Michele's wiki/blog

Authors: Sascha Husa, Ian Hinder, Christiane Lechner

Date: 6 Apr 2004

Abstract: We present a suite of Mathematica-based computer-algebra packages, termed "Kranc", which comprise a toolbox to convert (tensorial) systems of partial differential evolution equations to parallelized C or Fortran code. Kranc can be used as a "rapid prototyping" system for physicists or mathematicians handling very complicated systems of partial differential equations, but through integration into the Cactus computational toolkit we can also produce efficient parallelized production codes. Our work is motivated by the field of numerical relativity, where Kranc is used as a research tool by the authors. In this paper we describe the design and implementation of both the Mathematica packages and the resulting code, we discuss some example applications, and provide results on the performance of an example numerical code for the Einstein equations.

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Authors: Claudio M. G. de Sousa

Date: 13 Jul 2002

Abstract: Considering plane gravitational waves propagating through flat spacetime, it is shown that curvatures experienced both in the starting point and during their arrival at the earth can cause a considerable shift in the frequencies as measured by earth and space-based detectors. Particularly for the case of resonant bar detectors this shift can cause noise-filters to smother the signal.

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Authors: Eric Gourgoulhon (LUTH, CNRS / Observatoire de Paris)

Date: 6 Mar 2007

Abstract: These lecture notes provide some introduction to the 3+1 formalism of general relativity, which is the foundation of most modern numerical relativity. The text is rather self-contained, with detailed calculations and numerous examples. Contents: 1. Introduction, 2. Geometry of hypersurfaces, 3. Geometry of foliations, 4. 3+1 decomposition of Einstein equation, 5. 3+1 equations for matter and electromagnetic field, 6. Conformal decomposition, 7. Asymptotic flatness and global quantities, 8. The initial data problem, 9. Choice of foliation and spatial coordinates, 10. Evolution schemes.

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Authors: James G. Williams, Slava G. Turyshev, Dale H. Boggs

Date: 19 Jul 2005

Abstract: A primary objective of the Lunar Laser Ranging (LLR) experiment is to provide precise observations of the lunar orbit that contribute to a wide range of science investigations. Time series of the highly accurate measurements of the distance between the Earth and Moon provide unique information used to determine whether, in accordance with the Equivalence Principle (EP), both of these celestial bodies are falling towards the Sun at the same rate, despite their different masses, compositions, and gravitational self-energies. Current LLR solutions give $(-1.0 \pm 1.4) \times 10ˆ{-13}$ for any possible inequality in the ratios of the gravitational and inertial masses for the Earth and Moon, $\Delta(M_G/M_I)$. This result, in combination with laboratory experiments on the weak equivalence principle, yields a strong equivalence principle (SEP) test of $\Delta(M_G/M_I)_{\tt SEP} = (-2.0 \pm 2.0) \times 10ˆ{-13}$. Such an accurate result allows other tests of gravitational theories. The result of the SEP test translates into a value for the corresponding SEP violation parameter $\eta$ of $(4.4 \pm 4.5)\times10ˆ{-4}$, where $\eta = 4\beta -\gamma -3$ and both $\gamma$ and $\beta$ are parametrized post-Newtonian (PPN) parameters. The PPN parameter $\beta$ is determined to be $\beta - 1 = (1.2 \pm 1.1) \times 10ˆ{-4}$. Focusing on the tests of the EP, we discuss the existing data, and characterize the modeling and data analysis techniques. The robustness of the LLR solutions is demonstrated with several different approaches that are presented in the text. We emphasize that near-term improvements in the LLR ranging accuracy will further advance the research of relativistic gravity in the solar system, and, most notably, will continue to provide highly accurate tests of the Equivalence Principle.

