Numerical Relativity: from Black Hole collisions to the Quark-Gluon Plasma

Transcription

1 Numerical Relativity: from Black Hole collisions to the Quark-Gluon Plasma Miguel Zilhão Departament de Física Quàntica i Astrofísica & Institut de Ciències del Cosmos, Universitat de Barcelona February , ICCUB Winter Meeting 2017 Miguel Zilhão (UB) Numerical Relativity ICCUB Winter Meeting / 26

2 Outline Contents 1 Introduction Milestones 2 Formalism Cauchy-based approach Characteristic-based approach 3 Final remarks Miguel Zilhão (UB) Numerical Relativity ICCUB Winter Meeting / 26

3 Introduction Outline 1 Introduction Milestones 2 Formalism Cauchy-based approach Characteristic-based approach 3 Final remarks Miguel Zilhão (UB) Numerical Relativity ICCUB Winter Meeting / 26

4 Introduction What is numerical relativity Numerical Relativity: solving numerically the full GR equations, typically for dynamical spacetimes in the strong field regime, where no approximations hold. Goals: understanding gravity in its full non-linear glory. Challenges: very difficult problem... Miguel Zilhão (UB) Numerical Relativity ICCUB Winter Meeting / 26

5 Introduction Why numerical relativity Study of systems with strong and dynamical gravitational fields Gravitational radiation Astrophysics, gravitational wave astronomy Mathematical and theoretical Physics Cosmic censorship, Instabilities (Black hole interior, Myers-Perry) High-energy particle systems AdS/CFT correspondence; Black hole production at the LHC; Miguel Zilhão (UB) Numerical Relativity ICCUB Winter Meeting / 26

6 Introduction Gravitational waves Accelerated bodies emit gravitational radiation Interact weakly with matter carry unique information about astronomical phenomena New window to the universe Difficult to detect directly Need theoretical models for the structure of the waveform Miguel Zilhão (UB) Numerical Relativity ICCUB Winter Meeting / 26

7 Introduction Gravitational waves First detected indirectly by measurements of the Hulse-Taylor binary system (1993 Nobel Prize) Detected directly by the LIGO and Virgo collaborations on 14 September 2015 Miguel Zilhão (UB) Numerical Relativity ICCUB Winter Meeting / 26

8 Introduction Mathematical and theoretical Physics Cosmic censorship hypothesis: does it hold under extreme conditions? [Sperhake, Cardoso, Pretorius, Berti, Gonzales, 2008] No no-hair theorem for D > 4 black hole solutions with non-spherical topology. (Non-)Linear stability of higher-dimensional black objects: Black string [Choptuik, Lehner, Olabarrieta, Petryk, Pretorius, Villegas, 2003 ] [Lehner, Pretorius 2010] Myers-Perry black hole [Shibata & Yoshino, 2010] Black ring... [Emparan & Reall, 2008] Miguel Zilhão (UB) Numerical Relativity ICCUB Winter Meeting / 26

9 Introduction Ultra-relativistic heavy-ion collisions two nuclei approach, collide, form a QGP, the QGP expands and hadronizes, finally hadrons rescatter and freeze out Miguel Zilhão (UB) Numerical Relativity ICCUB Winter Meeting / 26

10 Introduction AdS/CFT N = 4 super-yang-mills is dual to IIB string theory on AdS 5 S 5 [Maldacena, Gubser, Klebanov, Polyakov, Witten 1998] We can learn about strongly coupled phenomena through gravity computations Miguel Zilhão (UB) Numerical Relativity ICCUB Winter Meeting / 26

11 Introduction AdS/CFT QCD non-conformal confinement not supersymmetric N = 4 SYM conformally invariant no confinement supersymmetric Miguel Zilhão (UB) Numerical Relativity ICCUB Winter Meeting / 26

12 Outline Introduction Milestones 1 Introduction Milestones 2 Formalism Cauchy-based approach Characteristic-based approach 3 Final remarks Miguel Zilhão (UB) Numerical Relativity ICCUB Winter Meeting / 26

13 History and milestones Introduction Milestones 1915 Einstein s equations are published Einstein 1964 First documented attempts at numerical simulations: evolving Hahn & Lindquist two wormholes 1976 Head-on collision of two black holes (in axisymmetry) Smarr & Eppley 1990 s "Binary Black Hole Grand Challenge Project" Matzner et al 1993 Critical phenomena in gravitational collapse Choptuik 1997 Release of Cactus 1.0 Seidel et al 1998 Generic (3D) single BH simulation (using a characteristic approach) Gomez et al 1999 BSSN evolution system Baumgarte & Shapiro; Shibata & Nakamura 2005 First simulations of BH binaries through inspiral, merger and Pretorius ringdown (Two-body problem in GR) (GHG code) 2006 "Moving puncture" simulations (BSSN code) UTB/RIT; NASA Goddard 2008 High-energy collision of two BHs Berti, Cardoso, Gonzalez, Sperhake, Pretorius 2010 Collision of gravitational shock waves in AAdS5 spacetimes Chesler & Yaffe (2+1 code) 2010 Black hole collisions in higher dimensions Witek, M.Z. et al; Yoshino & Shibata 2012 Simulations of AAdS5 spacetimes (GHG code) Bantilan, Pretorius, Gubser 2015 Off-center collisions of shock waves in AAdS5 spacetimes (4+1 code) Chesler &Yaffe Miguel Zilhão (UB) Numerical Relativity ICCUB Winter Meeting / 26

