arXiv subjects

Leor Barack

Publications and source records attributed to Leor Barack.

At least 73 records · Page 4Linked to original sources

arXiv2005

Perturbations of Schwarzschild black holes in the Lorenz gauge: Formulation and numerical implementation

We reformulate the theory of Schwarzschild black hole perturbations in terms of the metric perturbation in the Lorenz gauge. In this formulation, each tensor-harmonic mode of the perturbation is constructed algebraically from 10 scalar functions, satisfying a set of 10 wavelike equations, which are decoupled at their principal parts. We solve these equations using numerical evolution in the time domain, for the case of a pointlike test particle set in a circular geodesic orbit around the black hole. Our code uses characteristic coordinates, and incorporates a constraint damping scheme. The axially-symmetric, odd-parity modes of the perturbation are obtained analytically. The approach developed here is especially advantageous in applications requiring knowledge of the local metric perturbation near a point particle; in particular, it offers a useful framework for calculations of the gravitational self force.

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arXiv2005

Confusion Noise from Extreme-Mass-Ratio Inspirals

Captures of compact objects (COs) by massive black holes in galactic nuclei (aka ``extreme-mass-ratio inspirals'') will be an important source for LISA. However, a large fraction of captures will not be individually resolvable, and so will constitute a source of ``confusion noise,'' obscuring other types of sources. Here we estimate the shape and overall magnitude of the spectrum of confusion noise from CO captures. The overall magnitude depends on the capture rates, which are rather uncertain, so we present results for a plausible range of rates. We show that the impact of capture confusion noise on the total LISA noise curve ranges from insignificant to modest, depending on these rates. Capture rates at the high end of estimated ranges would raise LISA's overall (effective) noise level by at most a factor $\sim 2$. While this would somewhat decrease LISA's sensitivity to other classes of sources, it would be a pleasant problem for LISA to have, overall, as it would also imply that detection rates for CO captures were at nearly their maximum possible levels (given LISA's baseline design).

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arXiv2004

Confusion Noise from LISA Capture Sources

Captures of compact objects (COs) by massive black holes (MBHs) in galactic nuclei will be an important source for LISA, the space-based gravitational-wave (GW) detector. However, a large fraction of captures will not be individually resolvable--either because they are too distant, have unfavorable orientation, or have too many years to go before final plunge--and so will constitute a source of ``confusion noise,'' obscuring other types of sources. Here we estimate the shape and overall magnitude of the spectrum of confusion noise from CO captures. The overall magnitude depends on the capture rates, which are rather uncertain, so we present results for a plausible range of rates. We show that the impact of capture confusion noise on the total LISA noise curve ranges from insignificant to modest, depending on these rates. Capture rates at the high end of estimated ranges would raise LISA's overall (effective) noise level by at most a factor \sim 2. While this slightly elevated noise level would somewhat decrease LISA's sensitivity to other classes of sources, overall, this would be a pleasant problem for LISA to have: It would also imply that detection rates for CO captures were at nearly their maximum possible levels (given LISA's baseline design). This paper includes several other results that should be useful in further studies of LISA capture sources, including (i) a calculation of the total GW energy output from generic inspirals into Kerr MBHs, and (ii) an approximate GW energy spectrum for a typical capture.

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arXiv2004

LISA Capture Sources: Approximate Waveforms, Signal-to-Noise Ratios, and Parameter Estimation Accuracy

