8 research outputs found
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
A fully relativistic radial fall
Radial fall has historically played a momentous role. It is one of the most
classical problems, the solutions of which represent the level of understanding
of gravitation in a given epoch. A {\it gedankenexperiment} in a modern frame
is given by a small body, like a compact star or a solar mass black hole,
captured by a supermassive black hole. The mass of the small body itself and
the emission of gravitational radiation cause the departure from the geodesic
path due to the back-action, that is the self-force. For radial fall, as any
other non-adiabatic motion, the instantaneous identity of the radiated energy
and the loss of orbital energy cannot be imposed and provide the perturbed
trajectory. In the first part of this letter, we present the effects due to the
self-force computed on the geodesic trajectory in the background field.
Compared to the latter trajectory, in the Regge-Wheeler, harmonic and all
others smoothly related gauges, a far observer concludes that the self-force
pushes inward (not outward) the falling body, with a strength proportional to
the mass of the small body for a given large mass; further, the same observer
notes an higher value of the maximal coordinate velocity, this value being
reached earlier on during infall. In the second part of this letter, we
implement a self-consistent approach for which the trajectory is iteratively
corrected by the self-force, this time computed on osculating geodesics.
Finally, we compare the motion driven by the self-force without and with
self-consistent orbital evolution. Subtle differences are noticeable, even if
self-force effects have hardly the time to accumulate in such a short orbit.Comment: To appear in Int. J. Geom. Meth. Mod. Phy
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
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 and self-force computation for a compact object around a super-massive black hole
Cette thèse s'inscrit dans le cadre de la modélisation des ondes gravitationnelles et du mouvement relativiste associés aux systèmes binaires à grand rapport de masses (Extreme Mass Ratio Inspiral - EMRI). Ces systèmes sont formés d'un trou noir super massif autour duquel gravite un objet compact de masse stellaire. Dans le formalisme de la théorie perturbative des trous noirs, on développe une méthode numérique qui calcule les formes d'ondes produites par une particule ponctuelle en orbite autour d'un trou noir de Schwarzschild. Il s'agit de résoudre l'équation d’onde de Regge-Wheeler-Zerilli dans le domaine temporel dont la solution, invariante de jauge, peut être reliée aux modes de polarisation, à l'énergie et au moment cinétique emporté par les ondes gravitationnelles. En réaction à l'énergie et au moment perdu, la trajectoire de la particule est affectée au cours du temps. Dans le cadre du formalisme de MiSATaQuWa, on calcule la force propre agissant sur une particule, initialement au repos, est en chute libre sur un trou noir de Schwarzschild. Nous montrons comment cette quantité est définie dans la jauge de Regge-Wheeler par le biais de la régularisation mode-sum. L'effet de la force propre sur le mouvement de la particule est ensuite pris en compte de façon itérative et auto-consistante grâce à un algorithme utilisant une méthode d'orbites osculatrices que nous avons développé. Nous quantifions cet effet en calculant soit la déviation orbitale par rapport au mouvement géodésique, soit les formes d'ondes perturbées et l'énergie rayonnée associée.This thesis focuses on modelling the gravitational waves and the relativistic motion associated to Extreme Mass Ratio Inspiral (EMRI) systems. These systems consist of a stellar mass compact object gravitationally captured by a super-massive black hole. In black hole perturbation theory, we further develop a numerical method which computes waveforms generated by a point mass particle orbiting a Schwarzschild black hole. The Regge-Wheeler-Zerilli wave equation is solved in time domain. The gauge invariant solution is related to the polarisation modes, the energy and the angular momentum carried by the gravitational waves. In reaction to the energy and the moment lost, the trajectory is modified all along. In the MiSaTaQuWa formalism, we compute the self-force acting upon a point particle which is initially at rest, and then falling into a Schwarzschild black hole. We show how this quantity is defined in the Regge-Wheeler gauge by using the mode-sum regularisation technique. We take into account the self-force effect on the motion of the particle by using an iterative and osculating orbit method conceived herein. We quantify the orbital deviation with respect to the geodesic motion, but also the perturbed wave forms and the associated radiated energy
Ondes gravitationnelles et calcul de la force propre pour un astre compact en mouvement autour d'un trou noir supermassif
This thesis focuses on modelling the gravitational waves and the relativistic motion associated to Extreme Mass Ratio Inspiral (EMRI) systems. These systems consist of a stellar mass compact object gravitationally captured by a super-massive black hole. In black hole perturbation theory, we further develop a numerical method which computes waveforms generated by a point mass particle orbiting a Schwarzschild black hole. The Regge-Wheeler-Zerilli wave equation is solved in time domain. The gauge invariant solution is related to the polarisation modes, the energy and the angular momentum carried by the gravitational waves. In reaction to the energy and the moment lost, the trajectory is modified all along. In the MiSaTaQuWa formalism, we compute the self-force acting upon a point particle which is initially at rest, and then falling into a Schwarzschild black hole. We show how this quantity is defined in the Regge-Wheeler gauge by using the mode-sum regularisation technique. We take into account the self-force effect on the motion of the particle by using an iterative and osculating orbit method conceived herein. We quantify the orbital deviation with respect to the geodesic motion, but also the perturbed wave forms and the associated radiated energy.Cette thèse s'inscrit dans le cadre de la modélisation des ondes gravitationnelles et du mouvement relativiste associés aux systèmes binaires à grand rapport de masses (Extreme Mass Ratio Inspiral - EMRI). Ces systèmes sont formés d'un trou noir super massif autour duquel gravite un objet compact de masse stellaire. Dans le formalisme de la théorie perturbative des trous noirs, on développe une méthode numérique qui calcule les formes d'ondes produites par une particule ponctuelle en orbite autour d'un trou noir de Schwarzschild. Il s'agit de résoudre l'équation d'onde de Regge-Wheeler-Zerilli dans le domaine temporel dont la solution, invariante de jauge, peut être reliée aux modes de polarisation, à l'énergie et au moment cinétique emporté par les ondes gravitationnelles. En réaction à l'énergie et au moment perdu, la trajectoire de la particule est affectée au cours du temps. Dans le cadre du formalisme de MiSATaQuWa, on calcule la force propre agissant sur une particule, initialement au repos, est en chute libre sur un trou noir de Schwarzschild. Nous montrons comment cette quantité est définie dans la jauge de Regge-Wheeler par le biais de la régularisation mode-sum. L'effet de la force propre sur le mouvement de la particule est ensuite pris en compte de façon itérative et auto-consistante grâce à un algorithme utilisant une méthode d'orbites osculatrices que nous avons développé. Nous quantifions cet effet en calculant soit la déviation orbitale par rapport au mouvement géodésique, soit les formes d'ondes perturbées et l'énergie rayonnée associée
Self-force driven motion in curved spacetime
International audienceWe adopt the Dirac-Detweiler-Whiting radiative and regular effective field in curved spacetime. Thereby, we derive straightforwardly the first order perturbative correction to the geodesic of the background in a covariant form, for the extreme mass ratio two-body problem. The correction contains the self-force contribution and a background metric dependent term