On Black String/Brane Instability and its Fate

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On Black String/Brane Instability and its Fate
Mar. 22, 2006 at the NR Spring School

• Gungwon Kang at KISTI

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• Introduction
• Black string or brane solutions
• Stability
• Fate of the GL instability
• II. Stability of various black branes
• Various black Dp-branes
• Black strings in AdS space
• Black branes in D 4
• Higher order gravity theories
• III. Fate of the GL instability
• Horowitz-Maeda conjecture
• Numerical evolution
• IV. Research plan

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I. Introduction

• Black string or brane solutions

x(t,r,?,f)
z
Ex)
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Stability?

• Schwarzschild black holes in any dimensions
• STABLE under linearized perturbations
• This property seems to hold for any stationary
• black hole having spherical event horizon.
• What about for black strings/branes?

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• Gravitational perturbations 93 GL

Lichnerowicz Eq.
Massive spin-2 fields!
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0
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• Fate of the GL instability?

• Black string fragmentation

• The GL instability and this fragmentation
  scenario are used in various discussions such as
• black holes in M theory, various unstable
  D-brane configurations, etc.
• black holes in brane world models
• instability of rapidly rotating black holes in
  higher dimensions (D gt 5)
• instability of black rings in D5

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• If the black string horizon pinches off, a naked
  singularity may occur.
• Violation of the cosmic censorship conjecture!?
• For the case of charged black strings,
• Violation of the charge conservation!?

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• Horowitz Maeda (01)

The bs horizon cannot pinch off in a finite time,
but becomes a non-uniform one as a final state.
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Issues

• How robust is the GL instability?
• ? Stability in a wider class of black
  string/brane backgrounds, in a different
  dynamics, etc.
• Any confirmation for the final fate of the GL
  instability?
• ? Full nonlinear evolution numerically,
  perturbative analyses in higher order
• Any sort of uniqueness theorem for black
  string/brane configuration?
• ? Studies on solution space

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II. Stability of various black branes

• Basic features of the GL instability

• If L , no instability.
• The extremal black string should be stable.
• Strong curvature on the horizon probably gives
  strong GL instability.
• Non-uniformity may give stabilization effect.

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• Charged black Dp-branes in type II supergravity
• 03 Hirayama, GK Y. Lee

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For s-wave fluctuations
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Results for some interesting objects

• All extremal black branes are
• STABLE (BPS states)

• Magnetically charged black NS5, D5,D6 branes
• UNSTABLE ALWAYS

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• Black strings in AdS space 01 Hirayama GK

Not uniform, but warped!
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• Thus,
• dS_4/M_4-Schwarzschild black strings
• UNSTABLE ALWAYS
• But,
• AdS_4-Schwarzschild black string
• STABLE if r_ gt

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Perturbed horizon in the case of ?_4 0 with a
3-brane 00 Gregory
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• Black branes in D 4

• BTZ black string 05 GK Y. Lee in preparation

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NO UNSTABLE MODE SOLUTION!
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• Higher order gravity theories

• Motivations
• - String theory
• - Relevant for strong gravity region
• e.g., pinching off of a black string
• Work in progress D. Park, M. Park GK

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III. Fate of the GL instability

• Horowitz-Maeda conjecture

gt 0 (Area theorem)
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Thus,
The sphere cannot shrink to zero size in finite
affine time. A non-uniform bs would be the
end-state of the GL instability.
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• Numerical simulations for a neutral black
  string 03 Choptuik et al.

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F. Pretorius www.tapir.caltech.edu/fransp/
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• Garfinkle, Lehner Pretorius 04

It might be true that the neutral BS pinches off
in an infinite affine time.
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IV. Research plan

• The issue about the end-state of the GL
  instability has not been resolved yet.
• All numerical results for full evolutions so far
  are based on the studies only for neutral black
  strings.
• We have seen that charged black strings, black
  strings in AdS space, and BTZ black strings
  behave differently under small perturbations.
• ? Expect that numerical studies for these black
  string spacetimes may give some hints at
  understanding the end-state of the GL instability!

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• Propose investigations on the full numerical
  evolution of these types of perturbed black
  strings near the critical point

• Charged black branes in supergravity
• - Very interesting, but probably not easy due
  to
• the gauge field!

• AdS_4-Schwarzschild black string in 5D
• - Fairly easy due to the absence of matter
  field!
• - Exists some reason for expecting quick
• stabilization! gt 1st example confirming
  HMs?

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Potential for the mode solutions in the
z-direction
Effective box potential!
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• BTZ black string in 4D
• - Stable always!
• - No matter field!

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Accommodation at Daejeon

• Matt and his family ? Spapia hotel
• D. Choi, Martin, and others
• ? KAIST Intl Village A

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