Captures of stellar-mass compact objects (COs) by massive ($\sim 10^6 M_\odot$) black holes (MBHs) are potentially an important source for LISA, the proposed space-based gravitational-wave (GW) detector. The orbits of the inspiraling COs are highly complicated; they can remain rather eccentric up until the final plunge, and display extreme versions of relativistic perihelion precession and Lense-Thirring precession of the orbital plane. The strongest capture signals will be ~10 times weaker than LISA's instrumental noise, but in principle (with sufficient computing power) they can be disentangled from the noise by matched filtering. The associated template waveforms are not yet in hand, but theorists will very likely be able to provide them before LISA launches. Here we introduce a family of approximate (post-Newtonian) capture waveforms, given in (nearly) analytic form, for use in advancing LISA studies until more accurate versions are available. Our model waveforms include most of the key qualitative features of true waveforms, and cover the full space of capture-event parameters (including orbital eccentricity and the MBH's spin). Here we use our approximate waveforms to (i) estimate the relative contributions of different harmonics (of the orbital frequency) to the total signal-to-noise ratio, and (ii) estimate the accuracy with which LISA will be able to extract the physical parameters of the capture event from the measured waveform. For a typical source (a $10 M_\odot$ CO captured by a $10^6 M_\odot$ MBH at a signal-to-noise ratio of 30), we find that LISA can determine the MBH and CO masses to within a fractional error of $\sim 10^{-4}$, measure $S/M^2$ (where $S$ and $M$ are the MBH's mass and spin) to within $\sim 10^{-4}$, and determine the sky location of the source to within $\sim 10^{-3}$ stradians.

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arXiv2004

Event rate estimates for LISA extreme mass ratio capture sources

One of the most exciting prospects for the LISA gravitational wave observatory is the detection of gravitational radiation from the inspiral of a compact object into a supermassive black hole. The large inspiral parameter space and low amplitude of the signal makes detection of these sources computationally challenging. We outline here a first cut data analysis scheme that assumes realistic computational resources. In the context of this scheme, we estimate the signal-to-noise ratio that a source requires to pass our thresholds and be detected. Combining this with an estimate of the population of sources in the Universe, we estimate the number of inspiral events that LISA could detect. The preliminary results are very encouraging -- with the baseline design, LISA can see inspirals out to a redshift z=1 and should detect over a thousand events during the mission lifetime.

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arXiv2003

Gravitational self-force on a particle orbiting a Kerr black hole

We present a practical method for calculating the gravitational self-force, as well as the electromagnetic and scalar self forces, for a particle in a generic orbit around a Kerr black hole. In particular, we provide the values of all the regularization parameters needed for implementing the (previously introduced) {\it mode-sum regularization} method. We also address the gauge-regularization problem, as well as a few other issues involved in the calculation of gravitational radiation-reaction in Kerr spacetime.

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arXiv2002

Regularization parameters for the self force in Schwarzschild spacetime: II. gravitational and electromagnetic cases

We obtain all ``regularization parameters'' (RP) needed for calculating the gravitational and electromagnetic self forces for an arbitrary geodesic orbit around a Schwarzschild black hole. These RP values are required for implementing the previously introduced mode-sum method, which allows a practical calculation of the self force by summing over contributions from individual multipole modes of the particle's field. In the gravitational case, we provide here full details of the analytic method and results briefly reported in a recent Letter [Phys. Rev. Lett. {\bf 88}, 091101 (2002)]. In the electromagnetic case, the RP are obtained here for the first time.

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arXiv2002

Regularization parameters for the self force in Schwarzschild spacetime: I. scalar case

We derive the explicit values of all regularization parameters (RP) for a scalar particle in an arbitrary geodesic orbit around a Schwarzschild black hole. These RP are required within the previously introduced mode-sum method, for calculating the local self-force acting on the particle. In this method one first calculates the (finite) contribution to the self-force due to each individual multipole mode of the particle's field, and then applies a certain regularization procedure to the mode sum, involving the RP. The explicit values of the RP were presented in a recent Letter [Phys. Rev. Lett. {\bf 88}, 091101 (2002)]. Here we give full details of the RP derivation in the scalar case. The calculation of the RP in the electromagnetic and gravitational cases will be discussed in an accompanying paper.

