1. Vitor Cardoso (The University of Mississippi) 16 th MidWest Relativity Meeting St. Louis, 17-18 November 2006 Black Holes and Strings in the Water Tap VC & Ó. Dias, Phys. Rev. Lett. 96, 181601 (2006) VC & L. Gualtieri, Class. Quantum Grav. 23, 7151 (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. Black string: Perturb the BS: S-wave perturbations (Gregory-Laflamme, 1993) z Gregory-Laflamme instability (D-1)-dimensional

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

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

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

7. Rayleigh-Plateau threshold mode: Gregory-Laflamme threshold mode: Kol & Sorkin, 2004 GL: RP: D567891050100 kR 0 1.411.732.002.242.452.666.789.80 kR 0 0.871.271.581.852.092.306.729.75 Cardoso & Dias, 2006 Threshold Mode in Higher Dimensions RP: GL:

8. Non-axisymmetric perturbations are stable: Kudoh, 2006 General Perturbations RP: GL:

9. ( Rayleigh, 1878) (Myers) Instability Timescale  =D/2-2 RP: GL:

10. Rotation: de-stabilizes (Johns & Narayanan, 2002) Rotation and Charge Effects Hint: Take an ultra-rotating black string: They are unstable (Cardoso and Gualtieri, 2006) Charge: stabilizes (Chandrasekhar, 1953) Rotation: ? Charge: stabilizes (Gregory and Laflame, 1994) RP: GL:

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!