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EMMI - Hot Matter 24-28 Aug 2010 | Vienna, Austria

Colliding black holes Vitor Cardoso (CENTRA/IST & Olemiss). PRL101:161101,2008; PRL103:131102,2009; arXiv:1006.3081. . EMMI - Hot Matter 24-28 Aug 2010 | Vienna, Austria. Why study dynamics. Gravitational-wave detection, GW astrophysics Mathematical physics High-energy physics.

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EMMI - Hot Matter 24-28 Aug 2010 | Vienna, Austria

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  1. Colliding black holes Vitor Cardoso (CENTRA/IST & Olemiss) PRL101:161101,2008; PRL103:131102,2009; arXiv:1006.3081  EMMI - Hot Matter 24-28 Aug 2010 | Vienna, Austria

  2. Why study dynamics Gravitational-wave detection, GW astrophysics Mathematical physics High-energy physics

  3. Typical signal for coalescing binaries Typical stretch of data

  4. A typical problem!

  5. Why study dynamics Gravitational-wave detection, GW astrophysics Mathematical physics High-energy physics

  6. Cosmic Censorship: do horizons always form? •  • Are black objects always stable? Phase diagrams... •  • Universal limit on maximum luminosity G/c^5 (Dyson ‘63) •  Critical behavior, resonant excitation of QNMs? •  • Test analytical techniques, their predictions and power • (Penrose ’74, D’Eath & Payne ’93, Eardley & Giddings ’02)

  7. Why study dynamics Gravitational-wave detection, GW astrophysics Mathematical physics High-energy physics

  8. Braneworlds At large distances, one recovers Newton’s gravity!  Holography and HIC (Amsel et al ’08; Gubser et al ’08; this workshop)

  9. “An imploding object forms a BH when, and only when, a circular hoop with circumference 2 the Schwarzschild radiusof the object can be made that encloses the object in all directions.” Large amount of energy in small region Hoop Conjecture(Thorne 1972) This is the hoop R=2GM/c2 Size of electron: 10^(-17) cm Schwarzschild radius: 10^(-55) cm

  10. (Choptuik & Pretorius, Phys.Rev.Lett. 104:111101,2010)

  11. (Choptuik & Pretorius, Phys.Rev.Lett. 104:111101,2010)

  12. High energy collisions Black holes do form in high energy collisions  Transplanckian scattering well described by BH collisions!  How to go around and study BH collisions?

  13. Perturbation theory(Regge & Wheeler, ’57; DRPP ’71; Cardoso & Lemos ’02) Metric=Schwarzschild + small perturbation due to infalling particle

  14. Velocity Radiated energyArea theorem Point particle Equal mass Point particle Equal mass

  15. dE/d flat at sufficiently low, multipole Roughly 65% of maximum possible at =3 Berti et al, 2010

  16. ZFL(Weinberg ’64; Smarr ‘77) Take two free particles, changing abruptly at t=0 Radiation isotropic in the UR limit, multipole structure Functional relation Erad(), flat spectrum Roughly 65% of maximum possible at =3 With cutoff M 0.4 we get 25% efficiency for conversion of gws

  17. M. Lemos, MSc (2010); Berti et al 2010

  18. Trapped surface formation(Penrose ’74, Eardley & Giddings ’02) • Superpose two Aichelburg-Sexl metrics, find future trapped surface Upper limit on gravitational radiation: 29% M Perturb superposed A-S metric, correction: 16% M (D’Eath & Payne ’90s)

  19. A very brief history Pioneers:Hahn and Lindquist 1960s, Eppley and Smarr 1970s Numerical simulations:Grand Challenge ’90s Breakthrough:Pretorius, Brownsville, NASA Goddard 2005

  20. Numerical evolution GR:“Space and time exist together as Spacetime’’ Numerical relativity: reverse this process! Arnowitt, Deser, Misner (1962) York (1979) Choquet-Bruhat, York (1980) ADM 3+1 decomposition 3-metric lapse shift lapse, shiftGauge

  21. Time projection Hamiltonian constraint Mixed projection Momentum constraints Spatial projection Evolution equations

  22. Numerical simulations LEAN code (Sperhake ’07) Based on the Cactus computational toolkit BSSN formulation (ADM-like, but strongly hyperbolic) Puncture initial data (Brandt & Brügmann 1996) Elliptic solver: TwoPunctures (Ansorg 2005) Mesh refinement: Carpet (Schnetter ’04) Numerically very challenging! Length scales: MADM  M0 Horizon Lorentz-contracted “Pancake” Mergers extremely violent Substantial amounts of unphysical “junk” radiation

  23. Rest Results (Witek et al, arXiv:1006.3081 [gr-qc])

  24. High energy head-ons Results =0.93 (Sperhake et al, Phys.Rev.Lett. 101:161101, 2008)

  25. Waveform is almost just ringdown • Spectrum is flat, in good agreement with ZFL • Cutoff frequency at the lowest quasinormal frequency

  26. 14%

  27. Grazing collisions Plunge, zoom-whirl and scattering (Sperhake et al, Phys.Rev.Lett. 103:131102, 2008)

  28. More than 25% CM energy radiated for v=0.75 c! Final BH rapidly spinning

  29. Light ring & QNMs ZFL

  30. Cosmic Censor: as strong as ever Production Cross-section: b/M=2.5/v Peak luminosity: Close to Dyson limit c^5/G Maximum spin: >0.95 Radiated energy: >35% CM Junk: ~2 Erad, interesting topic for further study Radiation: Almost just ringdown, relation with ZFL…

  31. Other spacetimes

  32. Axial symmetry Head-on in D>4 Grazing in D>5 Can be reduced to effective 3+1

  33. D-dimensional Einstein equations imply

  34. Effective 3+1 system with sources

  35. BH collisions are a fascinating topic in GR •  • Cosmic Censorship preserved •  • Much remains to be done: • Understand initial data, add charge, go to higher boosts, higher dimensional spacetimes, compactified EDs, • anti-de Sitter

  36. Thank you

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