[0910.4677] Some new views on the low-energy side of gravity

Authors: Federico Piazza

Date: 26 Oct 2009

Abstract: Common wisdom associates all the unraveled and theoretically challenging aspects of gravity with its UV-completion. However, there appear to be few difficulties afflicting the effective framework for gravity already at low energy that are likely to be detached from the high-energy structure. Those include the black hole information paradox, the cosmological constant problem and the rather involved and fine tuned model building required to explain our cosmological observations. I review some directions of on-going research that aim to generalize and extend the low-energy framework for gravity.

abs pdf

Oct 29, 2009

0910.4677 (/preprints)
2009-10-29, 09:33 [edit]


[0910.4593] The Close-limit Approximation for Black Hole Binaries with Post-Newtonian Initial Conditions

Authors: Alexandre Le Tiec, Luc Blanchet

Date: 23 Oct 2009

Abstract: The ringdown phase of a black hole formed from the merger of two orbiting black holes is described by means of the close-limit (CL) approximation starting from second-post-Newtonian (2PN) initial conditions. The 2PN metric of point-particle binaries is formally expanded in CL form and identified with that of a perturbed Schwarzschild black hole. The multipolar coefficients describing the even-parity (or polar) and odd-parity (axial) components of the linear perturbation consistently satisfy the 2PN-accurate perturbative field equations. We use these coefficients to build initial conditions for the Regge-Wheeler and Zerilli wave equations, which we then evolve numerically. The ringdown waveform is obtained in two cases: head-on collision with zero-angular momentum, composed only of even modes, and circular orbits, for which both even and odd modes contribute. In a separate work, this formalism is applied to the study of the gravitational recoil produced during the ringdown phase of coalescing binary black holes.

abs pdf

Oct 29, 2009

0910.4593 (/preprints)
2009-10-29, 09:33 [edit]


[0910.4594] Gravitational-Wave Recoil from the Ringdown Phase of Coalescing Black Hole Binaries

Authors: Alexandre Le Tiec, Luc Blanchet, Clifford M. Will

Date: 23 Oct 2009

Abstract: The gravitational recoil or "kick" of a black hole formed from the merger of two orbiting black holes, and caused by the anisotropic emission of gravitational radiation, is an astrophysically important phenomenon. We combine (i) an earlier calculation, using post-Newtonian theory, of the kick velocity accumulated up to the merger of two non-spinning black holes, (ii) a "close-limit approximation" calculation of the radiation emitted during the ringdown phase, and based on a solution of the Regge-Wheeler and Zerilli equations using initial data accurate to second post-Newtonian order. We prove that ringdown radiation produces a significant "anti-kick". Adding the contributions due to inspiral, merger and ringdown phases, our results for the net kick velocity agree with those from numerical relativity to 10-15 percent over a wide range of mass ratios, with a maximum velocity of 180 km/s at a mass ratio of 0.38.

abs pdf

Oct 29, 2009

0910.4594 (/preprints)
2009-10-29, 09:33 [edit]


[0910.3954] Stellar-mass black holes in star clusters: implications for gravitational wave radiation

