Authors: C. M. Zhang, H.X. Yin, Y. Kojima, H. K. Chang, R. X. Xu, X. D. Li, B. Zhang, B. Kiziltan

Date: Tue, 21 Nov 2006

Abstract: We propose to determine the mass and the radius of a neutron star (NS) using three measurable mass-radius relationships, namely the ‘apparent’ radius inferred from neutron star thermal emission, the gravitational redshift inferred from the absorption lines, as well as the averaged stellar mass density inferred from the orbital Keplerian frequency derived from the kilohertz quasi periodic oscillation (kHz QPO) data. We apply the method to constrain the NS mass and the radius of the X-ray sources, 1E 1207.4-5209, Aql X-1 and EXO 0748-676.

Dec 28, 2006

0611659 (/preprints/astro-ph)
2006-12-28, 21:37 

[astro-ph/9911279] Quasi Periodic Oscillations in X-ray Neutron Star and Probes of Perihelion Precession of General Relativity

Authors: C.M. Zhang

Date: Fri, 18 Feb 2000

Abstract: We ascribe the twin kilohertz Quasi Periodic Oscillations (kHz QPOs) of X-ray spectra of Low Mass X-Ray Binaries (LMXBs) to the pseudo-Newtonian Keplerian frequency and the apogee and perigee precession frequency of the same matter in the inner disk, and ascribe 15 - 60 Hz QPO (HBO) to the apogee (or perigee) precession and its second harmonic frequency to both apogee and perigee precession in the outer disk boundary of the neutron star (NS) magnetosphere. The radii of the inner and outer disks are correlated each other by a factor of two is assumed. The obtained conclusions include: all QPO frequencies increase and frequency difference of twin kHz QPOs decreases with increasing the accretion rate. The obtained theoretical relations between HBO frequency and twin kHz QPOs are simlilar to the measured empirical formula. Further, the theoretical formula to calculate the NS mass by the twin kHz QPOs is proposed, and the resultant values are in the range of 1.4 to 1.8 solar masses. QPOs from LMXBs likely provide an accurate laboratory for a strong gravitational field, by which a new method to determine the NS masses of LMXBs is suggested.

Dec 28, 2006

9911279 (/preprints/astro-ph)
2006-12-28, 21:37 

[gr-qc/0612151] Binary black hole merger waveforms in the extreme mass ratio limit

Authors: Thibault Damour, Alessandro Nagar

Date: Sat, 23 Dec 2006

Abstract: We discuss the transition from quasi-circular inspiral to plunge of a system of two nonrotating black holes of masses $m_1$ and $m_2$ in the extreme mass ratio limit $m_1m_2\ll (m_1+m_2)ˆ2$. In this limit, we compare the merger waveforms obtained by two different methods: a {\it numerical} (Regge-Wheeler-Zerilli) one, and an {\it analytical} (Effective One Body) one. This is viewed as a contribution to the matching between analytical and numerical methods.

Dec 28, 2006

0612151 (/preprints/gr-qc)
2006-12-28, 16:01 

[gr-qc/0612152] LISA and LISA PathFinder, the endeavour to detect low frequency GWs

Authors: Henrique Araujo, Cesar Boatella, Mokhtar Chmeissani, Aleix Conchillo, Enrique Garcia-Berro, Catia Grimani, Wojtek Hajdas, Alberto Lobo, Lluis Martinez, Miquel Nofrarias, Jose Antonio Ortega, Carles Puigdengoles, Juan Ramos-Castro, Josep Sanjuan, Peter Wass, Xevi Xirgu

Date: Sat, 23 Dec 2006

Abstract: This is a review about LISA and its technology demonstrator, LISA PathFinder. We first describe the conceptual problems which need to be overcome in order to set up a working interferometric detector of low frequency Gravitational Waves (GW), then summarise the solutions to them as currently conceived by the LISA mission team. This will show that some of these solutions require new technological abilities which are still under development, and which need proper test before being fully implemented. LISA PathFinder (LPF) is the the testbed for such technologies. The final part of the paper will address the ideas and concepts behind the PathFinder as well as their impact on LISA.

