Caltech 01/2002L 1 Numerical Relativity: Promises, Challenges, Status and Prospects Luis Lehner (UBC-PIMS-CITA) Caltech 01/2002L 2 Outline Promises : why we do it Challenges : what/how we do; problems? Status where we are at Prospects what can we do now/later Caltech 01/2002L 3 NRwhy Numerical construction of spacetimes Support? Critical Phenomena in GR; (1D) [Choptuik] Cauchy Horizons in charged/rot BHs. (1D) [Piran,Brady,etc..] Toroidal E.H. [Shapiro-Teukolsky] analytical understanding [Shapiro-Teukolsky-Winicour] generic [L.L.,Husa, Winicour] If we think hard enough we wont need a computer With the right resources we can simulate situations we can't even begin to think through, and thereby provide us with completely new and unexpected things to think about Caltech 01/2002L 4 Promises Strongly gravitating/highly dynamical spacetimes GW detection GW astronomy Critical behavior in higher dim. astrophysically relevant systems Spacetimes in the large No hair? Is there a I +,i + ? How about peeling? Help out in quantum gravity? Caltech 01/2002L 5 Meeting the challenge? Solve G T through simulations nonlinear PDE system (10 eqns) evolution (?) Initial and boundary data Singularities Coordinate issues Non-vacuum Fluid?, shocks (and all that) Initial and boundary data + Computat Resources: ALGORITHM ISSUES (too?) Many options! One size doesnt fit all Caltech 01/2002L 6 Status Approaches and particular issues 3+1; characteristic and Conformal Einstein approaches Representative examples Where we are and (some of) what lies head Caltech 01/2002L 7 Singularities Tricky to handle analytically Computational nightmare! What to do? Avoid Excise (in principle, OK, if cosmological censorship ) Event Horizon Trapped Surface Surface of Star Event Horizon Trapped Surface Surface of Star Caltech 01/2002L 8 Singularity Excision Introduces an inner bdry: boundary values? Use eqns (exploiting causal structure inside EH) Prevent leakage to outside-world Used to achieve rigorously stable evols Routinely in 1D (eg, critical phenomena) 2D in new efforts 3D charact. formulation (single BHs forever [Bishop,Gomez,LL, Winicour 98]) 3+1, getting there.. Caltech 01/2002L 9 GR Hydrodynamics Continuity and Bianchi identities: Requirement: . Numerical energy loss due to baryon non-conservation must be (quite) less than GW emission Conservation form of general relativistic hydro. Use numerical techniques to prevent high frequency. Integrate along fluid characteristic (to solve Rieman problem) Primitive recovery: in general, expensive inversion process but g 00 =0 inversion trivial (explicit) if polytropic eqn of state Caltech 01/2002L approach Several Flavors: ADM; BSSN; EC, Ashtekar vars, ADM: Geometrical: oldest BSSN: gauge separating: very popular, close to ADM Hyperbolic: well posedness and cleaner boundary treament Coordinate conditions defined by i ID needs to satisfy constraints. Caltech 01/2002L status (II) 1.Coordinate conditions: ISO co-moving coordinates: On-going studies. Explicit display of causality inside EH 2.Boundary conditions: Far-out is not enough anymore Consistency / Avoid-reflections 3. ID : Lichnerowicz-York app: Moving to realistic set-up Not assuming conformal flatness and/or time-symmetry. (Kerr cant be defined this way. Garat-Price 00) Several proposals [Bishop et.al, Huq, et.al Marronetti-Matzner;Dain] Caltech 01/2002L 12 ADM formulation. Singularities excised ID: seed metric superposed Kerr bhs (in IEF coordinates) Coord. Conds: supersposed conditions of isolated black holes. OB conditions: blending (Dirichlet conds + viscous damping in a neighb) Full evolution: Grazing collision of BHs Caltech 01/2002L 13 How does it look? (g xx | z=0 ) Caltech 01/2002L 14 How does it look? (g xx | z=0 ) Caltech 01/2002L 15 Grazing collisions (continued) AppHorAppHor Apparent horizons used for: Singularity locations Monitor surface area Instabilities dominant at t>20M Numerical dissipation can control these, but too much influence on the outcome!. Requirement: numerical dissipation