Authors: Sambaran Banerjee, Holger Baumgardt, Pavel Kroupa

Date: 20 Oct 2009

Abstract: We study the dynamics of stellar-mass black holes (BH) in star clusters with particular attention to the formation of BH-BH binaries, which are interesting as sources of gravitational waves (GW). We examine the properties of these BH-BH binaries through direct N-body simulations of star clusters using the GPU-enabled NBODY6 code. We perform simulations of N <= 10ˆ5 Plummer clusters of low-mass stars with an initial population of BHs. Additionally, we do several calculations of star clusters confined within a reflective boundary mimicking only the core of a massive cluster. We find that stellar-mass BHs with masses ~ 10 solar mass segregate rapidly into the cluster core and form a sub-cluster of BHs within typically 0.2 - 0.5 pc radius, which is dense enough to form BH-BH binaries through 3-body encounters. While most BH binaries are ejected from the cluster by recoils received during super-elastic encounters with the single BHs, few of them harden sufficiently so that they can merge via GW emission within the cluster. We find that for clusters with $N \ga 5\times 10ˆ4$, typically 1 - 2 BH-BH mergers occur within them during the first ~ 4 Gyr of evolution. Also for each of these clusters, there are a few escaping BH binaries that can merge within a Hubble time, most of the merger times being within a few Gyr. These results indicate that intermediate-age massive clusters constitute the most important class of candidates for producing dynamical BH-BH mergers. Old globular clusters cannot contribute significantly to the present-day BH-BH merger rate since most of the mergers from them would have occurred earlier. In contrast, young massive clusters are too young to produce significant number of BH-BH mergers. Our results imply significant BH-BH merger detection rates for the proposed "Advanced LIGO" GW detector. (Abridged)

abs pdf

Oct 23, 2009

0910.3954 (/preprints)
2009-10-23, 09:08 [edit]


[0910.3197] Statistical studies of Spinning Black-Hole Binaries

Authors: Carlos O. Lousto, Hiroyuki Nakano, Yosef Zlochower, Manuela Campanelli

Date: 16 Oct 2009

Abstract: We study the statistical distributions of the spins of generic black-hole binaries during the inspiral and merger, as well as the distributions of the remnant mass, spin, and recoil velocity. For the inspiral regime, we start with a random uniform distribution of spin directions S1 and S2 and magnitudes S1=S2=0.97 for different mass ratios. Starting from a fiducial initial separation of ri=50m, we perform 3.5PN evolutions down to rf=5m. At this final fiducial separation, we compute the angular distribution of the spins with respect to the final orbital angular momentum, L. We perform 16ˆ4 simulations for six mass ratios between q=1 and q=1/16 and compute the distribution of the angles between L and Delta and L and S, directly related to recoil velocities and total angular momentum. We find a small but statistically significant bias of the distribution towards counter-alignment of both scalar products. To study the merger of black-hole binaries, we turn to full numerical techniques. We introduce empirical formulae to describe the final remnant black hole mass, spin, and recoil velocity for merging black-hole binaries with arbitrary mass ratios and spins. We then evaluate those formulae for randomly chosen directions of the individual spins and magnitudes as well as the binary's mass ratio. We found that the magnitude of the recoil velocity distribution decays as P(v) \exp(-v/2500km/s), <v>=630km/s, and sqrt{<vˆ2> - <v>ˆ2}= 534km/s, leading to a 23% probability of recoils larger than 1000km/s, and a highly peaked angular distribution along the final orbital axis. The final black-hole spin magnitude show a universal distribution highly peaked at Sf/mfˆ2=0.73 and a 25 degrees misalignment with respect to the final orbital angular momentum.

abs pdf

Oct 23, 2009

0910.3197 (/preprints)
2009-10-23, 09:08 [edit]


[0910.3206] On strong mass segregation around a massive black hole: Implications for lower-frequency gravitational-wave astrophysics

Authors: Miguel Preto, Pau Amaro-Seoane

Date: 16 Oct 2009

Abstract: We present, for the first time, a clear $N$-body realization of the {\it strong mass segregation} solution for the stellar distribution around a massive black hole. We compare our $N$-body results with those obtained by solving the orbit-averaged Fokker-Planck (FP) equation in energy space. The $N$-body segregation is slightly stronger than in the FP solution, but both confirm the {\it robustness} of the regime of strong segregation when the number fraction of heavy stars is a (realistically) small fraction of the total population. In view of recent observations revealing a dearth of giant stars in the sub-parsec region of the Milky Way, we show that the time scales associated with cusp re-growth are not longer than $(0.1-0.25) \times T_{rlx}(r_h)$. These time scales are shorter than a Hubble time for black holes masses $\mbul \lesssim 4 \times 10ˆ6 M_\odot$ and we conclude that quasi-steady, mass segregated, stellar cusps may be common around MBHs in this mass range. Since EMRI rates scale as $\mbulˆ{-\alpha}$, with $\alpha \in [1\4,1]$, a good fraction of these events should originate from strongly segregated stellar cusps.