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Authors: Mihaela D. Iftime

Date: 21 Oct 2006

Abstract: The 'hole argument'(the English translation of German 'Lochbetrachtung') was formulated by Albert Einstein in 1913 in his search for a relativistic theory of gravitation. The hole argument was deemed to be based on a trivial error of Einstein, until 1980 when John Stachel (Talk on Einsteins Search for General Covariance, 1912-1915 at the GRG meeting in Jena 1980) recognized its highly non-trivial character. Since then the argument has been intensively discussed by many physicists and philosophers of science. (See e.g., Earman & Norton (1987), Gaul & Rovelli (1999), Stachel & Iftime(2005}, and Iftime & Stachel(2006).)
I shall provide here a coordinate-free formulation of the argument using the language of categories and bundles, and generalize the argument for arbitrary covariant and permutable theories (see Iftime & Stachel(2006). In conclusion I shall point out a way of avoiding the hole argument, by looking at the structure of the space of solutions of Einstein's equations on a space-time manifold. This superspace Q(M) is defined as the orbit space of space-time solutions on M under the action of the diffeomorphisms of M, and it plays an important role in the study of the gravitational field and attempts to find a theory of quantum gravity (QG).

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Authors: Daniele Colosi, Carlo Rovelli

Date: 14 Sep 2004

Abstract: Theoretical developments related to the gravitational interaction have questioned the notion of particle in quantum field theory (QFT). For instance, uniquely-defined particle states do not exist in general, in QFT on a curved spacetime. More in general, particle states are difficult to define in a background-independent quantum theory of gravity. These difficulties have lead some to suggest that in general QFT should not be interpreted in terms of particle states, but rather in terms of eigenstates of local operators. Still, it is not obvious how to reconcile this view with the empirically-observed ubiquitous particle-like behavior of quantum fields, apparent for instance in experimental high-energy physics, or "particle"-physics. Here we offer an element of clarification by observing that already in flat space there exist --strictly speaking-- two distinct notions of particles: globally defined $n$-particle Fock-states and *local particle states*. The last describe the physical objects detected by finite-size particle detectors and are eigenstates of local field operators. In the limit in which the particle detectors are appropriately large, global and local particle states converge in a weak topology (but not in norm). This observation has little relevance for flat-space theories --it amounts to a reminder that there are boundary effects in realistic detectors--; but is relevant for gravity. It reconciles the two points of view mentioned above. More importantly, it provides a definition of local particle state that remains well-defined even when the conventional global particle states are not defined. This definition plays an important role in quantum gravity.

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Authors: Xavier Amador

Date: 16 Apr 2006

Abstract: This is an updated introductory review of 2 possible gravitational anomalies that has attracted part of the Scientific community: the Allais effect that occur during solar eclipses, and the Pioneer 10 spacecraft anomaly, experimented also by Pioneer 11 and Ulysses spacecrafts. It seems that, to date, no satisfactory conventional explanation exist to these phenomena, and this suggests that possible new physics will be needed to account for them. The main purpose of this review is to announce 3 other new measurements that will be carried on during the 2005 solar eclipses in Panama and Colombia (Apr. 8) and in Portugal (Oct.15).

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Authors: Duncan A. Brown, Jeandrew Brink, Hua Fang, Jonathan R. Gair, Chao Li, Geoffrey Lovelace, Ilya Mandel, Kip S. Thorne

Date: 11 Dec 2006

Abstract: We explore the prospects for Advanced LIGO to detect gravitational waves from neutron stars and stellar mass black holes spiraling into intermediate-mass ($M\sim 50 M_\odot$ to $350 M_\odot$) black holes. We estimate an event rate for such \emph{intermediate-mass-ratio inspirals} (IMRIs) of up to $\sim 10$--$30 \mathrm{yr}ˆ{-1}$. Our numerical simulations show that if the central body is not a black hole but its metric is stationary, axisymmetric, reflection symmetric and asymptotically flat then the waves will likely be tri-periodic, as for a black hole. We report generalizations of a theorem due to Ryan (1995) which suggest that the evolutions of the waves' three fundamental frequencies and of the complex amplitudes of their spectral components encode (in principle) a full map of the central body's metric, full details of the energy and angular momentum exchange between the central body and the orbit, and the time-evolving orbital elements. We estimate that Advanced LIGO can measure or constrain deviations of the central body from a Kerr black hole with modest but interesting accuracy.