Dec 28, 2006

0612152 (/preprints/gr-qc)
2006-12-28, 16:01 

[gr-qc/0612153] In-flight Diagnostics in LISA Pathfinder

Authors: Alberto Lobo, Miquel Nofrarias, Juan Ramos-Castro, Josep Sanjuan, Aleix Conchillo, Jose Antonio Ortega, Xevi Xirgu, Henrique Araujo, Cesar Boatella, Mokhtar Chmeissani, Catia Grimani, Carles Puigdengoles, Peter Wass, Enrique Garcia-Berro, Sergi Garcia, Lluis Martinez, Gustau Montero

Date: Sat, 23 Dec 2006

Abstract: LISA PathFinder (LPF) will be flown with the objective to test in space key technologies for LISA. However its sensitivity goals are, for good reason, one order of magnitude less than those which LISA will have to meet, both in drag-free and optical metrology requirements, and in the observation frequency band. While the expected success of LPF will of course be of itself a major step forward to LISA, one might not forget that a further improvement by an order of magnitude in performance will still be needed. Clues for the last leap are to be derived from proper disentanglement of the various sources of noise which contribute to the total noise, as measured in flight during the PathFinder mission. This paper describes the principles, workings and requirements of one of the key tools to serve the above objective: the diagnostics subsystem. This consists in sets of temperature, magnetic field, and particle counter sensors, together with generators of controlled thermal and magnetic perturbations. At least during the commissioning phase, the latter will be used to identify feed-through coefficients between diagnostics sensor readings and associated actual noise contributions. A brief progress report of the current state of development of the diagnostics subsystem will be given as well.

Dec 28, 2006

0612153 (/preprints/gr-qc)
2006-12-28, 16:01 

[gr-qc/0612142] Merger of black hole-neutron star binaries: nonspinning black hole case

Authors: Masaru Shibata, Koji Uryu

Date: Fri, 22 Dec 2006

Abstract: We perform a simulation for merger of a black hole (BH)-neutron star (NS) binary in full general relativity preparing a quasicircular state as initial condition. The BH is modeled by a moving puncture with no spin and the NS by the $\Gamma$-law equation of state with $\Gamma=2$. Corotating velocity field is assumed for the NS. The mass of the BH and the rest-mass of the NS are chosen to be $\approx 3.2 M_{\odot}$ and $\approx 1.4 M_{\odot}$ with relatively large radius of the NS $\approx 14$ km. The NS is tidally disrupted near the innermost stable orbit but $\sim 80%$ of the material is swallowed into the BH with small disk mass $\sim 0.3M_{\odot}$ even for such small BH mass $\sim 3M_{\odot}$. The result indicates that the system of a BH and a massive disk of $\sim M_{\odot}$ is not formed from nonspinning BH-NS binaries, although a disk of mass $\sim 0.1M_{\odot}$ is a possible outcome.

Dec 25, 2006

0612142 (/preprints/gr-qc)
2006-12-25, 09:38 

[astro-ph/0609377] The Effect of Orbital Eccentricity on Gravitational Wave Background Radiation from Supermassive Black Hole Binaries

Authors: Motohiro Enoki, Masahiro Nagashima

Date: Tue, 19 Dec 2006

Abstract: A compact binary on an eccentric orbit radiates gravitational waves (GWs) at all integer harmonics of its orbital frequency. In this study, we investigate the effect of orbital eccentricity on expected gravitational background radiation (GWBR) from supermassive black hole (SMBH) binaries in galaxy nuclei. For this purpose, we formulate the power spectrum of GWBR from cosmological evolving eccentric binaries. Then we apply this formulation to the case of the GWBR from SMBH binaries. The key to do this is correctly estimating the number density of coalescing SMBH binaries. In this study, we use a semi-analytic model of galaxy and SMBH formation. We find that the power spectrum of the GWBR from SMBH binaries on eccentric orbits is suppressed for frequencies $\lesssim 1 {\rm nHz}$ if the initial eccentricity is $e_0 > 0.2$ and the initial semi-major axis is 300 times Scwarzschild radius.
Our model predicts that while the overall shape and amplitude of the power spectrum depend largely on galaxy formation processes, eccentricity of binaries can affect the shape of the power spectrum for lower frequencies $\lesssim 1 {\rm nHz}$. Pulsar timing measurements, which can detect GW at this frequency range, would be able to constrain the effect of eccentricity on the power spectrum of the GWBR from SMBH binaries.