abs pdf

Oct 23, 2009

0910.3206 (/preprints)
2009-10-23, 09:07 [edit]


[0910.4302] Detecting gravitational waves from inspiraling binaries with a network of geographically separated detectors: coherent versus coincident strategies

Authors: Himan Mukhopadhyay, Hideyuki Tagoshi, Sanjeev Dhurandhar, Nobuyuki Kanda

Date: 22 Oct 2009

Abstract: We compare two strategies of multi-detector detection of compact binary inspiral signals, namely, the coincidence and the coherent for the realistic case of geographically separated detectors.We compare the performances of the methods by plotting the receiver operating characteristics (ROC) for the strategies. Several results are derived analytically in order to gain insight. Simulations are performed in order to plot the ROC curves. A single astrophysical source as well as a distribution of sources is considered. We find that the coherent strategy is superior to the two coincident strategies that we consider. Remarkably, the detection probability of the coherent strategy is 50% better than the naive coincident strategy. One the other hand, difference in performance between the coherent strategy and enhanced coincident strategy is not very large. Even in this situation, it is not difficult to perform the real data analysis with the coherent strategy. The bottom line is that the coherent strategy is a good detection strategy.

abs pdf

Oct 23, 2009

0910.4302 (/preprints)
2009-10-23, 09:07 [edit]


[0910.4152] Interruption of Tidal Disruption Flares By Supermassive Black Hole Binaries

Authors: F. K. Liu (1 and 2), S. Li (1), Xian Chen (1 and 3) ((1) Peking University, (2) KIAA at Peking University, (3) University of California at Santa Cruz)

Date: 21 Oct 2009

Abstract: Supermassive black hole binaries (SMBHBs) are products of galaxy mergers, and are important in testing LambdaCDM cosmology and locating gravitational-wave-radiation sources. A unique electromagnetic signature of SMBHBs in galactic nuclei is essential in identifying the binaries in observations from the IR band through optical to X-ray. Recently, the flares in optical, UV, and X-ray caused by supermassive black holes (SMBHs) tidally disrupting nearby stars have been successfully used to observationally probe single SMBHs in normal galaxies. In this letter, we investigate the accretion of the gaseous debris of a tidally disrupted star by a SMBHB. Using both stability analysis of three-body systems and numerical scattering experiments, we show that the accretion of stellar debris gas, which initially decays with time $\propto tˆ{-5/3}$, would stop at a time $T_{tr} \simeq \eta T_{b}$. Here $\eta \sim 0.25$ and $T_{b}$ is the orbital period of the SMBHB. After a period of interruption, the accretion recurs discretely at time $T_{r} \simeq \xi T_b$, where $\xi \sim 1$. Both $\eta$ and $\xi$ sensitively depend on the orbital parameters of the tidally disrupted star at the tidal radius and the orbit eccentricity of SMBHB. The interrupted accretion of the stellar debris gas gives rise to an interrupted tidal flare, which could be used to identify SMBHBs in non-active galaxies in the upcoming transient surveys.

abs pdf

Oct 23, 2009

0910.4152 (/preprints)
2009-10-23, 09:07 [edit]


[0910.4372] Alternative derivation of the response of interferometric gravitational wave detectors

Authors: Neil J. Cornish

Date: 22 Oct 2009

Abstract: It has recently been pointed out by Finn that the long-standing derivation of the response of an interferometric gravitational wave detector contains several errors. Here I point out that a contemporaneous derivation of the gravitational wave response for spacecraft doppler tracking and pulsar timing avoids these pitfalls, and when adapted to describe interferometers, recovers a simplified version of Finn's derivation. This simplified derivation may be useful for pedagogical purposes.

