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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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Ilga

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


La capture d toiles par tn et coalescence tn

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 ?


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1994 PP

2M

3M

1957 RW

1970 Z

2M


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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


R sultats ni oises

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.


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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


Initial data

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


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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.


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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


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Polar perturbations

Tensorial harmonics

First paper Regge-Wheeler 1957

46 years of reliable results


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Regge-Wheeler-Zerilli equation

Stability of BH

Close and far BH V=0


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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)


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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.


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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


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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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