Dec 19, 2006

0609377 (/preprints/astro-ph)
2006-12-19, 17:57 

[gr-qc/0612117] Binary black hole late inspiral: Simulations for gravitational wave observations

Authors: John G. Baker, Sean T. McWilliams, James R. van Meter, Joan Centrella, Dae-Il Choi, Bernard J. Kelly, Michael Koppitz

Date: Tue, 19 Dec 2006

Abstract: Coalescing binary black hole mergers are expected to be the strongest gravitational wave sources for ground-based interferometers, such as the LIGO, VIRGO, and GEO600, as well as the space-based interferometer LISA. Until recently it has been impossible to reliably derive the predictions of General Relativity for the final merger stage, which takes place in the strong-field regime. Recent progress in numerical relativity simulations is, however, revolutionizing our understanding of these systems. We examine here the specific case of merging equal-mass Schwarzschild black holes in detail, presenting new simulations in which the black holes start in the late inspiral stage on orbits with very low eccentricity and evolve for ~1200M through ~7 orbits before merging. We study the accuracy and consistency of our simulations and the resulting gravitational waveforms, which encompass ~14 cycles before merger, and highlight the importance of using frequency (rather than time) to set the physical reference when comparing models. Matching our results to PN calculations for the earlier parts of the inspiral provides a combined waveform with less than half a cycle of accumulated phase error through the entire coalescence. Using this waveform, we calculate signal-to-noise ratios (SNRs) for iLIGO, adLIGO, and LISA, highlighting the contributions from the late-inspiral and merger-ringdown parts of the waveform which can now be simulated numerically. Contour plots of SNR as a function of z and M show that adLIGO can achieve SNR >~ 10 for some IMBBHs out to z ~ 1, and that LISA can see MBBHs in the range 3x10ˆ4 <~ M/M_Sun <~ 10ˆ7 at SNR > 100 out to the earliest epochs of structure formation at z > 15.

Dec 19, 2006

0612117 (/preprints/gr-qc)
2006-12-19, 17:56 

[gr-qc/0612100] Learning about compact binary merger: the interplay between numerical relativity and gravitational-wave astronomy

Authors: Thomas Baumgarte, Patrick Brady, Jolien D E Creighton, Luis Lehner, Frans Pretorius, Ricky DeVoe

Date: Sat, 16 Dec 2006

Abstract: Activities in data analysis and numerical simulation of gravitational waves have to date largely proceeded independently. In this work we study how waveforms obtained from numerical simulations could be effectively used within the data analysis effort to search for gravitational waves from black hole binaries. We propose measures to quantify the accuracy of numerical waveforms for the purpose of data analysis and study how sensitive the analysis is to errors in the waveforms. We estimate that ~100 templates (and ~10 simulations with different mass ratios) are needed to detect waves from non-spinning binary black holes with total masses in the range 100 Msun < M < 400 Msun using initial LIGO. Of course, many more simulation runs will be needed to confirm that the correct physics is captured in the numerical evolutions. From this perspective, we also discuss sources of systematic errors in numerical waveform extraction and provide order of magnitude estimates for the computational cost of simulations that could be used to estimate the cost of parameter space surveys. Finally, we discuss what information from near-future numerical simulations of compact binary systems would be most useful for enhancing the detectability of such events with contemporary gravitational wave detectors and emphasize the role of numerical simulations for the interpretation of eventual gravitational-wave observations.

Dec 19, 2006

0612100 (/preprints/gr-qc)
2006-12-19, 09:58 

[gr-qc/0612096] Binary black hole merger in the extreme mass ratio limit

Authors: Alessandro Nagar, Thibault Damour, Angelo Tartaglia

Date: Fri, 15 Dec 2006

Abstract: We discuss the transition from quasi-circular inspiral to plunge of a system of two nonrotating black holes of masses $m_1$ and $m_2$ in the extreme mass ratio limit $m_1m_2\ll (m_1+m_2)ˆ2$. In the spirit of the Effective One Body (EOB) approach to the general relativistic dynamics of binary systems, the dynamics of the two black hole system is represented in terms of an effective particle of mass $\mu\equiv m_1m_2/(m_1+m_2)$ moving in a (quasi-)Schwarzschild background of mass $M\equiv m_1+m_2$ and submitted to an ${\cal O}(\mu)$ radiation reaction force defined by Padé resumming high-order Post-Newtonian results. We then complete this approach by numerically computing, à la Regge-Wheeler-Zerilli, the gravitational radiation emitted by such a particle. Several tests of the numerical procedure are presented. We focus on gravitational waveforms and the related energy and angular momentum losses. We view this work as a contribution to the matching between analytical and numerical methods within an EOB-type framework.