abs pdf

Oct 23, 2009

0910.4372 (/preprints)
2009-10-23, 09:07 [edit]


[0906.2901] LISA technology and instrumentation

Authors: O. Jennrich

Date: 16 Jun 2009

Abstract: This article reviews the present status of the technology and instrumentation for the joint ESA/NASA gravitational wave detector LISA. It briefly describes the measurement principle and the mission architecture including the resulting sensitivity before focussing on a description of the main payload items, such as the interferomtric measurement system, comprising the optical system with the optical bench and the telescope, the laser system, and the phase measurement system; and the disturbance reduction system with the inertial sensor, the charge control system, and the micropropulsion system. The article touches upon the requirements for the different subsystems that need to be fulfilled to obtain the overall sensitivity.

abs pdf

Oct 22, 2009

0906.2901 (/preprints)
2009-10-22, 19:35 [edit]


[0910.2857] Post-Newtonian methods: Analytic results on the binary problem

Authors: Gerhard Schaefer

Date: 15 Oct 2009

Abstract: A detailed account is given on approximation schemes to the Einstein theory of general relativity where the iteration starts from the Newton theory of gravity. Two different coordinate conditions are used to represent the Einstein field equations, the generalized isotropic ones of the canonical formalism of Arnowitt, Deser, and Misner and the harmonic ones of the Lorentz-covariant Fock-de Donder approach. Conserved quantities of isolated systems are identified and the Poincaré algebra is introduced. Post-Newtonian expansions are performed in the near and far (radiation) zones. The natural fitting of multipole expansions to post-Newtonian schemes is emphasized. The treated matter models are ideal fluids, pure point masses, and point masses with spin and mass-quadrupole moments modelling rotating black holes. Various Hamiltonians of spinning binaries are presented in explicit forms to higher post-Newtonian orders. The delicate use of black holes in post-Newtonian expansion calculations and of the Dirac delta function in general relativity find discussions.

abs pdf

Oct 20, 2009

0910.2857 (/preprints)
2009-10-20, 12:23 [edit]


[0910.2758] Emission coordinates for the navigation in space

Authors: A. Tartaglia

Date: 15 Oct 2009

Abstract: A general approach to the problem of positioning by means of pulsars or other pulsating sources located at infinity is described. The counting of the pulses for a set of different sources whose positions in the sky and periods are assumed to be known, is used to provide null emission, or light, coordinates for the receiver. The measurement of the proper time intervals between successive arrivals of the signals from the various sources is used to give the final localization of the receiver, within an accuracy controlled by the precision of the onboard clock. The deviation from the flat case is discussed, separately considering the different possible causes: local gravitational potential, finiteness of the distance of the source, proper motion of the source, period decay, proper acceleration due to non-gravitational forces. Calculations turn out to be simple and the result is highly positive. The method can also be applied to a constellation of satellites orbiting the Earth.

abs pdf

Oct 20, 2009

0910.2758 (/preprints)
2009-10-20, 12:23 [edit]


[0910.1780] Gravitational wave background from neutron star phase transition for a new class of equation of state

Authors: J. C. N. de Araujo, G. F. Marranghello

Date: 9 Oct 2009

Abstract: We study the generation of a stochastic gravitational wave (GW) background produced by a population of neutron stars (NSs) which go over a hadron-quark phase transition in its inner shells. We obtain, for example, that the NS phase transition, in cold dark matter scenarios, could generate a stochastic GW background with a maximum amplitude of $h_{\rm BG} \sim 10ˆ{-24}$, in the frequency band $\simeq 20-2000 {\rm Hz}$ for stars forming at redshifts of up to $z\simeq 20.$ We study the possibility of detection of this isotropic GW background by correlating signals of a pair of ‘advanced’ LIGO observatories.

