![Page 1: Black hole collisions · 2012. 8. 29. · BHs and higher dimensions 20-24 Sep 2010 | London, UK Black hole collisions Vitor Cardoso (CENTRA/IST & Olemiss) PRL101:161101,2008; PRL103:131102,2009;](https://reader033.vdocuments.mx/reader033/viewer/2022051905/5ff8054bf72a3370b16f09bd/html5/thumbnails/1.jpg)
BHs and higher dimensions 20-24 Sep 2010 | London, UK
Black hole collisions
Vitor Cardoso
(CENTRA/IST & Olemiss)
PRL101:161101,2008; PRL103:131102,2009; arXiv:1006.3081
![Page 2: Black hole collisions · 2012. 8. 29. · BHs and higher dimensions 20-24 Sep 2010 | London, UK Black hole collisions Vitor Cardoso (CENTRA/IST & Olemiss) PRL101:161101,2008; PRL103:131102,2009;](https://reader033.vdocuments.mx/reader033/viewer/2022051905/5ff8054bf72a3370b16f09bd/html5/thumbnails/2.jpg)
Why study dynamics
Gravitational-wave detection, GW astrophysics
Mathematical physics
High-energy physics
![Page 3: Black hole collisions · 2012. 8. 29. · BHs and higher dimensions 20-24 Sep 2010 | London, UK Black hole collisions Vitor Cardoso (CENTRA/IST & Olemiss) PRL101:161101,2008; PRL103:131102,2009;](https://reader033.vdocuments.mx/reader033/viewer/2022051905/5ff8054bf72a3370b16f09bd/html5/thumbnails/3.jpg)
Typical signal for coalescing binaries
Typical stretch of data
![Page 4: Black hole collisions · 2012. 8. 29. · BHs and higher dimensions 20-24 Sep 2010 | London, UK Black hole collisions Vitor Cardoso (CENTRA/IST & Olemiss) PRL101:161101,2008; PRL103:131102,2009;](https://reader033.vdocuments.mx/reader033/viewer/2022051905/5ff8054bf72a3370b16f09bd/html5/thumbnails/4.jpg)
A typical problem!
![Page 5: Black hole collisions · 2012. 8. 29. · BHs and higher dimensions 20-24 Sep 2010 | London, UK Black hole collisions Vitor Cardoso (CENTRA/IST & Olemiss) PRL101:161101,2008; PRL103:131102,2009;](https://reader033.vdocuments.mx/reader033/viewer/2022051905/5ff8054bf72a3370b16f09bd/html5/thumbnails/5.jpg)
Why study dynamics
Gravitational-wave detection, GW astrophysics
Mathematical physics
High-energy physics
![Page 6: Black hole collisions · 2012. 8. 29. · BHs and higher dimensions 20-24 Sep 2010 | London, UK Black hole collisions Vitor Cardoso (CENTRA/IST & Olemiss) PRL101:161101,2008; PRL103:131102,2009;](https://reader033.vdocuments.mx/reader033/viewer/2022051905/5ff8054bf72a3370b16f09bd/html5/thumbnails/6.jpg)
Cosmic Censorship: do horizons always form?
Are black objects always stable? Phase diagrams...
Universal limit on maximum luminosity c^5/G (Dyson ‘63)
Critical behavior, resonant excitation of QNMs?
Test analytical techniques, their predictions and power
(Penrose ’74, D’Eath & Payne ’93, Eardley & Giddings ’02)
![Page 7: Black hole collisions · 2012. 8. 29. · BHs and higher dimensions 20-24 Sep 2010 | London, UK Black hole collisions Vitor Cardoso (CENTRA/IST & Olemiss) PRL101:161101,2008; PRL103:131102,2009;](https://reader033.vdocuments.mx/reader033/viewer/2022051905/5ff8054bf72a3370b16f09bd/html5/thumbnails/7.jpg)
Why study dynamics
Gravitational-wave detection, GW astrophysics
Mathematical physics
High-energy physics
![Page 8: Black hole collisions · 2012. 8. 29. · BHs and higher dimensions 20-24 Sep 2010 | London, UK Black hole collisions Vitor Cardoso (CENTRA/IST & Olemiss) PRL101:161101,2008; PRL103:131102,2009;](https://reader033.vdocuments.mx/reader033/viewer/2022051905/5ff8054bf72a3370b16f09bd/html5/thumbnails/8.jpg)
Holography and HIC
(Nastase ’05; Amsel et al ’08; Gubser et al ’08)
At large distances, one recovers Newton’s gravity!