14 Formalism Outline 1 Introduction Milestones 2 Formalism Cauchy-based approach Characteristic-based approach 3 Final remarks Miguel Zilhão (UB) Numerical Relativity ICCUB Winter Meeting / 26

15 Formalism Einstein s equations R µν 1 2 R g µν = 8π T µν Miguel Zilhão (UB) Numerical Relativity ICCUB Winter Meeting / 26

16 Formalism Einstein s equations Γ α βγ = 1 g αδ ( γ g δβ + β g δγ δ g βγ ) 2 δ=t,x 1,...,x D 1 8πT αβ = [ δ Γ δ αβ αγ δ δβ + ] (Γ δ αβ Γγ δγ Γδ γβ Γγ δα ) δ γ { 1 2 g αβ g [ δγ µ Γ µ δγ δγ µ µδ + ] } (Γ µ δγ Γν µν Γ µ νγγ ν µδ ) µ ν δ,γ Miguel Zilhão (UB) Numerical Relativity ICCUB Winter Meeting / 26

17 Outline Formalism Cauchy-based approach 1 Introduction Milestones 2 Formalism Cauchy-based approach Characteristic-based approach 3 Final remarks Miguel Zilhão (UB) Numerical Relativity ICCUB Winter Meeting / 26

18 Formalism Cauchy-based approach 3+1 decomposition We write the metric as ds 2 = α 2 dt 2 + γ ij (dx i + β i dt ) ( ) dx j + β j dt, γ ij is the metric on surfaces of t = const K ij is the extrinsic curvature Miguel Zilhão (UB) Numerical Relativity ICCUB Winter Meeting / 26

19 Formalism Cauchy-based approach ADM-York evolution equations Evolution equations ( t Lβ ) γij = 2αKij, h ( t Lβ ) Kij = i j α + α Rij + KKij 2Kik K k j i 8π (S E)γij 2Sij, + D 2 Constraints R + K 2 Kij K ij = 16πE, j K ij γ ij K = 8πpi. Miguel Zilhão (UB) Numerical Relativity ICCUB Winter Meeting / 26

20 Formalism Electromagnetic analogy Cauchy-based approach Evolution equations Constraints t E + H = 4π j t H + E = 0 E = 4πρ H = 0 Miguel Zilhão (UB) Numerical Relativity ICCUB Winter Meeting / 26

21 Examples Formalism Cauchy-based approach Inspiral Demo (Einstein Toolkit) Kick configuration [RIT] Miguel Zilhão (UB) Numerical Relativity ICCUB Winter Meeting / 26

22 Outline Formalism Characteristic-based approach 1 Introduction Milestones 2 Formalism Cauchy-based approach Characteristic-based approach 3 Final remarks Miguel Zilhão (UB) Numerical Relativity ICCUB Winter Meeting / 26

23 Formalism Characteristic-based approach Characteristic Initial-Boundary Value Problem D = 5 metric in Eddington-Finkelstein coordinates ( ds 2 = Adt 2 + Σ 2 e B dx 2 + e 2B dz 2) + 2dt(dr + Fdz), Schematic evolution equations: r S = H S (S, B) t r B = H B (B, S, t B) Miguel Zilhão (UB) Numerical Relativity ICCUB Winter Meeting / 26

24 Formalism Characteristic-based approach Example: shockwave collision in AdS 1.0 φ M =10, Lφ 0 =2, L 4 A =1, σ/l =0.32 t =10L t = ɛ/φ z/l Miguel Zilhão (UB) Numerical Relativity ICCUB Winter Meeting / 26

25 Final remarks Outline 1 Introduction Milestones 2 Formalism Cauchy-based approach Characteristic-based approach 3 Final remarks Miguel Zilhão (UB) Numerical Relativity ICCUB Winter Meeting / 26

26 Final remarks Final Remarks Numerical modelling of gravitational systems is as old as the advent of computing itself breakthroughs in NR marked a phase transition in the field. This allowed for the discovery of unexpected results (superkicks of thousands of km/s, zoom-whirl behaviour, etc.) Motivation for long-term NR efforts came originally mostly from the modeling of gravitation wave sources. Nowadays, NR is finding applications to other fields, such as high-energy physics, higherdimensional gravity, and AdS/CFT. What surprises will next 10 years of NR reveal? [M. Thierfelder] Miguel Zilhão (UB) Numerical Relativity ICCUB Winter Meeting / 26

27 Additional material Outline 4 Additional material Miguel Zilhão (UB) Numerical Relativity ICCUB Winter Meeting / 4

28 Additional material D = 4 Boosted collisions [Sperhake et al 2008] [U. Sperhake] Miguel Zilhão (UB) Numerical Relativity ICCUB Winter Meeting / 4

29 Additional material Grazing collisions Two distinct end-states to BH scattering problem: one BH or two BHs Near the critical impact parameter: sensitivity to initial conditions enhanced gravitational wave emission (even in scattering cases) Miguel Zilhão (UB) Numerical Relativity ICCUB Winter Meeting / 4

30 Additional material Whirl, merger [U. Sperhake] Miguel Zilhão (UB) Numerical Relativity ICCUB Winter Meeting / 4