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Black Holes and Strings in the Water Tap

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

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Black Holes and Strings in the Water Tap

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  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 Wheeler’s 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 dE=TdA(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-waveperturbations

  4. Gregory-Laflamme instability (Gregory-Laflamme, 1993) There are solutions with W>0: (From Kudoh, 2006)

  5. (Plateau, 1849; Rayleigh, 1878) Rayleigh-Plateau instability Water in my kitchen faucet Rain (with high speed camera)

  6. (Plateau, 1849; Rayleigh, 1878) Rayleigh-Plateau instability Perturbation: The threshold mode:

  7. Threshold Mode in Higher Dimensions Rayleigh-Plateau threshold mode: RP: Cardoso & Dias, 2006 GL: Gregory-Laflamme threshold mode: Kol & Sorkin, 2004 RP: GL:

  8. RP: General Perturbations 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: GL: Rotation: ? 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 drippingfrom faucet • Understand gravity and black objects with simple analogies Thank you!

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