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Authors: Matthew Pitkin, Graham Woan (University of Glasgow)

Date: 30 Mar 2007

Abstract: The majority of fast millisecond pulsars are in binary systems, so that any periodic signal they emit is modulated by both Doppler and relativistic effects. Here we show how well-established binary models can be used to account for these effects in searches for gravitational waves from known pulsars within binary systems. A seperate issue affecting certain pulsar signals is that of timing noise and we show how this, with particular reference to the Crab pulsar, can be compensated for by using regularly updated timing ephemerides.

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Authors: The LIGO Scientific Collaboration: B. Abbott, et al, M. Kramer, A. G. Lyne

Date: 7 Feb 2007

Abstract: We present upper limits on the gravitational wave emission from 78 radio pulsars based on data from the third and fourth science runs of the LIGO and GEO600 gravitational wave detectors. The data from both runs have been combined coherently to maximise sensitivity. For the first time pulsars within binary (or multiple) systems have been included in the search by taking into account the signal modulation due to their orbits. Our upper limits are therefore the first measured for 56 of these pulsars. For the remaining 22, our results improve on previous upper limits by up to a factor of 10. For example, our tightest upper limit on the gravitational strain is 2.6e-25 for PSRJ1603-7202, and the equatorial ellipticity of PSRJ2124-3358 is less than 10ˆ{-6}. Furthermore, our strain upper limit for the Crab pulsar is only 2.2 times greater than the fiducial spin-down limit.

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Authors: K A Arnaud, S Babak, J Baker, M J Benacquista, N J Cornish, C Cutler, L S Finn, S L Larson, T Littenberg, E K Porter, B S Sathyaprakash, M Vallisneri, A Vecchio, J-Y Vinet (the Mock LISA Data Challenge Task Force)

Date: 30 Jan 2007

Abstract: The Mock Data Challenges (MLDCs) have the dual purpose of fostering the development of LISA data-analysis tools and capabilities and of demonstrating the technical readiness already achieved by the gravitational-wave community in distilling a rich science payoff from the LISA data. The first round of MLDCs has just been completed and the second-round data sets are being released shortly after this workshop. The second-round data sets contain radiation from an entire Galactic population of stellar-mass binary systems, from massive--black-hole binaries, and from extreme--mass-ratio inspirals. These data sets are designed to capture much of the complexity that is expected in the actual LISA data, and should provide a fairly realistic setting to test advanced data-analysis techniques, and in particular the global aspect of the analysis. Here we describe the second round of MLDCs and provide details about its implementation.

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Authors: C. Messenger, G. Woan

Date: 30 Mar 2007

Abstract: We present a new type of search strategy designed specifically to find continuously emitting gravitational wave sources in known binary systems based on the incoherent sum of frequency modulated binary signal sidebands. The search pipeline can be divided into three stages: the first is a wide bandwidth, F-statistic search demodulated for sky position. This is followed by a fast second stage in which areas in frequency space are identified as signal candidates through the frequency domain convolution of the F-statistic with an approximate signal template. For this second stage only precise information on the orbit period and approximate information on the orbital semi-major axis are required apriori. For the final stage we propose a fully coherent Markov chain monte carlo based follow up search on the frequency subspace defined by the candidates identified by the second stage. This search is particularly suited to the low-mass X-ray binaries, for which orbital period and sky position are typically well known and additional orbital parameters and neutron star spin frequency are not. We note that for the accreting X-ray millisecond pulsars, for which spin frequency and orbital parameters are well known, the second stage can be omitted and the fully coherent search stage can be performed. We describe the search pipeline with respect to its application to a simplified phase model and derive the corresponding sensitivity of the search.