Braneworlds
![Page 9: Black hole collisions · 2012. 8. 29. · BHs and higher dimensions 20-24 Sep 2010 | London, UK Black hole collisions Vitor Cardoso (CENTRA/IST & Olemiss) PRL101:161101,2008; PRL103:131102,2009;](https://reader033.vdocuments.mx/reader033/viewer/2022051905/5ff8054bf72a3370b16f09bd/html5/thumbnails/9.jpg)
• “An imploding object forms a BH when, and only when, a circular hoop
with circumference 2 the Schwarzschild radius of 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
![Page 10: Black hole collisions · 2012. 8. 29. · BHs and higher dimensions 20-24 Sep 2010 | London, UK Black hole collisions Vitor Cardoso (CENTRA/IST & Olemiss) PRL101:161101,2008; PRL103:131102,2009;](https://reader033.vdocuments.mx/reader033/viewer/2022051905/5ff8054bf72a3370b16f09bd/html5/thumbnails/10.jpg)
(Choptuik & Pretorius, Phys.Rev.Lett. 104:111101,2010)
![Page 11: Black hole collisions · 2012. 8. 29. · BHs and higher dimensions 20-24 Sep 2010 | London, UK Black hole collisions Vitor Cardoso (CENTRA/IST & Olemiss) PRL101:161101,2008; PRL103:131102,2009;](https://reader033.vdocuments.mx/reader033/viewer/2022051905/5ff8054bf72a3370b16f09bd/html5/thumbnails/11.jpg)
(Choptuik & Pretorius, Phys.Rev.Lett. 104:111101,2010)
![Page 12: Black hole collisions · 2012. 8. 29. · BHs and higher dimensions 20-24 Sep 2010 | London, UK Black hole collisions Vitor Cardoso (CENTRA/IST & Olemiss) PRL101:161101,2008; PRL103:131102,2009;](https://reader033.vdocuments.mx/reader033/viewer/2022051905/5ff8054bf72a3370b16f09bd/html5/thumbnails/12.jpg)
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?
![Page 13: Black hole collisions · 2012. 8. 29. · BHs and higher dimensions 20-24 Sep 2010 | London, UK Black hole collisions Vitor Cardoso (CENTRA/IST & Olemiss) PRL101:161101,2008; PRL103:131102,2009;](https://reader033.vdocuments.mx/reader033/viewer/2022051905/5ff8054bf72a3370b16f09bd/html5/thumbnails/13.jpg)
Perturbation theory (Regge & Wheeler, ’57; DRPP ’71; Cardoso & Lemos ’02)
Metric=Schwarzschild + small perturbation due to infalling particle
![Page 14: Black hole collisions · 2012. 8. 29. · BHs and higher dimensions 20-24 Sep 2010 | London, UK Black hole collisions Vitor Cardoso (CENTRA/IST & Olemiss) PRL101:161101,2008; PRL103:131102,2009;](https://reader033.vdocuments.mx/reader033/viewer/2022051905/5ff8054bf72a3370b16f09bd/html5/thumbnails/14.jpg)
Velocity Radiated energy Area theorem
Point particle
Equal mass
Point particle
Equal mass
![Page 15: Black hole collisions · 2012. 8. 29. · BHs and higher dimensions 20-24 Sep 2010 | London, UK Black hole collisions Vitor Cardoso (CENTRA/IST & Olemiss) PRL101:161101,2008; PRL103:131102,2009;](https://reader033.vdocuments.mx/reader033/viewer/2022051905/5ff8054bf72a3370b16f09bd/html5/thumbnails/15.jpg)
dE/d flat at sufficiently low , multipole
Roughly 65% of maximum possible at =3
(Berti et al, 2010)
![Page 16: Black hole collisions · 2012. 8. 29. · BHs and higher dimensions 20-24 Sep 2010 | London, UK Black hole collisions Vitor Cardoso (CENTRA/IST & Olemiss) PRL101:161101,2008; PRL103:131102,2009;](https://reader033.vdocuments.mx/reader033/viewer/2022051905/5ff8054bf72a3370b16f09bd/html5/thumbnails/16.jpg)
