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On Horizons and Plane Waves

James T. Liu, Leopoldo A. Pando Zayas, Diana Vaman

TL;DR

The paper analyzes whether event horizons can exist in geometries that asymptote to the maximally supersymmetric IIB plane wave (BFHP). It exploits a separation property arising from a null Killing vector to generate new $ ext{H}$-deformed solutions from seed brane backgrounds, uncovering cases where extremal horizons survive and many non-extremal deformations yield naked singularities. A general no-go theorem shows horizons are incompatible with backgrounds admitting only null matter and a null Killing vector, and additional sources do not typically evade this obstruction. The authors then argue, via a perturbative approach, that removing the null Killing vector could allow horizon formation, highlighting a path toward horizon-bearing, asymptotically BFHP spacetimes. Overall, the work clarifies the constraints on black-hole-like objects in plane-wave backgrounds and emphasizes the need to break the null direction to realize horizons in this setting.

Abstract

We investigate the possibility of having an event horizon within several classes of metrics that asymptote to the maximally supersymmetric IIB plane wave. We show that the presence of a null Killing vector (not necessarily covariantly constant) implies an effective separation of the Einstein equations into a standard and a wave component. This feature may be used to generate new supergravity solutions asymptotic to the maximally supersymmetric IIB plane wave, starting from standard seed solutions such as branes or intersecting branes in flat space. We find that in many cases it is possible to preserve the extremal horizon of the seed solution. On the other hand, non-extremal deformations of the plane wave solution result in naked singularities. More generally, we prove a no-go theorem against the existence of horizons for backgrounds with a null Killing vector and which contain at most null matter fields. Further attempts at turning on a nonzero Hawking temperature by introducing additional matter have proven unsuccessful. This suggests that one must remove the null Killing vector in order to obtain a horizon. We provide a perturbative argument indicating that this is in fact possible.

On Horizons and Plane Waves

TL;DR

The paper analyzes whether event horizons can exist in geometries that asymptote to the maximally supersymmetric IIB plane wave (BFHP). It exploits a separation property arising from a null Killing vector to generate new -deformed solutions from seed brane backgrounds, uncovering cases where extremal horizons survive and many non-extremal deformations yield naked singularities. A general no-go theorem shows horizons are incompatible with backgrounds admitting only null matter and a null Killing vector, and additional sources do not typically evade this obstruction. The authors then argue, via a perturbative approach, that removing the null Killing vector could allow horizon formation, highlighting a path toward horizon-bearing, asymptotically BFHP spacetimes. Overall, the work clarifies the constraints on black-hole-like objects in plane-wave backgrounds and emphasizes the need to break the null direction to realize horizons in this setting.

Abstract

We investigate the possibility of having an event horizon within several classes of metrics that asymptote to the maximally supersymmetric IIB plane wave. We show that the presence of a null Killing vector (not necessarily covariantly constant) implies an effective separation of the Einstein equations into a standard and a wave component. This feature may be used to generate new supergravity solutions asymptotic to the maximally supersymmetric IIB plane wave, starting from standard seed solutions such as branes or intersecting branes in flat space. We find that in many cases it is possible to preserve the extremal horizon of the seed solution. On the other hand, non-extremal deformations of the plane wave solution result in naked singularities. More generally, we prove a no-go theorem against the existence of horizons for backgrounds with a null Killing vector and which contain at most null matter fields. Further attempts at turning on a nonzero Hawking temperature by introducing additional matter have proven unsuccessful. This suggests that one must remove the null Killing vector in order to obtain a horizon. We provide a perturbative argument indicating that this is in fact possible.

Paper Structure

This paper contains 20 sections, 1 theorem, 159 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Asymptotic time and event horizons in plane waves
  3. Other asymptotic times
  4. Solution generation with a null Killing vector
  5. The Ricci tensor in the presence of a null Killing vector
  6. Solution generating technique
  7. The BFHP solution
  8. ${\cal H}$-deformed 3-branes
  9. Intersecting branes
  10. Non-extremal deformations
  11. An $SO(8)$ invariant deformation
  12. An $SO(4)\times SO(4)$ deformation
  13. No horizons for metrics admitting a null Killing vector
  14. Turning on additional sources
  15. Sourcing a string
  16. ...and 5 more sections

Key Result

Theorem 1

In the presence of matter contributing only to $T_{++}$, and with $\partial/\partial x^+$ asymptotically a timelike Killing vector, the following metric cannot admit a regular $SO(n+1)$ invariant horizon.

Figures (1)

  • Figure 1: The functions $g_1$ and $g_2$ normalized such that $g_i\to1$ as $r\to\infty$. Note that $g_2$ vanishes at the horizon.

Theorems & Definitions (1)

  • Theorem 1