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Authors: J. Clark, I.S. Heng, M. Pitkin, G. Woan

Date: Wed, 28 Mar 2007

Abstract: The excitation of quadrupolar quasi-normal modes in a neutron star leads to the emission of a short, distinctive, burst of gravitational radiation in the form of a decaying sinusoid or ‘ring-down’. We present a Bayesian analysis method which incorporates relevant prior information about the source and known instrumental artifacts to conduct a robust search for the gravitational wave emission associated with pulsar glitches and soft $\gamma$-ray repeater flares. Instrumental transients are modelled as sine-Gaussian and their evidence, or marginal likelihood, is compared with that of Gaussian white noise and ring-downs via the ‘odds-ratio’. Tests using simulated data with a noise spectral density similar to the LIGO interferometer around 1 kHz yield 50% detection efficiency and 1% false alarm probability for ring-down signals with signal-to-noise ratio $\rho=5.5$. For a source at 15 kpc this requires an energy of $2.8\times 10ˆ{-5}M_{\astrosun}cˆ2$ to be emitted as gravitational waves.

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Authors: S. Pireaux (Observatoire de la Cote d'Azur, Department ARTEMIS, Grasse, France)

Date: Fri, 23 Mar 2007

Abstract: The LISA mission is a space interferometer aiming at the detection of gravitational waves in the [$10ˆ{-4}$,$10ˆ{-1}$] Hz frequency band. In order to reach the gravitational wave detection level, a Time Delay Interferometry (TDI) method must be applied to get rid of (most of) the laser frequency noise and optical bench noise. This TDI analysis is carried out in terms of the coordinate time corresponding to the Barycentric Coordinate Reference System (BCRS), TCB, whereas the data at each of the three LISA stations is recorded in terms of each station proper time. We provide here the required proper time versus BCRS time transformation. We show that the difference in rate of station proper time versus TCB is of the order of $5 10ˆ{-8}$. The difference between station proper times and TCB exhibits an oscillatory trend with a maximum amplitude of about $10ˆ{-3}$ s.

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Authors: Silvano Bonazzola (LUTH), Jos{é}-Luis Jaramillo (IAA-CSIC), Jerome Novak (LUTH)

Date: Fri, 23 Mar 2007

Abstract: We present a numerical technique for solving evolution equations, as the wave equation, in the description of rotating astrophysical compact objects in comoving coordinates, which avoids the problems associated with the light cylinder. The technique implements a fast spectral matching between two domains in relative rotation: an inner spherical domain, comoving with the sources and lying strictly inside the light cylinder, and an outer inertial spherical shell. Even though the emphasis is placed on spectral techniques, the matching is independent of the specific manner in which equations are solved inside each domain, and can be adapted to different schemes. We illustrate the strategy with some simple but representative examples.

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Authors: Florian Dubath, Jorge V. Rocha

Date: Wed, 21 Mar 2007

Abstract: We consider a population of small, high-velocity cosmic string loops. We assume the typical length of these loops is determined by the gravitational radiation scale and use the results of \cite{Polchinski:2007rg} which pointed out their highly relativistic nature. A study of the gravitational wave emission from such a population is carried out. The large Lorentz boost involved causes the lowest harmonics of the loops to fall within the frequency band of the LIGO detector. Due to this feature the gravitational waves emitted by such loops can be detected in a periodic search rather than in burst or stochastic analysis.
It is shown that, for interesting values of the string tension ($10ˆ{-10}\lsim G\mu\lsim 10ˆ{-8}$) the detector can observe loops at reasonably high redshifts and that detection is, in principle, possible. We compute the number of expected observations produced by such a process. For a 10 hour search we find that this number is of order $O(10ˆ{-4})$. This is a consequence of the low effective number density of the loops traveling along the line of sight. However, small probabilities of reconnection and longer observation times can improve the result.