D Radiated energy Area theorem
Point particle
Equal mass
Point particle
Equal mass
Generic D (Kodama & Ishibashi, ’03; Berti, Cardoso & Kipapa, to appear)
v=1: (Berti, Cavaglia & Gualtieri, ’03)
![Page 17: Black hole collisions · 2012. 8. 29. · BHs and higher dimensions 20-24 Sep 2010 | London, UK Black hole collisions Vitor Cardoso (CENTRA/IST & Olemiss) PRL101:161101,2008; PRL103:131102,2009;](https://reader033.vdocuments.mx/reader033/viewer/2022051905/5ff8054bf72a3370b16f09bd/html5/thumbnails/17.jpg)
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
![Page 18: Black hole collisions · 2012. 8. 29. · BHs and higher dimensions 20-24 Sep 2010 | London, UK Black hole collisions Vitor Cardoso (CENTRA/IST & Olemiss) PRL101:161101,2008; PRL103:131102,2009;](https://reader033.vdocuments.mx/reader033/viewer/2022051905/5ff8054bf72a3370b16f09bd/html5/thumbnails/18.jpg)
(M. Lemos, MSc (2010); Berti et al 2010)
![Page 19: Black hole collisions · 2012. 8. 29. · BHs and higher dimensions 20-24 Sep 2010 | London, UK Black hole collisions Vitor Cardoso (CENTRA/IST & Olemiss) PRL101:161101,2008; PRL103:131102,2009;](https://reader033.vdocuments.mx/reader033/viewer/2022051905/5ff8054bf72a3370b16f09bd/html5/thumbnails/19.jpg)
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)
Trapped surface formation (Penrose ’74, Eardley & Giddings ’02)
![Page 20: Black hole collisions · 2012. 8. 29. · BHs and higher dimensions 20-24 Sep 2010 | London, UK Black hole collisions Vitor Cardoso (CENTRA/IST & Olemiss) PRL101:161101,2008; PRL103:131102,2009;](https://reader033.vdocuments.mx/reader033/viewer/2022051905/5ff8054bf72a3370b16f09bd/html5/thumbnails/20.jpg)
GR: “Space and time exist together as Spacetime’’
Numerical relativity: reverse this process!
ADM 3+1 decomposition
Arnowitt, Deser, Misner (1962); York (1979); Choquet-Bruh)at, York (1980)
3-metric ij
lapse
shift
i
lapse, shift Gauge
Numerical evolution
![Page 21: Black hole collisions · 2012. 8. 29. · BHs and higher dimensions 20-24 Sep 2010 | London, UK Black hole collisions Vitor Cardoso (CENTRA/IST & Olemiss) PRL101:161101,2008; PRL103:131102,2009;](https://reader033.vdocuments.mx/reader033/viewer/2022051905/5ff8054bf72a3370b16f09bd/html5/thumbnails/21.jpg)
Time projection 0 nnR 02 ij
ijKKKR
Mixed projection 0
nR 0 ij
j
i KDKD
Spatial projection 0
R
]2[)( KKKKRDDKL ijjm
imijjiijt
Hamiltonian constraint
Momentum constraints
Evolution equations
![Page 22: Black hole collisions · 2012. 8. 29. · BHs and higher dimensions 20-24 Sep 2010 | London, UK Black hole collisions Vitor Cardoso (CENTRA/IST & Olemiss) PRL101:161101,2008; PRL103:131102,2009;](https://reader033.vdocuments.mx/reader033/viewer/2022051905/5ff8054bf72a3370b16f09bd/html5/thumbnails/22.jpg)
LEAN code (Sperhake ’07)
BSSN formulation (ADM-like, but strongly hyperbolic)
Puncture initial data (Brandt & Brügmann 1996)
Based on the Cactus computational toolkit
Mesh refinement: Carpet (Schnetter ’04)
Elliptic solver: TwoPunctures (Ansorg 2005)
Numerically very challenging!
