arXiv subjects

Piotr Jaranowski

Publications and source records attributed to Piotr Jaranowski.

At least 19 recordsLinked to original sources

arXiv2024

Hamiltonian formulation of general relativity and post-Newtonian dynamics of compact binaries

Hamiltonian formalisms provide powerful tools for the computation of approximate analytic solutions of the Einstein field equations. The post-Newtonian computations of the explicit analytic dynamics and motion of compact binaries are discussed within the most often applied Arnowitt-Deser-Misner formalism. The obtention of autonomous Hamiltonians is achieved by the transition to Routhians. Order reduction of higher derivative Hamiltonians results in standard Hamiltonians. Tetrad representation of general relativity is introduced for the tackling of compact binaries with spinning components. Compact objects are modeled by use of Dirac delta functions and their derivatives. Consistency is achieved through transition to $d$-dimensional space and application of dimensional regularization. At the fourth post-Newtonian level, tail contributions to the binding energy show up for the first time. The conservative dynamics of binary systems finds explicit presentation and discussion through the fifth post-Newtonian order for spinless masses. For masses with spin Hamiltonians are known through (next-to)$^3$-leading-order spin-orbit and spin-spin couplings as well as through next-to-leading order cubic and quartic in spin interactions. Parts of those are given explicitly. Tidal-interaction Hamiltonians are considered through (next-to)$^2$-leading post-Newtonian order. The radiation reaction dynamics is presented explicitly through the third-and-half post-Newtonian order for spinless objects, and, for spinning bodies, to leading-order in the spin-orbit and spin1-spin2 couplings. The most important historical issues get pointed out.

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arXiv2023

Gravitational-Wave Data Analysis. Formalism and Sample Applications: The Gaussian Case

The article reviews the statistical theory of signal detection in application to analysis of deterministic gravitational-wave signals in the noise of a detector. Statistical foundations for the theory of signal detection and parameter estimation are presented. Several tools needed for both theoretical evaluation of the optimal data analysis methods and for their practical implementation are introduced. They include optimal signal-to-noise ratio, Fisher matrix, false alarm and detection probabilities, $\mathcal{F}$-statistic, template placement, and fitting factor. These tools apply to the case of signals buried in a stationary and Gaussian noise. Algorithms to efficiently implement the optimal data analysis techniques are discussed. Formulas are given for a general gravitational-wave signal that includes as special cases most of the deterministic signals of interest.

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arXiv2023

Banks of templates for directed and all-sky narrow-band searches of continuous gravitational waves from spinning neutron stars with several spindowns

We construct efficient banks of templates suitable for searches of continuous gravitational waves from isolated spinning neutron stars. We assume that the search algorithm is based on the time-domain maximum-likelihood $\mathcal{F}$-statistic and we consider narrow-band searches with several spindown parameters included. Our template banks are suitable for both all-sky and directed searches and they enable the usage of the fast Fourier transform in the computation of the $\mathcal{F}$-statistic as well as, in the case of all-sky searches, efficient resampling of data to barycentric time.

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arXiv2023

Search for Postmerger Gravitational Waves from Binary Neutron Star Mergers Using a Matched-filtering Statistic

In this paper, we present a new method to search for a short, a few tens of milliseconds long, postmerger gravitational-wave signal following the merger of two neutron stars. Such a signal could follow the event GW170817 observed by LIGO and Virgo detectors. Our method is based on a matched filtering statistic and an approximate template of the postmerger signal in the form of a damped sinusoid. We test and validate our method using postmerger numerical simulations from the CoRe database. We find no evidence of the short postmerger signal in the LIGO data following the GW170817 event and we obtain upper limits. For short postmerger signals investigated, our best upper limit on the root sum square of the gravitational-wave strain emitted from 1.15 kHz to 4 kHz is $h_{\text{rss}}^{50\%}=1.8\times 10^{-22}/\sqrt{\text{Hz}}$ at 50% detection efficiency. The distance corresponding to this best upper limit is 4.64 Mpc.