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arXiv2002

Calculating the gravitational self force in Schwarzschild spacetime

We present a practical method for calculating the local gravitational self-force (often called ``radiation-reaction force'') for a pointlike particle orbiting a Schwarzschild black hole. This is an implementation of the method of {\it mode-sum regularization}, in which one first calculates the (finite) contribution to the force due to each individual multipole mode of the perturbation, and then applies a certain regularization procedure to the mode sum. Here we give the values of all the ``regularization parameters'' required for implementing this regularization procedure, for any geodesic orbit in Schwarzschild spacetime.

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arXiv2001

Gravitational self force by mode sum regularization

We propose a practical scheme for calculating the local gravitational self-force experienced by a test mass particle moving in a black hole spacetime. The method---equally effective for either weak or strong field orbits---employs the {\em mode-sum regularization scheme} previously developed for a scalar toy model. The starting point for the calculation, in this approach, is the formal expression for the regularized self-force derived by Mino et al. (and, independently, by Quinn and Wald), which involves a worldline integral over the tail part of the retarded Green's function. This force is decomposed into multipole (tensor harmonic) modes, whose sum is subjected to a carefully designed regularization procedure. This procedure involves an analytic derivation of certain ``regularization parameters'' by means of a local analysis of the Green's function. This manuscript contains the following main parts: (1) Introduction of the mode sum scheme as applied to the gravitational case. (2) Two simple cases studied: the test case of a static particle in flat spacetime, and the case of a particle at a turning point of a radial geodesic in Schwarzschild spacetime. In both cases we derive all necessary regularization parameters. (3) An Analytic foundation is set for applying the scheme in more general cases. (In this paper, the mode sum scheme is formulated within the harmonic gauge. The implementation of the scheme in other gauges shall be discussed in a separate, forthcoming paper.)

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arXiv2001

Gravitational self force and gauge transformations

We explore how the gravitational self force (or ``radiation reaction'' force), acting on a pointlike test particle in curved spacetime, is modified in a gauge transformation. We derive the general transformation law, describing the change in the self force in terms of the infinitesimal displacement vector associated with the gauge transformation. Based on this transformation law, we extend the regularization prescription by Mino et al. and Quinn and Wald (originally formulated within the harmonic gauge) to an arbitrary gauge. Then we extend the method of mode-sum regularization (which provides a practical means for calculating the regularized self force and was recently applied to the harmonic-gauge gravitational self force) to an arbitrary gauge. We find that the regularization parameters involved in this method are gauge-independent. We also explore the gauge transformation of the self force from the harmonic gauge to the Regge-Wheeler gauge and to the radiation gauge, focusing attention on the regularity of these gauge transformations. We conclude that the transformation of the self force to the Regge-Wheeler gauge in Schwarzschild spacetime is regular for radial orbits and irregular otherwise, whereas the transformation to the radiation gauge is irregular for all orbits.

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arXiv2000

Self-force on a scalar particle in spherically-symmetric spacetime via mode-sum regularization: radial trajectories

Recently, we proposed a method for calculating the ``radiation reaction'' self-force exerted on a charged particle moving in a strong field orbit in a black hole spacetime. In this approach, one first calculates the contribution to the ``tail'' part of the self force due to each multipole mode of the particle's self field. A certain analytic procedure is then applied to regularize the (otherwise divergent) sum over modes. This involves the derivation of certain regularization parameters using local analysis of the (retarded) Green's function. In the present paper we present a detailed formulation of this mode-sum regularization scheme for a scalar charge on a class of static spherically-symmetric backgrounds (including, e.g., the Schwarzschild, Reissner-Nordström, and Schwarzschild-de Sitter spacetimes). We fully implement the regularization scheme for an arbitrary radial trajectory (not necessarily geodesic) by explicitly calculating all necessary regularization parameters in this case.

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arXiv2000

Radiation-reaction force on a particle plunging into a black hole

We calculate the self force acting on a scalar particle which is falling radially into a Schwarzschild black hole. We treat the particle's self-field as a linear perturbation over the fixed Schwarzschild background. The force is calculated by numerically solving the appropriate wave equation for each mode of the field in the time domain, calculating its contribution to the self force, and summing over all modes using Ori's mode-sum regularization prescription. The radial component of the force is attractive at large distances, and becomes repulsive as the particle approaches the event horizon.

