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Phase Structure of Black Holes and Strings on Cylinders

T. Harmark, N. A. Obers

TL;DR

This work extends the neutral, static black hole/string phase analysis on cylinders by proving that all such solutions admit the Harmark two-function ansatz and by deriving a general first-law of thermodynamics in the $(M,n)$ framework. It introduces an explicit solution-generator that unwrapps solutions to generate infinite copies, reshaping the non-uniform string and black-hole branches and constraining possible phase transitions associated with the Gregory-Laflamme instability. The paper systematically compares existing scenarios and proposes additional possibilities, aided by detailed phase-diagram reasoning and a striking near-linear TS–M behavior observed in Wiseman’s non-uniform string data. These results sharpen questions about horizon topology changes, entropy ordering, and the uniqueness of static solutions on cylinders, with potential implications for stability and cosmic censorship in higher-dimensional GR.

Abstract

We use the (M,n) phase diagram recently introduced in hep-th/0309116 to investigate the phase structure of black holes and strings on cylinders. We first prove that any static neutral black object on a cylinder can be put into an ansatz for the metric originally proposed in hep-th/0204047, generalizing a result of Wiseman. Using the ansatz, we then show that all branches of solutions obey the first law of thermodynamics and that any solution has an infinite number of copies. The consequences of these two results are analyzed. Based on the new insights and the known branches of solutions, we finally present an extensive discussion of the possible scenarios for the Gregory-Laflamme instability and the black hole/string transition.

Phase Structure of Black Holes and Strings on Cylinders

TL;DR

This work extends the neutral, static black hole/string phase analysis on cylinders by proving that all such solutions admit the Harmark two-function ansatz and by deriving a general first-law of thermodynamics in the framework. It introduces an explicit solution-generator that unwrapps solutions to generate infinite copies, reshaping the non-uniform string and black-hole branches and constraining possible phase transitions associated with the Gregory-Laflamme instability. The paper systematically compares existing scenarios and proposes additional possibilities, aided by detailed phase-diagram reasoning and a striking near-linear TS–M behavior observed in Wiseman’s non-uniform string data. These results sharpen questions about horizon topology changes, entropy ordering, and the uniqueness of static solutions on cylinders, with potential implications for stability and cosmic censorship in higher-dimensional GR.

Abstract

We use the (M,n) phase diagram recently introduced in hep-th/0309116 to investigate the phase structure of black holes and strings on cylinders. We first prove that any static neutral black object on a cylinder can be put into an ansatz for the metric originally proposed in hep-th/0204047, generalizing a result of Wiseman. Using the ansatz, we then show that all branches of solutions obey the first law of thermodynamics and that any solution has an infinite number of copies. The consequences of these two results are analyzed. Based on the new insights and the known branches of solutions, we finally present an extensive discussion of the possible scenarios for the Gregory-Laflamme instability and the black hole/string transition.

Paper Structure

This paper contains 20 sections, 59 equations, 10 figures.

Table of Contents

  1. Introduction
  2. New type of phase diagram
  3. Derivation of ansatz for solutions
  4. Derivation of ansatz
  5. Ansatz for black holes and strings on cylinders
  6. First law of thermodynamics
  7. Proof of the first law
  8. Consequences for space of solutions
  9. Copies of solutions
  10. Solution generator
  11. Consequences for non-uniform black strings
  12. Consequences for black hole branch
  13. Possible scenarios and phase diagrams
  14. Review of three proposed scenarios
  15. Phase diagrams for the three scenarios
  16. ...and 5 more sections

Figures (10)

  • Figure 1: $(M,n)$ phase diagram for $d=5$ containing the uniform string branch and the non-uniform string branch of Wiseman. The black hole branch is sketched.
  • Figure 2: Part of the $(M,n)$ phase diagram for $d=5$ with copies of the non-uniform string branch of Wiseman.
  • Figure 3: Scenario I. Gubser's proposal for the non-uniform string branch plus a black hole branch that terminates at the critical point.
  • Figure 4: Scenario II. Gubser's proposal for the non-uniform string branch plus a black hole branch that continues into another non-uniform string branch which continues to arbitrarily large masses.
  • Figure 5: Scenario III. The scenario of Kol where the black hole branch is connected to the non-uniform branch.
  • ...and 5 more figures