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Splitting hairs of the three charge black hole

Iosif Bena

TL;DR

This work derives the large-radius limit of the metric for three-charge supertubes and BPS black rings by exploiting shared supersymmetry with constituent branes via Killing spinor methods. It shows that the near-tube geometries are smooth for regular tubes and develop horizons for black tubes, with the horizon area growing with the multiplicity of tube configurations, aligning with the black hole microstate program. The analysis uncovers a density-ratio constraint for tubes with two dipoles and identifies a critical parameter c_z that separates regular tubes from black rings in the large-radius limit, providing a concrete bridge between Born-Infeld results and supergravity. The results offer a framework to count microstates of three-charge tubes and test the proposal that black hole hair corresponds to a multitude of regular tube geometries, potentially proving aspects of Mathur’s conjecture.

Abstract

We construct the large radius limit of the metric of three charge supertubes and three charge BPS black rings by using the fact that supertubes preserve the same supersymmetries as their component branes. Our solutions reproduce a few of the properties of three charge supertubes found recently using the Born Infeld description. Moreover, we find that these solutions pass a number of rather nontrivial tests which they should pass if they are to describe some of the hair of three charge black holes and three charge black rings.

Splitting hairs of the three charge black hole

TL;DR

This work derives the large-radius limit of the metric for three-charge supertubes and BPS black rings by exploiting shared supersymmetry with constituent branes via Killing spinor methods. It shows that the near-tube geometries are smooth for regular tubes and develop horizons for black tubes, with the horizon area growing with the multiplicity of tube configurations, aligning with the black hole microstate program. The analysis uncovers a density-ratio constraint for tubes with two dipoles and identifies a critical parameter c_z that separates regular tubes from black rings in the large-radius limit, providing a concrete bridge between Born-Infeld results and supergravity. The results offer a framework to count microstates of three-charge tubes and test the proposal that black hole hair corresponds to a multitude of regular tube geometries, potentially proving aspects of Mathur’s conjecture.

Abstract

We construct the large radius limit of the metric of three charge supertubes and three charge BPS black rings by using the fact that supertubes preserve the same supersymmetries as their component branes. Our solutions reproduce a few of the properties of three charge supertubes found recently using the Born Infeld description. Moreover, we find that these solutions pass a number of rather nontrivial tests which they should pass if they are to describe some of the hair of three charge black holes and three charge black rings.

Paper Structure

This paper contains 11 sections, 27 equations, 1 figure.

Table of Contents

  1. Introduction
  2. The large radius limit of the three charge supertube solution.
  3. The physics of the solutions - special cases
  4. The two charge supertube -- two charges and one dipole charge
  5. Three charges and two dipole charges
  6. Three charges and one dipole charge
  7. The generic case -- supertubes and black supertubes
  8. Regular three charge supertubes
  9. Black supertubes
  10. Black Hole Physics
  11. Conclusions

Figures (1)

  • Figure 1: As one increases $Q$, the multiplicity of supertubes and the horizon area of the black tube increase.