A source-free integration method for black hole perturbations and self-force computation: Radial fall

Perturbations of Schwarzschild-Droste black holes in the Regge-Wheeler gauge benefit from the availability of a wave equation and from the gauge invariance of the wave function, but lack smoothness. Nevertheless, the even perturbations belong to the C\textsuperscript{0} continuity class, if the wave function and its derivatives satisfy specific conditions on the discontinuities, known as jump conditions, at the particle position. These conditions suggest a new way for dealing with finite element integration in time domain. The forward time value in the upper node of the $(t, r^*$) grid cell is obtained by the linear combination of the three preceding node values and of analytic expressions based on the jump conditions. The numerical integration does not deal directly with the source term, the associated singularities and the potential. This amounts to an indirect integration of the wave equation. The known wave forms at infinity are recovered and the wave function at the particle position is shown. In this series of papers, the radial trajectory is dealt with first, being this method of integration applicable to generic orbits of EMRI (Extreme Mass Ratio Inspiral).Comment: This arXiv version differs from the one to be published by Phys. Rev. D for the use of British English and other minor editorial difference

Towards a self-consistent orbital evolution for EMRIs

We intend to develop part of the theoretical tools needed for the detection of gravitational waves coming from the capture of a compact object, 1-100 solar masses, by a Supermassive Black Hole, up to a 10 billion solar masses, located at the centre of most galaxies. The analysis of the accretion activity unveils the star population around the galactic nuclei, and tests the physics of black holes and general relativity. The captured small mass is considered a probe of the gravitational field of the massive body, allowing a precise measurement of the particle motion up to the final absorption. The knowledge of the gravitational signal, strongly affected by the self-force - the orbital displacement due to the captured mass and the emitted radiation - is imperative for a successful detection. The results include a strategy for wave equations with a singular source term for all type of orbits. We are now tackling the evolution problem, first for radial fall in Regge- Wheeler gauge, and later for generic orbits in the harmonic or de Donder gauge for Schwarzschild-Droste black holes. In the Extreme Mass Ratio Inspiral, the determination of the orbital evolution demands that the motion of the small mass be continuously corrected by the self-force, i.e. the self-consistent evolution. At each of the integration steps, the self-force must be computed over an adequate number of modes; further, a differential-integral system of general relativistic equations is to be solved and the outputs regularised for suppressing divergences. Finally, for the provision of the computational power, parallelisation is under examination.Comment: IX Lisa Conference (held the 21-25 May 2012 in Paris) Proceedings by the Astronomical Society of the Pacific Conference Seri

Fourth order indirect integration method for black hole perturbations: even modes

On the basis of a recently proposed strategy of finite element integration in time domain for partial differential equations with a singular source term, we present a fourth order algorithm for non-rotating black hole perturbations in the Regge-Wheeler gauge. Herein, we address even perturbations induced by a particle plunging in. The forward time value at the upper node of the $(r^*,t)$ grid cell is obtained by an algebraic sum of i) the preceding node values of the same cell, ii) analytic expressions, related to the jump conditions on the wave function and its derivatives, iii) the values of the wave function at adjacent cells. In this approach, the numerical integration does not deal with the source and potential terms directly, for cells crossed by the particle world line. This scheme has also been applied to circular and eccentric orbits and it will be object of a forthcoming publication.Comment: This series of papers deals with EMRI for LISA. With the respect to the v1 version, the algorithm has been improved; convergence tests and references have been added; v2 is composed by 23 pages, and 6 figures. Paper accepted by Class. Quantum Gravity for the special issue on Theory Meets Data Analysis at Comparable and Extreme Mass Ratios (Capra and NRDA) at Perimeier Institute in June 201