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arXiv2017

On the four-loop static contribution to the gravitational interaction potential of two point masses

We compute a subset of three, velocity-independent four-loop (and fourth post-Newtonian) contributions to the harmonic-coordinates effective action of a gravitationally interacting system of two point-masses. We find that, after summing the three terms, the coefficient of the total contribution is rational, due to a remarkable cancellation between the various occurrences of $π^2$. This result, obtained by a classical field-theory calculation, corrects the recent effective-field-theory-based calculation by Foffa et al. [arXiv:1612.00482]. Besides showing the usefulness of the saddle-point approach to the evaluation of the effective action, and of x-space computations, our result brings a further confirmation of the current knowledge of the fourth post-Newtonian effective action. We also show how the use of the generalized Riesz formula [Phys. Rev. D 57, 7274 (1998)] allows one to analytically compute a certain four-loop scalar master integral (represented by a four-spoked wheel diagram) which was, so far, only numerically computed.

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arXiv2016

Conservative dynamics of two-body systems at the fourth post-Newtonian approximation of general relativity

The fourth post-Newtonian (4PN) two-body dynamics has been recently tackled by several different approaches: effective field theory, Arnowitt-Deser-Misner Hamiltonian, action-angle-Delaunay averaging, effective-one-body, gravitational self-force, first law of dynamics, and Fokker action. We review the achievements of these approaches and discuss the complementarity of their results. Our main conclusions are: (i) the results of the first complete derivation of the 4PN dynamics [T.Damour, P.Jaranowski, and G.Schäfer, Phys. Rev. D 89, 064058 (2014)] have been, piecewise, fully confirmed by several subsequent works; (ii) the results of the Delaunay-averaging technique [T.Damour, P.Jaranowski, and G.Schäfer, Phys. Rev. D 91, 084024 (2015)] have been confirmed by several independent works; and (iii) several claims in a recent Fokker-action computation [L.Bernard et al., arXiv:1512.02876v2 [gr-qc]] are incorrect, but can be corrected by the addition of a couple of ambiguity parameters linked to subtleties in the regularization of infrared and ultraviolet divergences.

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arXiv2016

Derivation of local-in-time fourth post-Newtonian ADM Hamiltonian for spinless compact binaries

The paper gives full details of the computation within the canonical formalism of Arnowitt, Deser, and Misner of the local-in-time part of the fourth post-Newtonian, i.e. of power eight in one over speed of light, conservative Hamiltonian of spinless compact binary systems. The Hamiltonian depends only on the bodies' positions and momenta. Dirac delta distributions are taken as source functions. Their full control is furnished by dimensional continuation, by means of which the occurring ultraviolet (UV) divergences are uniquely regularized. The applied near-zone expansion of the time-symmetric Green function leads to infrared (IR) divergences. Their analytic regularization results in one single ambiguity parameter. Unique fixation of it was successfully performed in T.Damour, P.Jaranowski, and G.Schäfer, Phys. Rev. D 89, 064058 (2014) through far-zone matching. Technically as well as conceptually (backscatter binding energy), the level of the Lamb shift in quantum electrodynamics is reached. In a first run a computation of all terms is performed in three-dimensional space using analytic Riesz-Hadamard regularization techniques. Then divergences are treated locally (i.e., around particles' positions for UV and in the vicinity of spatial infinity for IR divergences) by means of combined dimensional and analytic regularization. Various evolved analytic expressions are presented for the first time. The breakdown of the Leibniz rule for distributional derivatives is addressed as well as the in general nondistributive law when regularizing value of products of functions evaluated at their singular point.

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arXiv2015

Banks of templates for all-sky narrow-band searches of gravitational waves from spinning neutron stars

We construct efficient banks of templates suitable for all-sky narrow-band searches of almost monochromatic gravitational waves originating from spinning neutron stars in our Galaxy in data collected by interferometric detectors. We consider waves with one spindown parameter included and we assume that both the position of the gravitational-wave source in the sky and the wave's frequency together with spindown parameter are unknown. In the construction we employ simplified model of the signal with constant amplitude and phase which is a linear function of unknown parameters. Our template banks enable usage of the fast Fourier transform algorithm in the computation of the maximum-likelihood $\mathcal{F}$-statistic for nodes of the grids defining the bank and fulfill an additional constraint needed to resample the data to barycentric time efficiently. All these template bank features were employed in the recent all-sky $\mathcal{F}$-statistic-based search for continuous gravitational waves in Virgo VSR1 data [J.Aasi et al., Classical Quantum Gravity 31, 165014 (2014)]. Here we improve that template bank by constructing templates suitable for larger range of search parameters and of smaller thicknesses for certain values of search parameters. One of our template banks has thickness 12% smaller than the thickness of the template bank used in the all-sky search of Virgo VSR1 data and only 4% larger than the thickness of 4-dimensional optimal lattice covering $A_4^\star$.

