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A Charged Rotating Black Ring

Henriette Elvang

TL;DR

This work constructs a charged rotating black ring in five-dimensional heterotic supergravity by applying Hassan–Sen transformations to the neutral Emparan–Reall ring, extending higher-dimensional non-uniqueness to charged solutions. The neutral ring is shown to satisfy an exact lower bound J^2/M^3 ≥ 1/π, with the minimum corresponding to maximum entropy for fixed M; the charged ring permits arbitrarily small J^2/M^3 while keeping Q/M finite, due to uniform ring charge. The charged ring carries electric charge Q and local fundamental string charge q_H, with a gyromagnetic ratio g that ranges between 3/2 and 2, and an extremal limit where |Q| = M and the horizon coincides with a singularity. The paper also relates the local near-ring physics to charged boosted black strings and discusses two extremal limits of charged black strings, highlighting non-uniqueness and potential supersymmetry considerations within heterotic string theory. Overall, it provides explicit charged ring solutions, analyzes their global and near-horizon properties, and explores implications for entropy, stability, and string-theoretic interpretations of higher-dimensional black objects.

Abstract

We construct a supergravity solution describing a charged rotating black ring with S^2xS^1 horizon in a five dimensional asymptotically flat spacetime. In the neutral limit the solution is the rotating black ring recently found by Emparan and Reall. We determine the exact value of the lower bound on J^2/M^3, where J is the angular momentum and M the mass; the black ring saturating this bound has maximum entropy for the given mass. The charged black ring is characterized by mass M, angular momentum J, and electric charge Q, and it also carries local fundamental string charge. The electric charge distributed uniformly along the ring helps support the ring against its gravitational self-attraction, so that J^2/M^3 can be made arbitrarily small while Q/M remains finite. The charged black ring has an extremal limit in which the horizon coincides with the singularity.

A Charged Rotating Black Ring

TL;DR

This work constructs a charged rotating black ring in five-dimensional heterotic supergravity by applying Hassan–Sen transformations to the neutral Emparan–Reall ring, extending higher-dimensional non-uniqueness to charged solutions. The neutral ring is shown to satisfy an exact lower bound J^2/M^3 ≥ 1/π, with the minimum corresponding to maximum entropy for fixed M; the charged ring permits arbitrarily small J^2/M^3 while keeping Q/M finite, due to uniform ring charge. The charged ring carries electric charge Q and local fundamental string charge q_H, with a gyromagnetic ratio g that ranges between 3/2 and 2, and an extremal limit where |Q| = M and the horizon coincides with a singularity. The paper also relates the local near-ring physics to charged boosted black strings and discusses two extremal limits of charged black strings, highlighting non-uniqueness and potential supersymmetry considerations within heterotic string theory. Overall, it provides explicit charged ring solutions, analyzes their global and near-horizon properties, and explores implications for entropy, stability, and string-theoretic interpretations of higher-dimensional black objects.

Abstract

We construct a supergravity solution describing a charged rotating black ring with S^2xS^1 horizon in a five dimensional asymptotically flat spacetime. In the neutral limit the solution is the rotating black ring recently found by Emparan and Reall. We determine the exact value of the lower bound on J^2/M^3, where J is the angular momentum and M the mass; the black ring saturating this bound has maximum entropy for the given mass. The charged black ring is characterized by mass M, angular momentum J, and electric charge Q, and it also carries local fundamental string charge. The electric charge distributed uniformly along the ring helps support the ring against its gravitational self-attraction, so that J^2/M^3 can be made arbitrarily small while Q/M remains finite. The charged black ring has an extremal limit in which the horizon coincides with the singularity.

Paper Structure

This paper contains 15 sections, 80 equations, 1 figure.

Table of Contents

  1. Introduction
  2. The Black Ring
  3. Review of the Neutral Rotating Black Ring
  4. An Exact Result for the Black Ring
  5. Review of Hassan-Sen Transformations
  6. The Charged Black Ring
  7. The Solution
  8. Physical Properties
  9. Extremal Limit
  10. A Charged Boosted Black String
  11. Black Strings with Charge
  12. Discussion
  13. Hassan-Sen Transformed Solutions
  14. Transformation of a Static Metric
  15. Transformation of a Stationary Metric ($\alpha_2 = 0$)

Figures (1)

  • Figure 1: As in Ref. Emparan:2001wn, we plot the dimensionless ratio $\frac{27 \pi}{32}\,\frac{J^2}{M^3}$ versus $\nu$ for $0 < \nu < 2/(3\sqrt{3})$. The solid line is the ratio for the black ring and the dashed line is the ratio for a Myers-Perry black hole with only one nonzero angular momentum. The dotted lines represent the constant functions $1$ and $27/32$. For the black ring, $\frac{27 \pi}{32}\,\frac{J^2}{M^3} = 1$ at $\nu \approx 0.211645$.