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Authors: Michele Vallisneri

Date: Thu, 15 Mar 2007

Abstract: The Fisher-matrix formalism is used routinely in the literature on gravitational-wave detection to characterize the parameter-estimation performance of gravitational-wave measurements, given parametrized models of the waveforms, and assuming detector noise of known colored Gaussian distribution. Unfortunately, the Fisher matrix can be a poor predictor of the amount of information obtained from typical observations, especially for waveforms with several parameters and relatively low expected signal-to-noise ratios (SNR), or for waveforms depending weakly on one or more parameters, when their priors are not taken into proper consideration. In this paper I discuss these pitfalls; show how they occur, even for relatively strong signals, with a commonly used template family for binary-inspiral waveforms; and describe practical recipes to recognize them and cope with them.
Specifically, I answer the following questions: (i) What is the significance of (quasi-)singular Fisher matrices, and how must we deal with them? (ii) When is it necessary to take into account prior probability distributions for the source parameters? (iii) When is the signal-to-noise ratio high enough to believe the Fisher-matrix result? In addition, I provide general expressions for the higher-order, beyond-Fisher-matrix terms in the 1/SNR expansions for the expected parameter accuracies.

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Authors: Emanuele Berti, Vitor Cardoso, Jose A. Gonzalez, Ulrich Sperhake, Mark Hannam, Sascha Husa, Bernd Bruegmann

Date: Thu, 8 Mar 2007

Abstract: We study the inspiral, merger and ringdown of unequal mass black hole binaries by analyzing a catalogue of numerical simulations for seven different values of the mass ratio (from q=M2/M1=1 to q=4). We compare numerical and Post-Newtonian results by projecting the waveforms onto spin-weighted spherical harmonics, characterized by angular indices (l,m). We find that the Post-Newtonian equations predict remarkably well the relation between the wave amplitude and the orbital frequency for each (l,m), and that the convergence of the Post-Newtonian series to the numerical results is non-monotonic. To leading order the total energy emitted in the merger phase scales like etaˆ2 and the spin of the final black hole scales like eta, where eta=q/(1+q)ˆ2 is the symmetric mass ratio. We study the multipolar distribution of the radiation, finding that odd-l multipoles are suppressed in the equal mass limit. Higher multipoles carry a larger fraction of the total energy as q increases. We introduce and compare three different definitions for the ringdown starting time. Applying linear estimation methods (the so-called Prony methods) to the ringdown phase, we find resolution-dependent time variations in the fitted parameters of the final black hole. By cross-correlating information from different multipoles we show that ringdown fits can be used to obtain precise estimates of the mass and spin of the final black hole, which are in remarkable agreement with energy and angular momentum balance calculations.

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Authors: Mátyás Vasúth, Balázs Mikóczi, László Á. Gergely

Date: Thu, 8 Mar 2007

Abstract: We derive the rate of increase of the orbital frequency up to the second post-Newtonian order for inspiralling compact binaries with spin, mass quadrupole and magnetic dipole moments on eccentric orbits. We give this result in terms of orbital elements.

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Authors: Jonathan R Gair

Date: Tue, 6 Mar 2007

Abstract: The inspirals of compact objects into massive black holes are some of the most exciting of the potential sources of gravitational waves for the planned Laser Interferometer Space Antenna (LISA). Observations of such extreme mass ratio inspirals (EMRIs) will not only reveal to us the properties of black holes in the Universe, but will allow us to verify that the space-time structure around massive compact objects agrees with the predictions of relativity. Detection of EMRI signals via matched filtering and interpretation of the observations will require models of the gravitational waveforms. The extreme mass ratio allows accurate waveforms to be computed from black hole perturbation theory, but this is computationally expensive and has not yet been fully developed. Ongoing research to scope out LISA data analysis algorithms requires waveforms that can be generated quickly in large numbers. To fulfil this purpose, families of approximate, "kludge", EMRI waveforms have been developed that capture the main features of true EMRI waveforms, but that can also be generated for a comparatively small computational cost. In this proceedings article, we briefly outline one such waveform family (the "numerical kludge"), its accuracy and some possible ways in which it might be improved in the future. Although accurate parameter extraction will require use of perturbative waveforms, these approximate waveforms are sufficiently faithful to the true waveforms that they may be able to play a role in detection of EMRIs in the LISA data.

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