Length scales: MADM M0
Horizon Lorentz-contracted “Pancake”
Mergers extremely violent
Substantial amounts of unphysical “junk” radiation
Numerical simulations
![Page 23: Black hole collisions · 2012. 8. 29. · BHs and higher dimensions 20-24 Sep 2010 | London, UK Black hole collisions Vitor Cardoso (CENTRA/IST & Olemiss) PRL101:161101,2008; PRL103:131102,2009;](https://reader033.vdocuments.mx/reader033/viewer/2022051905/5ff8054bf72a3370b16f09bd/html5/thumbnails/23.jpg)
Results Rest
(Witek et al, arXiv:1006.3081 [gr-qc])
![Page 24: Black hole collisions · 2012. 8. 29. · BHs and higher dimensions 20-24 Sep 2010 | London, UK Black hole collisions Vitor Cardoso (CENTRA/IST & Olemiss) PRL101:161101,2008; PRL103:131102,2009;](https://reader033.vdocuments.mx/reader033/viewer/2022051905/5ff8054bf72a3370b16f09bd/html5/thumbnails/24.jpg)
Results
=0.93
High energy head-ons
(Sperhake et al, Phys.Rev.Lett. 101:161101, 2008)
![Page 25: Black hole collisions · 2012. 8. 29. · BHs and higher dimensions 20-24 Sep 2010 | London, UK Black hole collisions Vitor Cardoso (CENTRA/IST & Olemiss) PRL101:161101,2008; PRL103:131102,2009;](https://reader033.vdocuments.mx/reader033/viewer/2022051905/5ff8054bf72a3370b16f09bd/html5/thumbnails/25.jpg)
Waveform is almost just ringdown
Spectrum is flat, in good agreement with ZFL
Cutoff frequency at the lowest quasinormal frequency
![Page 26: Black hole collisions · 2012. 8. 29. · BHs and higher dimensions 20-24 Sep 2010 | London, UK Black hole collisions Vitor Cardoso (CENTRA/IST & Olemiss) PRL101:161101,2008; PRL103:131102,2009;](https://reader033.vdocuments.mx/reader033/viewer/2022051905/5ff8054bf72a3370b16f09bd/html5/thumbnails/26.jpg)
14%
![Page 27: Black hole collisions · 2012. 8. 29. · BHs and higher dimensions 20-24 Sep 2010 | London, UK Black hole collisions Vitor Cardoso (CENTRA/IST & Olemiss) PRL101:161101,2008; PRL103:131102,2009;](https://reader033.vdocuments.mx/reader033/viewer/2022051905/5ff8054bf72a3370b16f09bd/html5/thumbnails/27.jpg)
Plunge, zoom-whirl and scattering
(Sperhake et al, Phys.Rev.Lett. 103:131102, 2008)
Grazing collisions
![Page 28: Black hole collisions · 2012. 8. 29. · BHs and higher dimensions 20-24 Sep 2010 | London, UK Black hole collisions Vitor Cardoso (CENTRA/IST & Olemiss) PRL101:161101,2008; PRL103:131102,2009;](https://reader033.vdocuments.mx/reader033/viewer/2022051905/5ff8054bf72a3370b16f09bd/html5/thumbnails/28.jpg)
More than 25% CM energy radiated for v=0.75 c!
Final BH rapidly spinning
![Page 29: Black hole collisions · 2012. 8. 29. · BHs and higher dimensions 20-24 Sep 2010 | London, UK Black hole collisions Vitor Cardoso (CENTRA/IST & Olemiss) PRL101:161101,2008; PRL103:131102,2009;](https://reader033.vdocuments.mx/reader033/viewer/2022051905/5ff8054bf72a3370b16f09bd/html5/thumbnails/29.jpg)
Light ring & QNMs
ZFL
![Page 30: Black hole collisions · 2012. 8. 29. · BHs and higher dimensions 20-24 Sep 2010 | London, UK Black hole collisions Vitor Cardoso (CENTRA/IST & Olemiss) PRL101:161101,2008; PRL103:131102,2009;](https://reader033.vdocuments.mx/reader033/viewer/2022051905/5ff8054bf72a3370b16f09bd/html5/thumbnails/30.jpg)
Cosmic Censor: as strong as ever
Peak luminosity: Close to Dyson limit c^5/G
Production Cross-section: b/M=2.5/v
Maximum spin: >0.95
Radiated energy: >35% CM
Junk: ~2 Erad, interesting topic for further study
Radiation: Almost just ringdown, relation with ZFL…
![Page 31: Black hole collisions · 2012. 8. 29. · BHs and higher dimensions 20-24 Sep 2010 | London, UK Black hole collisions Vitor Cardoso (CENTRA/IST & Olemiss) PRL101:161101,2008; PRL103:131102,2009;](https://reader033.vdocuments.mx/reader033/viewer/2022051905/5ff8054bf72a3370b16f09bd/html5/thumbnails/31.jpg)