abs pdf

Oct 13, 2009

0910.1780 (/preprints)
2009-10-13, 08:13 [edit]


[0910.1929] The twin paradox and Mach's principle

Authors: Herbert I.M. Lichtenegger, Lorenzo Iorio

Date: 10 Oct 2009

Abstract: The problem of absolute motion in the context of the twin paradox is discussed. It is shown that the various versions of the clock paradox feature some aspects which Mach might have been appreciated. However, the ultimate cause of the behavior of the clocks must be attributed to the autonomous status of spacetime, thereby proving the relational program advocated by Mach as impracticable.

abs pdf

Oct 13, 2009

0910.1929 (/preprints)
2009-10-13, 08:12 [edit]


[0910.1587] Triplets of supermassive black holes: Astrophysics, Gravitational Waves and Detection

Authors: Pau Amaro-Seoane, Alberto Sesana, Loren Hoffman, Matthew Benacquista, Christoph Eichhorn, Junichiro Makino, Rainer Spurzem

Date: 8 Oct 2009

Abstract: Supermassive black holes (SMBHs) found in the centers of many galaxies have been recognized to play a fundamental active role in the cosmological structure formation process. In hierarchical formation scenarios, SMBHs are expected to form binaries following the merger of their host galaxies. If these binaries do not coalesce before the merger with a third galaxy, the formation of a black hole triple system is possible. Numerical simulations of the dynamics of triples within galaxy cores exhibit phases of very high eccentricity (as high as $e \sim 0.99$). During these phases, intense bursts of gravitational radiation can be emitted at orbital periapsis. This produces a gravitational wave signal at frequencies substantially higher than the orbital frequency. The likelihood of detection of these bursts with pulsar timing and the Laser Interferometer Space Antenna ({\it LISA}) is estimated using several population models of SMBHs with masses $\gtrsim 10ˆ7 {\rm M_\odot}$. Assuming a fraction of binaries $\ge 0.1$ in triple system, we find that few to few dozens of these bursts will produce residuals $>1$ ns, within the sensitivity range of forthcoming pulsar timing arrays (PTAs). However, most of such bursts will be washed out in the underlying confusion noise produced by all the other 'standard' SMBH binaries emitting in the same frequency window. A detailed data analysis study would be required to assess resolvability of such sources. Implementing a basic resolvability criterion, we find that the chance of catching a resolvable burst at a one nanosecond precision level is 2-50%, depending on the adopted SMBH evolution model. On the other hand, the probability of detecting bursts produced by massive binaries (masses $\gtrsim 10ˆ7\msun$) with {\it LISA} is negligible.

abs pdf

Oct 13, 2009

0910.1587 (/preprints)
2009-10-13, 08:12 [edit]


[0910.1008] Canonical formulation of gravitating spinning objects at 3.5PN

Authors: Jan Steinhoff, Han Wang

Date: 6 Oct 2009

Abstract: The third-and-a-half post-Newtonian (PN) level is tackled by extending the canonical formalism of Arnowitt, Deser, and Misner to spinning objects. This extension is constructed order by order in the PN setting by utilizing the global Poincaré invariance as the important consistency condition. The formalism is valid to linear order in the single spin variables. Agreement with a recent action approach is found. A general formula for the interaction Hamiltonian between matter and transverse-traceless part of the metric at 3.5PN is derived. The wave equation resulting from this Hamiltonian is considered in the case of the constructed formalism for spinning objects. Agreement with the Einstein equations is found in this case. The energy flux at the spin-orbit level is computed.

abs pdf

Oct 07, 2009

0910.1008 (/preprints)
2009-10-07, 10:01 [edit]


[0910.0254] Detection of IMBHs with ground-based gravitational wave observatories: A biography of a binary of black holes, from birth to death