Dec 19, 2006

0612096 (/preprints/gr-qc)
2006-12-19, 09:57 

[astro-ph/0612337] Gravitational wave bursts from the Galactic massive black hole

Authors: Clovis Hopman (Leiden University), Marc Freitag (Cambridge), Shane L. Larson (Weber State University)

Date: Wed, 13 Dec 2006

Abstract: The Galactic massive black hole (MBH), with a mass of Mbh=3.6\times10ˆ6 Solar masses, is the closest known MBH, at a distance of only 8 kpc. The proximity of this MBH makes it possible to observe gravitational waves from stars with periapse in the observational frequency window of the Laser Interferometer Space Antenna (LISA). This is possible even if the orbit of the star is very eccentric, so that the orbital frequency is many orders of magnitude below the LISA frequency window, as suggested by Rubbo et al. (2006). Here we give an analytical estimate of the detection rate of such gravitational wave bursts. The burst rate is critically sensitive to the inner cut-off of the stellar density profile. Our model accounts for mass-segregation and for the physics determining the inner radius of the cusp, such as stellar collisions, energy dissipation by gravitational wave emission, and consequences of the finite number of stars. We find that stellar black holes have a burst rate of the order of 1 per year, while the rate is of order 0.1 per year for main sequence stars and white dwarfs. These analytical estimates are supported by a series of Monte Carlo samplings of the expected distribution of stars around the Galactic MBH, which yield the full probability distribution for the rates. We estimate that no burst will be observable from the Virgo cluster.

Dec 19, 2006

0612337 (/preprints/astro-ph)
2006-12-19, 09:57 

[gr-qc/0612091] The Search for SuperMassive Black Hole Binaries with LISA

Authors: Neil J. Cornish, Edward K. Porter

Date: Thu, 14 Dec 2006

Abstract: In this work we focus on the search and detection of Supermassive black hole binary systems, including systems at high redshift. As well as expanding on previous works where we used a variant of Markov Chain Monte Carlo (MCMC) with simulated annealing, we introduce a new search method based on frequency annealing which leads to a more rapid and robust detection. We compare the two search methods on systems where we do and do not see the merger of the black holes. In the non-merger case, we also examine the posterior distribution exploration using a 7-D MCMC algorithm. We demonstrate that this method is quite effective in dealing with the high correlations between parameters, has a higher acceptance rate than previously proposed methods and produces posterior distribution functions that are extremely close to the prediction from the Fisher matrix. Finally, after carrying out searches where there is only one binary in the data stream, we examine the case where two black hole binaries are present in the same data stream. We demonstrate that we have no problems in pulling out the two binaries, displaying that there is virtually no correlation between overlapping binary black holes, and more importantly showing that we can safely extract the SMBHB sources without contaminating the rest of the data stream.

Dec 15, 2006

0612091 (/preprints/gr-qc)
2006-12-15, 01:42 

[gr-qc/0612076] Spin Flips and Precession in Black-Hole-Binary Mergers

Authors: Manuela Campanelli, Carlos O. Lousto, Yosef Zlochower, Badri Krishnan, David Merritt

Date: Thu, 14 Dec 2006

Abstract: We use the ‘moving puncture’ approach to perform fully non-linear evolutions of spinning quasi-circular black-hole binaries with individual spins not aligned with the orbital angular momentum. We evolve configurations with the individual spins (parallel and equal in magnitude) pointing in the orbital plane and 45-degrees above the orbital plane. We introduce a technique to measure the spin direction and track the precession of the spin during the merger, as well as measure the spin flip in the remnant horizon. The former configuration completes 1.75 orbits before merging, with the spin precessing by 98-degrees and the final remnant horizon spin flipped by ~72-degrees with respect to the component spins. The latter configuration completes 2.25 orbits, with the spins precessing by 151-degrees and the final remnant horizon spin flipped ~34-degrees with respect to the component spins. These simulations show for the first time how the spins are reoriented during the final stage of binary black hole mergers verifying the hypothesis of the spin-flip phenomenon. We also compute the track of the holes before merger and observe a precession of the orbital plane with frequency similar to the orbital frequency and amplitude increasing with time.

Dec 15, 2006

0612076 (/preprints/gr-qc)
2006-12-15, 01:41 

[gr-qc/0612085] Compact binary inspiral and the science potential of third-generation ground-based gravitational wave detectors

Authors: Chris Van Den Broeck, Anand S. Sengupta

Date: Wed, 13 Dec 2006

Abstract: We consider EGO as a possible third-generation ground-based gravitational wave detector and evaluate its capabilities for the detection and interpretation of compact binary inspiral signals. We identify areas of astrophysics and cosmology where EGO would have qualitative advantages, using Advanced LIGO as a benchmark for comparison.