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arXiv2000

Mode sum regularization approach for the self-force in black hole spacetime

We present a method for calculating the self-force (the ``radiation reaction force'') acting on a charged particle moving in a strong field orbit in black hole spacetime. In this approach, one first calculates the contribution to the self-force due to each multipole mode of the particle's field. Then, the sum over modes is evaluated, subject to a certain regularization procedure. Here we develop this regularization procedure for a scalar charge on a Schwarzschild background, and present the results of its implementation for radial trajectories (not necessarily geodesic).

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arXiv1999

Calculating the self force in Schwarzschild spacetime by mode-sum regularization

We outline a method for calculating the self force (the "radiation reaction force") acting on a scalar particle in a strong field orbit in a Schwarzschild spacetime. In this method, the contribution to the self force associated with each multipole mode of the particle's field is calculated separately, and the sum over modes is then evaluated, subject to a certain regularization procedure. We present some explicit results concerning the implementation of the calculation scheme for a static particle, and also for a uniform circular motion, on the Schwarzschild background.

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arXiv1999

Late time decay of scalar, electromagnetic, and gravitational perturbations outside rotating black holes

We study analytically, via the Newman-Penrose formalism, the late time decay of scalar, electromagnetic, and gravitational perturbations outside a realistic rotating (Kerr) black hole. We find a power-law decay at timelike infinity, as well as at null infinity and along the event horizon (EH). For generic initial data we derive the power-law indices for all radiating modes of the various fields. We also give an exact analytic expression (accurate to leading order in 1/t) for the r-dependence of the late time tail at any r. Some of our main conclusions are: (i) For generic initial data, the late time behavior of the fields is dominated by the mode l=|s| (with s being the spin parameter), which dies off at fixed $r$ as $t^{-2|s|-3}$ --- as in the Schwarzschild background. (ii) However, other modes admit decay rates slower than in the Schwarzschild case. (iii) For s>0 fields, non-axially symmetric modes dominate the late time behavior along the EH. These modes oscillate along the null generators of the EH.

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arXiv1999

Late-time decay of gravitational and electromagnetic perturbations along the event horizon

We study analytically, via the Newman-Penrose formalism, the late-time decay of linear electromagnetic and gravitational perturbations along the event horizon (EH) of black holes. We first analyze in detail the case of a Schwarzschild black hole. Using a straightforward local analysis near the EH, we show that, generically, the ``ingoing'' ($s>0$) component of the perturbing field dies off along the EH more rapidly than its ``outgoing'' ($s<0$) counterpart. Thus, while along $r=const>2M$ lines both components of the perturbation admit the well-known $t^{-2l-3}$ decay rate, one finds that along the EH the $s<0$ component dies off in advanced-time $v$ as $v^{-2l-3}$, whereas the $s>0$ component dies off as $v^{-2l-4}$. We then describe the extension of this analysis to a Kerr black hole. We conclude that for axially symmetric modes the situation is analogous to the Schwarzschild case. However, for non-axially symmetric modes both $s>0$ and $s<0$ fields decay at the same rate (unlike in the Schwarzschild case).

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arXiv1999

Late-time decay of scalar perturbations outside rotating black holes

We present an analytic method for calculating the late-time tails of a linear scalar field outside a Kerr black hole. We give the asymptotic behavior at timelike infinity (for fixed $r$), at future null infinity, and along the event horizon (EH). In all three asymptotic regions we find a power-law decay. We show that the power indices describing the decay of the various modes at fixed $r$ differ from the corresponding Schwarzschild values. Also, the scalar field oscillates along the null generators of the EH (with advanced-time frequency proportional to the mode's magnetic number $m$).

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