Other spacetimes
![Page 32: Black hole collisions · 2012. 8. 29. · BHs and higher dimensions 20-24 Sep 2010 | London, UK Black hole collisions Vitor Cardoso (CENTRA/IST & Olemiss) PRL101:161101,2008; PRL103:131102,2009;](https://reader033.vdocuments.mx/reader033/viewer/2022051905/5ff8054bf72a3370b16f09bd/html5/thumbnails/32.jpg)
Head-on in D>4 Grazing in D>5
Axial symmetry
Can be reduced to effective 3+1
![Page 33: Black hole collisions · 2012. 8. 29. · BHs and higher dimensions 20-24 Sep 2010 | London, UK Black hole collisions Vitor Cardoso (CENTRA/IST & Olemiss) PRL101:161101,2008; PRL103:131102,2009;](https://reader033.vdocuments.mx/reader033/viewer/2022051905/5ff8054bf72a3370b16f09bd/html5/thumbnails/33.jpg)
D-dimensional Einstein equations imply
![Page 34: Black hole collisions · 2012. 8. 29. · BHs and higher dimensions 20-24 Sep 2010 | London, UK Black hole collisions Vitor Cardoso (CENTRA/IST & Olemiss) PRL101:161101,2008; PRL103:131102,2009;](https://reader033.vdocuments.mx/reader033/viewer/2022051905/5ff8054bf72a3370b16f09bd/html5/thumbnails/34.jpg)
Effective 3+1 system with sources
![Page 35: Black hole collisions · 2012. 8. 29. · BHs and higher dimensions 20-24 Sep 2010 | London, UK Black hole collisions Vitor Cardoso (CENTRA/IST & Olemiss) PRL101:161101,2008; PRL103:131102,2009;](https://reader033.vdocuments.mx/reader033/viewer/2022051905/5ff8054bf72a3370b16f09bd/html5/thumbnails/35.jpg)
![Page 36: Black hole collisions · 2012. 8. 29. · BHs and higher dimensions 20-24 Sep 2010 | London, UK Black hole collisions Vitor Cardoso (CENTRA/IST & Olemiss) PRL101:161101,2008; PRL103:131102,2009;](https://reader033.vdocuments.mx/reader033/viewer/2022051905/5ff8054bf72a3370b16f09bd/html5/thumbnails/36.jpg)
![Page 37: Black hole collisions · 2012. 8. 29. · BHs and higher dimensions 20-24 Sep 2010 | London, UK Black hole collisions Vitor Cardoso (CENTRA/IST & Olemiss) PRL101:161101,2008; PRL103:131102,2009;](https://reader033.vdocuments.mx/reader033/viewer/2022051905/5ff8054bf72a3370b16f09bd/html5/thumbnails/37.jpg)
![Page 38: Black hole collisions · 2012. 8. 29. · BHs and higher dimensions 20-24 Sep 2010 | London, UK Black hole collisions Vitor Cardoso (CENTRA/IST & Olemiss) PRL101:161101,2008; PRL103:131102,2009;](https://reader033.vdocuments.mx/reader033/viewer/2022051905/5ff8054bf72a3370b16f09bd/html5/thumbnails/38.jpg)
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
![Page 39: Black hole collisions · 2012. 8. 29. · BHs and higher dimensions 20-24 Sep 2010 | London, UK Black hole collisions Vitor Cardoso (CENTRA/IST & Olemiss) PRL101:161101,2008; PRL103:131102,2009;](https://reader033.vdocuments.mx/reader033/viewer/2022051905/5ff8054bf72a3370b16f09bd/html5/thumbnails/39.jpg)
Thank you
![Page 40: Black hole collisions · 2012. 8. 29. · BHs and higher dimensions 20-24 Sep 2010 | London, UK Black hole collisions Vitor Cardoso (CENTRA/IST & Olemiss) PRL101:161101,2008; PRL103:131102,2009;](https://reader033.vdocuments.mx/reader033/viewer/2022051905/5ff8054bf72a3370b16f09bd/html5/thumbnails/40.jpg)
LEAN code (Sperhake ’07)
BSSN formulation (ADM-like, but strongly hyperbolic)
Puncture initial data (Brandt & Brügmann 1996)
Based on the Cactus computational toolkit
Mesh refinement: Carpet (Schnetter ’04)
Elliptic solver: TwoPunctures (Ansorg 2005)
Numerically very challenging!
Length scales: MADM M0
Horizon Lorentz-contracted “Pancake”
Mergers extremely violent
Substantial amounts of unphysical “junk” radiation
Numerical simulations