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Singularities and closed time-like curves in type IIB 1/2 BPS geometries

Giuseppe Milanesi, Martin O'Loughlin

TL;DR

This work extends the LLM bubbling program by allowing singular geometries, showing the moduli space splits into non-singular, null-singular, and timelike (CTC-containing) time-machine classes. It proves null-singular solutions are in the same class as regular ones, while timelike singularities inevitably yield CTCs, and argues AdS/CFT describes only the non-singular/null-singular sector. The results link unitarity in the dual CFT to chronology protection in the bulk, suggesting that negative-dimension deformations correspond to pathological geometries. Overall, the paper offers a holographic perspective on causality, showing how boundary data, domain topology, and boundary conditions govern the presence of CTCs in 1/2-BPS IIB supergravity geometries.

Abstract

We study in detail the moduli space of solutions discovered in LLM relaxing the constraint that guarantees the absence of singularities. The solutions fall into three classes, non-singular, null-singular and time machines with a time-like naked singularity. We study the general features of these metrics and prove that there are actually just two generic classes of space-times - those with null singularities are in the same class as the non-singular metrics. AdS/CFT seems to provide a dual description only for the first of these two types of space-time in terms of a unitary CFT indicating the possible existence of a chronology protection mechanism for this class of geometries.

Singularities and closed time-like curves in type IIB 1/2 BPS geometries

TL;DR

This work extends the LLM bubbling program by allowing singular geometries, showing the moduli space splits into non-singular, null-singular, and timelike (CTC-containing) time-machine classes. It proves null-singular solutions are in the same class as regular ones, while timelike singularities inevitably yield CTCs, and argues AdS/CFT describes only the non-singular/null-singular sector. The results link unitarity in the dual CFT to chronology protection in the bulk, suggesting that negative-dimension deformations correspond to pathological geometries. Overall, the paper offers a holographic perspective on causality, showing how boundary data, domain topology, and boundary conditions govern the presence of CTCs in 1/2-BPS IIB supergravity geometries.

Abstract

We study in detail the moduli space of solutions discovered in LLM relaxing the constraint that guarantees the absence of singularities. The solutions fall into three classes, non-singular, null-singular and time machines with a time-like naked singularity. We study the general features of these metrics and prove that there are actually just two generic classes of space-times - those with null singularities are in the same class as the non-singular metrics. AdS/CFT seems to provide a dual description only for the first of these two types of space-time in terms of a unitary CFT indicating the possible existence of a chronology protection mechanism for this class of geometries.

Paper Structure

This paper contains 21 sections, 1 theorem, 115 equations, 7 figures.

Table of Contents

  1. Introduction
  2. LLM construction
  3. Boundary conditions
  4. Asymptotic behaviour
  5. Regular solutions and dual picture
  6. More general boundary conditions and singularities
  7. Singular solutions: some examples
  8. $\beta_i\leq1$ with at least one $\beta_i < 1$
  9. Some $\beta_i>1$
  10. Zooming
  11. The disk
  12. Lifting the sphere
  13. Singular solutions: generic properties
  14. Sufficient condition for CTCs
  15. (Lorentz) topology
  16. ...and 6 more sections

Key Result

Theorem 4.1

Geometries of the type studied in Section 2 have closed timelike curves if and only if $\partial\hat{\Sigma}\neq\emptyset$

Figures (7)

  • Figure 1: The domain of definition $\Sigma$
  • Figure 2: Two regions of $y=0$ plane, one with $\rho>1$ and the other with $\rho<0$, leading to a non trivial $\partial\hat{\Sigma}$ attached to the $y=0$ plane
  • Figure 3: Zoom showing light cone near a droplet with $\beta_i>1$ on the $\{x_1,x_2\}$ plane at $y=0$.
  • Figure 4: Singularity and velocity of light surface for a disk with $\beta>1$.
  • Figure 5: "Medusa" diagram: singularity, velocity of light surface and cylinder connecting the singularity ($\partial \hat{\Sigma}$) to the $y=0$ plane, for the lifted sphere.
  • ...and 2 more figures

Theorems & Definitions (1)

  • Theorem 4.1