Dec 15, 2006

0612085 (/preprints/gr-qc)
2006-12-15, 01:41 

[astro-ph/0607651] On the frequency of gravitational waves

Authors: Chiara Caprini, Ruth Durrer, Riccardo Sturani

Date: Fri, 8 Dec 2006

Abstract: We show that there are physically relevant situations where gravitational waves do not inherit the frequency spectrum of their source but its wavenumber spectrum.

Dec 15, 2006

0607651 (/preprints/astro-ph)
2006-12-15, 01:38 

[gr-qc/0611126] Dynamical determination of the quadrupole mass moment of a white dwarf

Authors: Lorenzo Iorio

Date: Fri, 8 Dec 2006

Abstract: In this letter we dynamically determine the quadrupole mass moment Q of the magnetic white dwarf WD 0137-349 by analyzing the period of the recently discovered brown dwarf moving around it in a close 2-hr orbit. It turns out that a purely Newtonian model for the orbit of WD 0137-349B, assumed circular and equatorial, is adequate, given the present-day accuracy in knowing the orbital parameters of such a binary system. Our result is Q=(-1.4615 +/- 0.9004) 10ˆ47 kg mˆ2 for i=35 deg. It is able to accommodate the 3-sigma significant discrepancy of (1.0 +/- 0.3) 10ˆ-8 sˆ-2 between the inverse square of the phenomenologically measured orbital period and the inverse square of the calculated Keplerian one. The impact of i, for which a range Delta i of possible values close to 35 deg is considered, is investigated as well; it amounts to Delta Q/Q\approx 83% for Delta i/i=11%.

Dec 15, 2006

0611126 (/preprints/gr-qc)
2006-12-15, 01:38 

[gr-qc/0612049] MHD of rotating compact stars with spectral methods: description of the algorithm and tests

Authors: S. Bonazzola, L. Villain, M. Bejger

Date: Fri, 8 Dec 2006

Abstract: A flexible spectral code for the study of general relativistic magnetohydrodynamics is presented. Aiming at investigating the physics of slowly rotating magnetized compact stars, this new code makes use of various physically motivated approximations. Among them, the relativistic anelastic approximation is a key ingredient of the current version of the code. In this article, we mainly outline the method, putting emphasis on algorithmic techniques that enable to benefit as much as possible of the non-dissipative character of spectral methods, showing also a potential astrophysical application and providing a few illustrative tests.

Dec 15, 2006

0612049 (/preprints/gr-qc)
2006-12-15, 01:37 

[gr-qc/0612037] Extracting Information about EMRIs using Time-Frequency Methods

Authors: Linqing Wen (MPI/AEI), Yanbei Chen (MPI/AEI), Jonathan Gair (University of Cambridge)

Date: Wed, 6 Dec 2006

Abstract: The inspirals of stellar-mass compact objects into supermassive black holes are some of the most exciting sources of gravitational waves for LISA. Detection of these sources using fully coherent matched filtering is computationally intractable, so alternative approaches are required. In Wen & Gair (2005), we proposed a detection method based on searching for significant deviation of power density from noise in a time-frequency spectrogram of the LISA data. The performance of the algorithm was assessed in Gair & Wen (2005) using Monte-Carlo simulations on several trial waveforms and approximations to the noise statistics. We found that typical extreme mass ratio inspirals (EMRIs) could be detected at distances of up to 1-3 Gpc, depending on the source parameters. In this paper, we first give an overview of our previous work in Wen & Gair (2005) and Gair & Wen (2005), and discuss the performance of the method in a broad sense. We then introduce a decomposition method for LISA data that decodes LISA's directional sensitivity. This decomposition method could be used to improve the detection efficiency, to extract the source waveform, and to help solve the source confusion problem. Our approach to constraining EMRI parameters using the output from the time-frequency method will be outlined.