Authors: Pau Amaro-Seoane, Lucia Santamaria

Date: 1 Oct 2009

Abstract: Even though the existence of intermediate-mass black holes has not yet been corroborated observationally, these objects are of high interest for astrophysics. Our understanding of formation and evolution of supermassive black holes (SMBHs), as well as galaxy evolution modeling and cosmography would dramatically change if an IMBH was observed. The prospect of detection and, possibly, observation and characterization of an IMBH has good chances in lower-frequency gravitational-wave (GW) astrophysics with ground-based detectors such as LIGO, Virgo and the future Einstein Telescope (ET). We present an analysis of the signal of a system of a binary of IMBHs based on a waveform model obtained with numerical relativity simulations coupled with post-Newtonian calculations at the highest available order so as to extend the waveform to lower frequencies. We find that initial LIGO and Virgo are in the position of detecting IMBHs with a signal-to-noise ratio (SNR) of $\sim 10$ for systems with total mass between 100 and $500 M_{\odot}$ situated at a distance of 100 Mpc. Nevertheless, the event rate is too low and the possibility that these signals are mistaken with a glitch is, unfortunately, non-negligible. When going to second- and third-generation detectors, such as Advanced LIGO or the proposed ET, the event rate becomes much more promising (tens per year for the first and thousands per year for the latter) and the SNR at 100 Mpc is as high as 100 -- 1000 and 1000 -- $10ˆ{5}$ respectively. The prospects for IMBH detection and characterization with ground-based GW observatories would not only provide us with a robust test of general relativity, but would also corroborate the existence of these systems. Such detections would be a probe to the stellar environments of IMBHs and their formation.

abs pdf

Oct 06, 2009

0910.0254 (/preprints)
2009-10-06, 12:48 [edit]


[0910.0758] Advanced drag-free concepts for future space-based interferometers: acceleration noise performance

Authors: D. Gerardi, G. Allen, J. W. Conklin, K-X. Sun, D. DeBra, S. Buchman, P. Gath, W. Fichter, R. L. Byer, U. Johann

Date: 5 Oct 2009

Abstract: Future drag-free missions for space-based experiments in gravitational physics require a Gravitational Reference Sensor with extremely demanding sensing and disturbance reduction requirements. A configuration with two cubical sensors is the current baseline for the Laser Interferometer Space Antenna (LISA) and has reached a high level of maturity. Nevertheless, several promising concepts have been proposed with potential applications beyond LISA and are currently investigated at HEPL, Stanford, and EADS Astrium, Germany. The general motivation is to exploit the possibility of achieving improved disturbance reduction, and ultimately understand how low acceleration noise can be pushed with a realistic design for future mission. In this paper, we discuss disturbance reduction requirements for LISA and beyond, describe four different payload concepts, compare expected strain sensitivities in the 'low-frequency' region of the frequency spectrum, dominated by acceleration noise, and ultimately discuss advantages and disadvantages of each of those concepts in achieving disturbance reduction for space-based detectors beyond LISA.

abs pdf

Oct 06, 2009

0910.0758 (/preprints)
2009-10-06, 12:47 [edit]


[0910.0373] An Overview of LISA Data Analysis Algorithms

Authors: Edward K. Porter

Date: 2 Oct 2009

Abstract: The development of search algorithms for gravitational wave sources in the LISA data stream is currently a very active area of research. It has become clear that not only does difficulty lie in searching for the individual sources, but in the case of galactic binaries, evaluating the fidelity of resolved sources also turns out to be a major challenge in itself. In this article we review the current status of developed algorithms for galactic binary, non-spinning supermassive black hole binary and extreme mass ratio inspiral sources. While covering the vast majority of algorithms, we will highlight those that represent the state of the art in terms of speed and accuracy.

abs pdf

Oct 06, 2009

0910.0373 (/preprints)
2009-10-06, 12:47 [edit]


