Vitor Cardoso

1
Black Holes and Strings in the Water Tap

• Vitor Cardoso
• (The University of Mississippi)

• VC Ó. Dias, Phys. Rev. Lett. 96, 181601 (2006)
  
• VC L. Gualtieri, Class. Quantum Grav. 23, 7151
  (2006)

16th MidWest Relativity Meeting St. Louis, 17-18
November 2006
2
Black Holes and Membranes

• Why not? Liquid drops as model for planets and
  stars. Bohr and Wheelers model of nuclear forces
  as surface tension.
• Membrane paradigm (Thorne et al 86 Parikh
  Wilczek 98) Event horizon behaves as a
  stretched membrane, with electrical conductivity
  and viscosity.
• The first law of BH Mechanics dETdA (Smarr 73)
  
• Fluids held by surface tension T.

3
Gregory-Laflamme instability
(Gregory-Laflamme, 1993)

• Black string

(D-1)-dimensional

• Perturb the BS

z

• S-wave perturbations

4
Gregory-Laflamme instability
(Gregory-Laflamme, 1993)
There are solutions with W gt0
(From Kudoh, 2006)
5
Rayleigh-Plateau instability
(Plateau, 1849 Rayleigh, 1878)
Water in my kitchen faucet
Rain (with high speed camera)
6
Rayleigh-Plateau instability
(Plateau, 1849 Rayleigh, 1878)
Perturbation
The threshold mode
7
Threshold Mode in Higher Dimensions
Rayleigh-Plateau threshold mode
RP
Cardoso Dias, 2006
Gregory-Laflamme threshold mode
GL
Kol Sorkin, 2004
D 5 6 7 8 9 10 50 100
kR0 1.41 1.73 2.00 2.24 2.45 2.66 6.78 9.80
kR0 0.87 1.27 1.58 1.85 2.09 2.30 6.72 9.75
RP
GL
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General Perturbations
RP
Non-axisymmetric perturbations are stable
GL
Non-axisymmetric perturbations are stable
Kudoh, 2006
9
Instability Timescale
(Rayleigh, 1878)
RP
?D/2-2
GL
(Myers)
10
Rotation and Charge Effects
Rotation de-stabilizes
Charge stabilizes
(Johns Narayanan, 2002)
(Chandrasekhar, 1953)
RP
Rotation ?
GL
Charge stabilizes
(Gregory and Laflame, 1994)
Hint Take an ultra-rotating black string
They are unstable
(Cardoso and Gualtieri, 2006)
11
Very Nice!
12
Extensions
13
USML2 space-lab flight 1995
14
Conclusions

• Membranes can mimic horizons
• Black strings are unstable water dripping from
  faucet
• Understand gravity and black objects with simple
  analogies

Thank you!