1 GWDAW9 Annecy S. Aoudia, A. Spallicci Decembre 2004 Issues on radiation reaction for capture LISA sources by super-massive black holes With reference to the plunge, or ideally radial trajectories, we are currently studying the non-radiative modes (L=0,1), the liaisons between the self-force and the pragmatic approaches and the proper development of the latter. Issues of fundamental physics and considerations on detection (SNR and influence of radiation reaction on waveforms) emerge. Spallicci A., Aoudia S., Class. Quantum. Grav., 21, S563. UMR 6162, Dépt ARTEMIS d’Astrophysique Relativiste Observatoire de la Côte d’Azur (OCA) Nice France

2 RR Plunging phase and radial fall ? Fundamental physics I.Classical problem of gravitation! (apple falling) II.Radiation reaction not adiabatic! III.Most rr (in radial fall) between 4M - 2M IV.pN N/A (convergence, v/c) At 10 M D pN = quadrupole Review of what do we know and what are we doing in Nice V.Entry problem, before tackling close and scattered orbits VI.Plunging and signal discrimination (known waveform) No 17 parameters + etc. problem VII.Plunging only visible (??) part of capture for low-end LISA frequency spectrum ( M Ÿ ) VIII.All captures finish in a plunge IX.Applicable to Last Phase in Coalescence (close limit) X.It’s all quasinormal.

3 Self force inst tail xx0x0  Some spacetimes determine tail effects when crossed by perturbations PM sign indicates derivative forward or backward r p L = l + 1/2 Work J.-Y. Vinet for Y determination ongoing  Poster Checked OK 35

4 Linearisation allows splitting of orders 0 and 1 Perturbations h mn << BH metric h Geometry = Matter Perturbed Geometry = Perturbing Matter Spherical symmetry  Rotationally invariant operator on h mn, equal to the variation of the energy momentum tensor, both expressed in spherical harmonics:

5 The pragmatic approach (geodesic or minimal action) a 1-5 represent the unperturbed field at the perturbed trajectory a 6 represent the perturbed field at the unperturbed trajectory a 7-8 represent the perturbed field at the perturbed trajectory (a 9 represent quadratic first order perturbations - optional -) a 1 correction Extension to 6 new terms Numerical simulation  Y + derivatives  H 0 H 1  a terms  D r p radiation reaction Work J.-Y. Vinet for Y determination ongoing  Poster

6 B C A a 9 (h 2 ) 2004.Class. Quantum. Grav., 21, S563.

7 Renormalisation This term needs renormalisation Hurwitz z function Riemann z function Similar behaviour for a 7 a 8 a 9 a 6-9 are L dependent terms. Each a is finite, but all together form a divergence (same pattern for L  oo 2004.Class. Quantum. Grav., 21, S563.

8 Brans-Dicke theory and capture (Poster B. Chauvineau, AS, J.-D. Fournier) BD non equal GR when regime is out of stationarity Unconsidered effect so far (apart from monopole, dipole, less than c speed features) f A B (B) A(+B) A t Schwarzschild Slope change l = l (M)

9 Conclusions / Status Two methods for radiation reaction: Self-force: Partial confirmation of mode-sum renormalisation results of other groups (A,B,C instantaneous values) Pragmatic: richer geodesic (addition of 6 terms) Riemann-Hurwitz renormalisation extended (3 terms) Connection self-force / pragmatic under investigation Non radiative modes (L=0,1) analysis under going Capture is a rich field for research (Fundamental physics, Relativistic Astrophysics, Data Analysis)

10 SPALLICCI A. Aoudia S., Perturbation method in the assessment of radiation reaction in the capture of stars by black holes, Class. Quantum. Grav., 21, S563. gr- qc/ SPALLICCI A Radiation reaction in free fall from perturbative geodesic equations in spherical coordinates, 8th Marcel Grossmann Meeting, June 1997, Jerusalem, T. Piran, R. Ruffini Eds., World Scientific, SPALLICCI A., On the perturbed Schwarzschild geometry for determination of particle motion, 2nd Amaldi Conf. on Gravitational Waves, 1-4 July 1997, Cern Geneve, E. Coccia, G. Veneziano, G. Pizzella Eds., World Scientific, 303. SPALLICCI A., Analytic solution of Regge-Wheeler differential equation for black hole perturbations in radial coordinate and time domains, Recent Developments in General Relativity, 13th Italian Conf. on General Rel. and Grav. Physics, September 1998 Monopoli (Bari), B. Casciaro, D. Fortunato, M. Francaviglia, A. Masiello, Eds., Springer, 371.