[0910.0380] Data Analysis Challenges for the Einstein Telescope

Authors: Leone Bosi, Edward K. Porter

Date: 2 Oct 2009

Abstract: The Einstein Telescope is a proposed third generation gravitational wave detector that will operate in the region of 1 Hz to a few kHz. As well as the inspiral of compact binaries composed of neutron stars or black holes, the lower frequency cut-off of the detector will open the window to a number of new sources. These will include the end stage of inspirals, plus merger and ringdown of intermediate mass black holes, where the masses of the component bodies are on the order of a few hundred solar masses. There is also the possibility of observing intermediate mass ratio inspirals, where a stellar mass compact object inspirals into a black hole which is a few hundred to a few thousand times more massive. In this article, we investigate some of the data analysis challenges for the Einstein Telescope such as the effects of increased source number, the need for more accurate waveform models and the some of the computational issues that a data analysis strategy might face.

abs pdf

Oct 06, 2009

0910.0380 (/preprints)
2009-10-06, 12:47 [edit]


[0910.0002] Black hole mergers: the first light

Authors: Elena M. Rossi, G. Lodato, P. J. Armitage, J. E. Pringle, A. R. King

Date: 1 Oct 2009

Abstract: The coalescence of supermassive black hole binaries occurs via the emission of gravitational waves, that can impart a substantial recoil to the merged black hole. We consider the energy dissipation, that results if the recoiling black hole is surrounded by a thin circumbinary disc. Our results differ significantly from those of previous investigations. We show analytically that the dominant source of energy is often potential energy, released as gas in the outer disc attempts to circularize at smaller radii. Thus, dimensional estimates, that include only the kinetic energy gained by the disc gas, underestimate the real energy loss. This underestimate can exceed an order of magnitude, if the recoil is directed close to the disc plane. We use three dimensional Smooth Particle Hydrodynamics (SPH) simulations and two dimensional finite difference simulations to verify our analytic estimates. We also compute the bolometric light curve, which is found to vary strongly depending upon the kick angle. A prompt emission signature due to this mechanism may be observable for low mass (10ˆ6 Solar mass) black holes whose recoil velocities exceed about 1000 km/s. Emission at earlier times can mainly result from the response of the disc to the loss of mass, as the black holes merge. We derive analytically the condition for this to happen.

abs pdf

Oct 02, 2009

0910.0002 (/preprints)
2009-10-02, 05:30 [edit]


[0910.0207] Post-Newtonian and Numerical Calculations of the Gravitational Self-Force for Circular Orbits in the Schwarzschild Geometry

Authors: Luc Blanchet, Steven Detweiler, Alexandre Le Tiec, Bernard F. Whiting

Date: 1 Oct 2009

Abstract: The problem of a compact binary system whose components move on circular orbits is addressed using two different approximation techniques in general relativity. The post-Newtonian (PN) approximation involves an expansion in powers of v/c<<1, and is most appropriate for small orbital velocities v. The perturbative self-force (SF) analysis requires an extreme mass ratio m1/m2<<1 for the components of the binary. A particular coordinate-invariant observable is determined as a function of the orbital frequency of the system using these two different approximations. The post-Newtonian calculation is pushed up to the third post-Newtonian (3PN) order. It involves the metric generated by two point particles and evaluated at the location of one of the particles. We regularize the divergent self-field of the particle by means of dimensional regularization. We show that the poles proportional to 1/(d-3) appearing in dimensional regularization at the 3PN order cancel out from the final gauge invariant observable. The 3PN analytical result, through first order in the mass ratio, and the numerical SF calculation are found to agree well. The consistency of this cross cultural comparison confirms the soundness of both approximations in describing compact binary systems. In particular, it provides an independent test of the very different regularization procedures invoked in the two approximation schemes.

abs pdf

Oct 02, 2009

0910.0207 (/preprints)
2009-10-02, 05:26 [edit]


  Login:   Password:   [rss] [cc] [w3] [css]

© M. Vallisneri 2012 — last modified on 2010/01/29

Tantum in modicis, quantum in maximis