This paper contains 5 sections, 42 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Brief review of solution generating technique
  3. Rod structure analysis
  4. $S^1$-rotating black multi-ring
  5. Summay and discussion

Figures (4)

  • Figure 1: Schematic pictures of rod structures of multi-ring and its seed. The left panel shows the rod structure of seed metric of $S^1$-rotating black multi-ring. The right panel shows the rod structure of $S^1$-rotating black multi-ring. The finite spacelike rod $[\eta_1\sigma,\eta_2\sigma]$ in the left panel is altered to the finite timelike rod by the solution-generating transformation. All static timelike rods may be transformmed to stationary ones by the solitonic transformation. To denote the rotation of the event horizons, we put the finite timelike rods between the lines of $x^0$ and $\phi$.
  • Figure 2: Schematic pictures of rod structures of black di-ring and its seed. The left panel shows the rod structure of seed metric of $S^1$-rotating black di-ring. The right panel shows the rod structure of $S^1$-rotating black di-ring. The finite spacelike rod $[\eta_1\sigma,\eta_2\sigma]$ in the left panel is altered to the finite timelike rod by the solution-generating transformation.
  • Figure 3: Plot of $\frac{a_0^2}{m^2}$ as a function of $\eta_1$ and $\delta_1$ where $\lambda$ and $\delta_2$ are determined by the equilibrium conditions and $\eta_2=1$. The bold line corespond to the single black ring of $\delta_1=\delta_2$.
  • Figure 4: Plot of $\frac{a_0^2}{m^2}$ of single black ring as a function of $\eta_1$. The region $0.5<\eta_1<1$ correspond to fat rings and $\eta_1<0.5$ thin rings.