15 research outputs found
A nonlinear scalar model of extreme mass ratio inspirals in effective field theory II. Scalar perturbations and a master source
The motion of a small compact object (SCO) in a background spacetime is
investigated further in a class of model nonlinear scalar field theories having
a perturbative structure analogous to the General Relativistic description of
extreme mass ratio inspirals (EMRIs). We derive regular expressions for the
scalar perturbations generated by the SCO's motion valid through third order in
, the size of the SCO to the background curvature length scale. Our
expressions are compared to those calculated through second order in
by Rosenthal in [E. Rosenthal, CQG 22, S859 (2005)] and found to agree but our
procedure for regularizing the scalar perturbations is considerably simpler.
Following the Detweiler-Whiting (DW) scheme, we use our regular expressions for
the field and derive the regular self-force corrections through third order. We
find agreement with our previous derivation based on a variational principle of
an effective action for the worldline associated with the SCO thus
demonstrating the internal consistency of our formalism. This also explicitly
demonstrates that the DW decomposition of Green's functions is a valid and
practical method of self force computation at higher orders in perturbation
theory and, as we show in an appendix, at all orders in perturbation theory.
Finally, we identify a master source from which all other physically relevant
quantities are derivable. Knowing the master source perturbatively allows one
to construct the waveform measured by an observer, the regular part of the
field on the worldline, the regular part of the self force, and orbital
quantities such as shifts of the innermost stable circular orbit, etc. The
existence of a master source together with the regularization methods
implemented in this series should be indispensable for derivations of
higher-order gravitational self force corrections.Comment: For Part 1 of this series, see arXiv:1012.4488. 20 pages, 7 figure
Effective source approach to self-force calculations
Numerical evaluation of the self-force on a point particle is made difficult
by the use of delta functions as sources. Recent methods for self-force
calculations avoid delta functions altogether, using instead a finite and
extended "effective source" for a point particle. We provide a review of the
general principles underlying this strategy, using the specific example of a
scalar point charge moving in a black hole spacetime. We also report on two new
developments: (i) the construction and evaluation of an effective source for a
scalar charge moving along a generic orbit of an arbitrary spacetime, and (ii)
the successful implementation of hyperboloidal slicing that significantly
improves on previous treatments of boundary conditions used for
effective-source-based self-force calculations. Finally, we identify some of
the key issues related to the effective source approach that will need to be
addressed by future work.Comment: Invited review for NRDA/Capra 2010 (Theory Meets Data Analysis at
Comparable and Extreme Mass Ratios), Perimeter Institute, June 2010, CQG
special issue - 22 pages, 8 figure
Detection Strategies for Extreme Mass Ratio Inspirals
The capture of compact stellar remnants by galactic black holes provides a
unique laboratory for exploring the near horizon geometry of the Kerr
spacetime, or possible departures from general relativity if the central cores
prove not to be black holes. The gravitational radiation produced by these
Extreme Mass Ratio Inspirals (EMRIs) encodes a detailed map of the black hole
geometry, and the detection and characterization of these signals is a major
scientific goal for the LISA mission. The waveforms produced are very complex,
and the signals need to be coherently tracked for hundreds to thousands of
cycles to produce a detection, making EMRI signals one of the most challenging
data analysis problems in all of gravitational wave astronomy. Estimates for
the number of templates required to perform an exhaustive grid-based
matched-filter search for these signals are astronomically large, and far out
of reach of current computational resources. Here I describe an alternative
approach that employs a hybrid between Genetic Algorithms and Markov Chain
Monte Carlo techniques, along with several time saving techniques for computing
the likelihood function. This approach has proven effective at the blind
extraction of relatively weak EMRI signals from simulated LISA data sets.Comment: 10 pages, 4 figures, Updated for LISA 8 Symposium Proceeding
A nonlinear scalar model of extreme mass ratio inspirals in effective field theory I. Self force through third order
The motion of a small compact object in a background spacetime is
investigated in the context of a model nonlinear scalar field theory. This
model is constructed to have a perturbative structure analogous to the General
Relativistic description of extreme mass ratio inspirals (EMRIs). We apply the
effective field theory approach to this model and calculate the finite part of
the self force on the small compact object through third order in the ratio of
the size of the compact object to the curvature scale of the background (e.g.,
black hole) spacetime. We use well-known renormalization methods and
demonstrate the consistency of the formalism in rendering the self force finite
at higher orders within a point particle prescription for the small compact
object. This nonlinear scalar model should be useful for studying various
aspects of higher-order self force effects in EMRIs but within a comparatively
simpler context than the full gravitational case. These aspects include
developing practical schemes for higher order self force numerical
computations, quantifying the effects of transient resonances on EMRI waveforms
and accurately modeling the small compact object's motion for precise
determinations of the parameters of detected EMRI sources.Comment: 30 pages, 8 figure
Implementation and testing of the first prompt search for gravitational wave transients with electromagnetic counterparts
Aims. A transient astrophysical event observed in both gravitational wave
(GW) and electromagnetic (EM) channels would yield rich scientific rewards. A
first program initiating EM follow-ups to possible transient GW events has been
developed and exercised by the LIGO and Virgo community in association with
several partners. In this paper, we describe and evaluate the methods used to
promptly identify and localize GW event candidates and to request images of
targeted sky locations.
Methods. During two observing periods (Dec 17 2009 to Jan 8 2010 and Sep 2 to
Oct 20 2010), a low-latency analysis pipeline was used to identify GW event
candidates and to reconstruct maps of possible sky locations. A catalog of
nearby galaxies and Milky Way globular clusters was used to select the most
promising sky positions to be imaged, and this directional information was
delivered to EM observatories with time lags of about thirty minutes. A Monte
Carlo simulation has been used to evaluate the low-latency GW pipeline's
ability to reconstruct source positions correctly.
Results. For signals near the detection threshold, our low-latency algorithms
often localized simulated GW burst signals to tens of square degrees, while
neutron star/neutron star inspirals and neutron star/black hole inspirals were
localized to a few hundred square degrees. Localization precision improves for
moderately stronger signals. The correct sky location of signals well above
threshold and originating from nearby galaxies may be observed with ~50% or
better probability with a few pointings of wide-field telescopes.Comment: 17 pages. This version (v2) includes two tables and 1 section not
included in v1. Accepted for publication in Astronomy & Astrophysic
Self-force: Computational Strategies
Building on substantial foundational progress in understanding the effect of
a small body's self-field on its own motion, the past 15 years has seen the
emergence of several strategies for explicitly computing self-field corrections
to the equations of motion of a small, point-like charge. These approaches
broadly fall into three categories: (i) mode-sum regularization, (ii) effective
source approaches and (iii) worldline convolution methods. This paper reviews
the various approaches and gives details of how each one is implemented in
practice, highlighting some of the key features in each case.Comment: Synchronized with final published version. Review to appear in
"Equations of Motion in Relativistic Gravity", published as part of the
Springer "Fundamental Theories of Physics" series. D. Puetzfeld et al.
(eds.), Equations of Motion in Relativistic Gravity, Fundamental Theories of
Physics 179, Springer, 201