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ILGA. Alessandro D.A.M. Spallicci ESA G. Colombo Senior Research Fellow Paris, 16 December 2003, ASSNA. Perturbation method for black holes binaries and stars capture Département ARTEMIS d'Astrophysique Relativiste Théories, Expériences, Mesures, Instrumentations, Signaux

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  1. ILGA Alessandro D.A.M. Spallicci ESA G. Colombo Senior Research Fellow Paris, 16 December 2003, ASSNA Perturbation method for black holes binaries and stars capture Département ARTEMIS d'Astrophysique Relativiste Théories, Expériences, Mesures, Instrumentations, Signaux Observatoire de la Côte d’Azur Nice

  2. La capture d’étoiles par TN et coalescence TN Régions centrales (plupart) galaxies abritent TN sm (capture pour LISA). Coalescence TN (pour VIRGO) Intérêt (physique TN, champ fort, énergie e.m.) et (plus) forte probabilité de détection Effort international (US - J - CA) pour la forme des trains d’ondes perturbative Lazarus né MPI mais Brownsville (US) pN Faible V et Champ : TNs éloigné Numérique GR Perturbations depuis ~ 3 M (close limit) But: coalescenceet Kerr (VIRGO) Effective 1-body (EOB) convergence ?

  3. 1994 PP 2M 3M 1957 RW 1970 Z 2M

  4. State of the art of coalescence of comparable masses (Baker J., Campanelli M., Lousto C.O., Takahashi R., 2002. Phys. Rev. D, 65, 124012) Two BH Schwarzschild in coalescence = 1 BH Kerr perturbed Initial separation 7.8 M Interfaces pN-FN, FN-CL (+ 3 modules for pN + FN + CL ) 1994

  5. Résultats niçoises Stratégie poursuivi : 1) l'acquisition des compétences (US, J, CA) 2) la production des contributions originelles 1 (contribution JYV): simulation capture étoile, chutant radialement, par un TN Schwarzschild (domaines Laplace et temps) Idéalisation mais: acquisition graduelle des connaissances mouvement Rel. Gen. (non adiabaticité) plongement radial = dernière phase 2 Réaction de radiation: problème important RG (p. 2 c. ?) et gabarits: l’erreur de phase entre signal et gabarit peut empêcher la détection. 2.1 Identification de la géodésique (1er ordre perturbations, 2em déviation trajectoire): 2.2 Normalisation termes divergents (fonction z de Riemann-Hurwitz) sur les modes 2.3 Corrections à des résultats et à des erreurs dans la littérature.

  6. gr-qc/0309039 A. Spallicci, S. Aoudia Amaldi 5th Class. Quantum Grav. (February, 2004) Perturbation method in the assessment of radiation reaction in the capture of stars by black holes J.-Y.Vinet, A. Spallicci (in progress) Numerical simulation of capture of stars by black holes and merge of black holes of comparable masses Artemis: 26 members Projet: Perturbations of black holes and gravitational waves Sofiane Aoudia Alessandro Spallicci Jean-Yves Vinet

  7. Initial data Long term simulations (BH collisions/coalescences) limited by Available memory Instabilities for implementation of fully non linear equations Simulations start at late stage where BH separation is modest Initial value problem: motion – gravitational waves status Apparent horizon Conformal-imaging Methods Puncture

  8. Standard 3+1 Hypersurfaces slices labeled by t nm future-pointing timelike unit normal to the slice nm = - aÑm t proper interval ds = a dt a lapse function But in general time vector tm = a nm + bmbmnm= 0 bm shift vector gij metric of the spacelike hypersurface induced by gmn (conformally flat) ds2 = - a dt2 + gij (dxi dxj + bibj dt2 + 2bi dxj dt) Slice extrinsic curvature kij = - ½ Lgij L Lie derivative along nm Lx Minimal set initial data gij and kij 6 evolution 4 constraint equations Apparent horizon kii = 0 gij = -4Gij kij = -2 Kij Conformal-imaging Methods Gij 3D flat space metric Puncture  conformal factor Kij traceless conformal extr. curv. Vacuum momentum constraint Ñj Kij = 0 Ñj flat space covariant deriv.

  9. Perturbations in time domain Conformally flatgij and longitudinalkij (CFL) data = no reproduction of (Lousto C.O., Price R.H., 1997. Phys. Rev. D, 56, 6439) numerical results differences of extrinsic curvature (numerical and CFL) Failure CFL = near-field close to test mass Solution 1 (Lousto C.O., Price R.H., 1998. Phys. Rev. D, 57, 1073) convective metric time derivative proportional to 4v of test mass Solution 2 (Martel K., Poisson E., 2002. Phys. Rev. D, 66, 084001) parametrisedtime symmetric initial data

  10. Polar perturbations Tensorial harmonics First paper Regge-Wheeler 1957 46 years of reliable results

  11. Regge-Wheeler-Zerilli equation Stability of BH Close and far BH V=0

  12. Initial data (MP) kijgij are specified on 3D spacelike hypersurface but must satisfy Hamiltonian and momentum non linear constraints 3difficulties (2 for nl): non trivial solutions hard to find, non-uniqueness, physicality (How to represent an initial amount of gravitational radiation) Brill-Linquist kij= 0 at t = 0 for time symmetry (H1=0) For H2 = c K conformally flat metric (c=1)

  13. Hamiltonian constraint r = r/2M Z(t-h,r*) = Z(t+h,r*) for t = 0 for time simmetry. This relation is valid if the cell is not crossed by test mass.

  14. Analyse de bruit LAL Orsay Données initiales LUTH Paris Rayonnement chute radial Schwarzschild JYV-AS Gabarits Applicabilité M1 = M2 et plongeon Mouvement étoile chute radial Schwarzschild AS Élaboration signal ECM FM Kerr Renormalisation chute radiale Schwarzschild SA-AS Développement pour Virgo

  15. Conclusions Petite équipe (modélisation des sources): besoin des humains plus que des machines Seule équipe en France-Europe (par contre ES, J,CA): nécessité pour la détection Autres méthodes (pN et numérique) déjà en France En plus non compatibles avec petite équipe, inefficaces ou faux pour la fusion Perturbations utiles à comprendre physique Recommandation ASSNA Coopération LUTH et autres numériciens

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