Gravitational waves: search results, data analysis and parameter estimation

The Amaldi 10 Parallel Session C2 on gravitational wave (GW) search results, data analysis and parameter estimation included three lively sessions of lectures by 13 presenters, and 34 posters. The talks and posters covered a huge range of material, including results and analysis techniques for ground-based GW detectors, targeting anticipated signals from different astrophysical sources: compact binary inspiral, merger and ringdown; GW bursts from intermediate mass binary black hole mergers, cosmic string cusps, core-collapse supernovae, and other unmodeled sources; continuous waves from spinning neutron stars; and a stochastic GW background. There was considerable emphasis on Bayesian techniques for estimating the parameters of coalescing compact binary systems from the gravitational waveforms extracted from the data from the advanced detector network. This included methods to distinguish deviations of the signals from what is expected in the context of General Relativity

Advanced VIRGO: detector optimization for gravitational waves by inspiralling binaries

For future configurations, we study the relation between the abatement of the noise sources and the Signal to Noise Ratio (SNR) for coalescing binaries. Our aim is not the proposition of a new design, but an indication of where in the bandwidth or for which noise source, a noise reduction would be most efficient. We take VIRGO as the reference for our considerations, solely applicable to the inspiralling phase of a coalescing binary. Thus, only neutron stars and small black holes of few solar masses are encompassed by our analysis. The contributions to the SNR given by final merge and quasi-normal ringing are neglected. It is identified that i) the reduction in the mirror thermal noise band provides the highest gain for the SNR, when the VIRGO bandwidth is divided according to the dominant noises; ii) it exists a specific frequency at which lies the potential largest increment in the SNR, and that the enlargement of the bandwidth, where the noise is reduced, produces a shift of such optimal frequency to higher values; iii) the abatement of the pendulum thermal noise provides the largest, but modest, gain, when noise sources are considered separately. Our recent astrophysical analysis on event rates for neutron stars leads to a detection rate of one every 148 or 125 years for VIRGO and LIGO, respectively, while a recently proposed and improved, but still conservative, VIRGO configuration would provide an increase to 1.5 events per year. Instead, a bi-monthly event rate, similar to advanced LIGO, requires a 16 times gain. We analyse the 3D (pendulum, mirror, shot noises) parameter space showing how such gain could be achieved.Comment: Change of title (Virgo detector optimization for gravitational waves by coalescing binaries) and partially of text. 6 figure

Science with the space-based interferometer eLISA. I: Supermassive black hole binaries

We compare the science capabilities of different eLISA mission designs, including four-link (two-arm) and six-link (three-arm) configurations with different arm lengths, low-frequency noise sensitivities and mission durations. For each of these configurations we consider a few representative massive black hole formation scenarios. These scenarios are chosen to explore two physical mechanisms that greatly affect eLISA rates, namely (i) black hole seeding, and (ii) the delays between the merger of two galaxies and the merger of the black holes hosted by those galaxies. We assess the eLISA parameter estimation accuracy using a Fisher matrix analysis with spin-precessing, inspiral-only waveforms. We quantify the information present in the merger and ringdown by rescaling the inspiral-only Fisher matrix estimates using the signal-to-noise ratio from non-precessing inspiral-merger-ringdown phenomenological waveforms, and from a reduced set of precessing numerical relativity/post-Newtonian hybrid waveforms. We find that all of the eLISA configurations considered in our study should detect some massive black hole binaries. However, configurations with six links and better low-frequency noise will provide much more information on the origin of black holes at high redshifts and on their accretion history, and they may allow the identification of electromagnetic counterparts to massive black hole mergers.Comment: 28 pages, 13 figures, 7 table

Capture des étoiles par les trous noirs et ondes gravitationnelles

NICE-BU Sciences (060882101) / SudocSudocFranceF

Perturbation method in the assessment of radiation reaction in the capture of stars by black holes

10 pages, no figures. Email: [email protected] To appear on Classical and Quantum Gravity March 2004This work deals with the motion of a radially falling star in Schwarzschild geometry and correctly identifies radiation reaction terms by the perturbative method. The results are: i) identification of all terms up to first order in perturbations, second in trajectory deviation, and mixed terms including lowest order radiation reaction terms; ii) renormalisation of all divergent terms by the $\zeta$ Riemann and Hurwitz functions. The work implements a method previously identified by one of the authors and corrects some current misconceptions and results