Dec 06, 2006

0612037 (/preprints/gr-qc)
2006-12-06, 18:58 

[gr-qc/0612029] Using LISA EMRI sources to test off-Kerr deviations in the geometry of massive black holes

Authors: Leor Barack, Curt Cutler

Date: Tue, 5 Dec 2006

Abstract: Inspirals of stellar-mass compact objects into $\sim 10ˆ6 M_{\odot}$ black holes are especially interesting sources of gravitational waves for LISA. We investigate whether the emitted waveforms can be used to strongly constrain the geometry of the central massive object, and in essence check that it corresponds to a Kerr black hole (BH). For a Kerr BH, all multipole moments of the spacetime have a simple, unique relation to $M$ and $S$, the BH's mass and spin; in particular, the spacetime's mass quadrupole moment is given by $Q=- Sˆ2/M$. Here we treat $Q$ as an additional parameter, independent of $M$ and $S$, and ask how well observation can constrain its difference from the Kerr value. This was already estimated by Ryan, but for simplified (circular, equatorial) orbits, and neglecting signal modulations due to the motion of the LISA satellites. Here we consider generic orbits and include these modulations. We use a family of approximate (post-Newtonian) waveforms, which represent the full parameter space of Inspiral sources, and exhibit the main qualitative features of true, general relativistic waveforms. We extend this parameter space to include (in an approximate manner) an arbitrary value of $Q$, and construct the Fisher information matrix for the extended parameter space. By inverting the Fisher matrix we estimate how accurately $Q$ could be extracted from LISA observations. For 1 year of coherent data from the inspiral of a $10 M_{\odot}$ BH into rotating BHs of masses $10ˆ{5.5} M_{\odot}$, $10ˆ6 M_{\odot}$, or $10ˆ{6.5} M_{\odot}$, we find $\Delta (Q/Mˆ3) \sim 10ˆ{-4}$, $10ˆ{-3}$, or $10ˆ{-2}$, respectively (assuming total signal-to-noise ratio of 100, typical of the brightest detectable EMRIs). These results depend only weakly on the eccentricity of the orbit or the BH's spin.

Dec 05, 2006

0612029 (/preprints/gr-qc)
2006-12-05, 18:14 

[gr-qc/0612024] Consistency of post-Newtonian waveforms with numerical relativity

Authors: John G. Baker, James R. van Meter, Sean T. McWilliams, Joan Centrella, Bernard J. Kelly

Date: Mon, 4 Dec 2006

Abstract: General relativity predicts the gravitational radiation signatures of mergers of compact binaries, such as coalescing binary black hole systems. Derivations of waveform predictions for such systems are required for optimal scientific analysis of observational gravitational wave data, and have so far been achieved primarily with the aid of the post-Newtonian (PN) approximation. The quality of this treatment is unclear, however, for the important late inspiral portion. We derive late-inspiral waveforms via a complementary approach, direct numerical simulation of Einstein's equations, which has recently matured sufficiently for such applications. We compare waveform phasing from simulations covering the last $\sim 14$ cycles of gravitational radiation from an equal-mass binary system of non-spinning black holes with the corresponding 3PN and 3.5PN orbital phasing. We find agreement consistent with internal error estimates based on either approach at the level of one radian over $\sim 10$ cycles. The result suggests that PN waveforms for this system are effective roughly until the system reaches its last stable orbit just prior to the final merger.

Dec 04, 2006

0612024 (/preprints/gr-qc)
2006-12-04, 21:57 

[gr-qc/0612003] Chaos and Order in Models of Black Hole Pairs

Authors: Janna Levin

Date: Fri, 1 Dec 2006

Abstract: Chaos in the orbits of black hole pairs has by now been confirmed by several independent groups. While the chaotic behavior of binary black hole orbits is no longer argued, it remains difficult to quantify the importance of chaos to the evolutionary dynamics of a pair of comparable mass black holes. None of our existing approximations are robust enough to offer convincing quantitative conclusions in the most highly nonlinear regime. It is intriguing to note that in three different approximations to a black hole pair built of a spinning black hole and a non-spinning companion, two approximations exhibit chaos and one approximation does not. The fully relativistic scenario of a spinning test-mass around a Schwarzschild black hole shows chaos, as does the Post-Newtonian Lagrangian approximation. However, the approximately equivalent Post-Newtonian Hamiltonian approximation does not show chaos when only one body spins. It is well known in dynamical systems theory that one system can be regular while an approximately related system is chaotic, so there is no formal conflict. However,the physical question remains, Is there chaos for comparable mass binaries when only one object spins? We are unable to answer this question given the poor convergence of the Post-Newtonian approximation to the fully relativistic system. A resolution awaits better approximations that can be trusted in the highly nonlinear regime.

Dec 03, 2006

0612003 (/preprints/gr-qc)
2006-12-03, 20:54