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Black Holes on Cylinders

Troels Harmark, Niels Obers

TL;DR

This work constructs explicit non-extremal, charged dilatonic brane solutions on a transverse circle by introducing a new interpolating coordinate system and a reduced ansatz governed by a single function. The formulation yields neutral black holes on cylinders and near-extremal branes, revealing that above a critical mass $M_c$ the horizon topology prefers non-translationally invariant configurations with higher entropy than the smeared black string. The results imply a quantum-like instability of the black string at large mass, as it can gain entropy by redistributing mass into the non-uniform solution, while remaining classically stable. The framework also provides a tractable route to studying thermodynamics of Little String Theory and related holographic systems, offering insights into phase structure and the role of horizon topology in higher-dimensional gravity.

Abstract

We take steps toward constructing explicit solutions that describe non-extremal charged dilatonic branes of string/M-theory with a transverse circle. Using a new coordinate system we find an ansatz for the solutions with only one unknown function. We show that this function is independent of the charge and our ansatz can therefore also be used to construct neutral black holes on cylinders and near-extremal charged dilatonic branes with a transverse circle. For sufficiently large mass $M > M_c$ these solutions have a horizon that connects across the cylinder but they are not translationally invariant along the circle direction. We argue that the neutral solution has larger entropy than the neutral black string for any given mass. This means that for $M > M_c$ the neutral black string can gain entropy by redistributing its mass to a solution that breaks translational invariance along the circle, despite the fact that it is classically stable. We furthermore explain how our construction can be used to study the thermodynamics of Little String Theory.

Black Holes on Cylinders

TL;DR

This work constructs explicit non-extremal, charged dilatonic brane solutions on a transverse circle by introducing a new interpolating coordinate system and a reduced ansatz governed by a single function. The formulation yields neutral black holes on cylinders and near-extremal branes, revealing that above a critical mass the horizon topology prefers non-translationally invariant configurations with higher entropy than the smeared black string. The results imply a quantum-like instability of the black string at large mass, as it can gain entropy by redistributing mass into the non-uniform solution, while remaining classically stable. The framework also provides a tractable route to studying thermodynamics of Little String Theory and related holographic systems, offering insights into phase structure and the role of horizon topology in higher-dimensional gravity.

Abstract

We take steps toward constructing explicit solutions that describe non-extremal charged dilatonic branes of string/M-theory with a transverse circle. Using a new coordinate system we find an ansatz for the solutions with only one unknown function. We show that this function is independent of the charge and our ansatz can therefore also be used to construct neutral black holes on cylinders and near-extremal charged dilatonic branes with a transverse circle. For sufficiently large mass these solutions have a horizon that connects across the cylinder but they are not translationally invariant along the circle direction. We argue that the neutral solution has larger entropy than the neutral black string for any given mass. This means that for the neutral black string can gain entropy by redistributing its mass to a solution that breaks translational invariance along the circle, despite the fact that it is classically stable. We furthermore explain how our construction can be used to study the thermodynamics of Little String Theory.

Paper Structure

This paper contains 37 sections, 289 equations, 6 figures.

Table of Contents

  1. Introduction
  2. A new coordinate system
  3. Defining the new coordinates
  4. Critical curve
  5. The flat metric
  6. Ansatz
  7. Conditions on a solution
  8. The ansatz
  9. Map of solution to neutral and near-extremal solutions
  10. Neutral black holes on a cylinder
  11. Near-extremal branes on transverse circle
  12. Newton limit of small black holes on cylinders
  13. The Newton limit of Einsteins equation
  14. The Newton potential and the $g_{00}$ component
  15. The metric in the Newton limit
  16. ...and 22 more sections

Figures (6)

  • Figure 1: Equipotential lines for $F_2(a,b)$ corresponding to $d=4$. Horizontal axis is $b$ and vertical axis is $a$.
  • Figure 2: Qualitative behavior of $\chi (R_0)$.
  • Figure 3: Qualitative behavior of $\gamma (R_0)$: scenario I
  • Figure 4: Qualitative behavior of $\gamma (R_0)$: scenario II
  • Figure 5: Phase diagram of supersymmetric $(2,0)$ LST.
  • ...and 1 more figures