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arXiv2015

Fourth post-Newtonian effective one-body dynamics

The conservative dynamics of gravitationally interacting two-point-mass systems has been recently determined at the fourth post-Newtonian (4PN) approximation [T.Damour, P.Jaranowski, and G.Schäfer, Phys. Rev. D 89, 064058 (2014)], and found to be nonlocal in time. We show how to transcribe this dynamics within the effective one-body (EOB) formalism. To achieve this EOB transcription, we develop a new strategy involving the (infinite-)order-reduction of a nonlocal dynamics to an ordinary action-angle Hamiltonian. Our final, equivalent EOB dynamics comprises two (local) radial potentials, $A(r)$ and $\bar{D}(r)$, and a nongeodesic mass-shell contribution $Q(r,p_r)$ given by an infinite series of even powers of the radial momentum $p_r$. Using an effective action technique, we complete our 4PN-level results by deriving two different, higher-order conservative contributions linked to tail-transported hereditary effects: the 5PN-level EOB logarithmic terms, as well as the 5.5PN-level, half-integral terms. We compare our improved analytical knowledge to previous, numerical gravitational-self-force computation of precession effects.

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arXiv2015

Virial tests for post-Newtonian stationary black-hole-disk systems

We investigated hydrodynamical post-Newtonian models of selfgravitating stationary black-hole-disk systems. The post-Newtonian scheme presented here and also in our recent paper is a continuation of previous, purely Newtonian studies of selfgravitating hydrodynamical disks rotating according to the Keplerian rotation law. The post-Newtonian relativistic corrections are significant even at the 1PN level. The 1PN correction to the angular velocity can be of the order of 10% of its Newtonian value. It can be expressed as a combination of geometric and hydrodynamical terms. Moreover, in contrast to the Newtonian Poincare-Wavre theorem, it depends both on the distance from the rotation axis and the distance from the equatorial plane.

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arXiv2014

General-relativistic versus Newtonian: geometric dragging and dynamic anti-dragging in stationary disks in the first post-Newtonian approximation

We evaluate general-relativistic effects in motion of stationary accretion disks around a Schwarzschild black hole, assuming the first post-Newtonian (1PN) approximation. There arises an integrability condition, that leads to the emergence of two types of general-relativistic corrections to a Newtonian rotation curve. The well known geometric dragging of frames accelerates rotation but the hitherto unknown dynamic term, that reflects the disk structure, deccelerates rotation. The net result can diminish the Newtonian angular velocity of rotation in a central disk zone but the geometric dragging of frames dominates in the disk boundary zone. Both effects are nonlinear in nature and they disappear in the limit of test fluids. Dust disks can be only geometrically dragged while uniformly rotating gaseous disk are untouched at the 1PN order. General-relativistic contributions can strongly affect rotation periods in Keplerian motion for compact systems.

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arXiv2014

Nonlocal-in-time action for the fourth post-Newtonian conservative dynamics of two-body systems

We complete the analytical determination, at the 4th post-Newtonian (4PN) approximation, of the conservative dynamics of gravitationally interacting two-point-mass systems. This completion is obtained by resolving the infra-red ambiguity which had blocked a previous 4PN calculation [P.Jaranowski and G.Schäfer, Phys. Rev. D 87, 081503(R) (2013)] by taking into account the 4PN breakdown of the usual near-zone expansion due to infinite-range tail-transported temporal correlations found long ago [L.Blanchet and T.Damour, Phys. Rev. D 37, 1410 (1988)]. This leads to a Poincaré-invariant 4PN-accurate effective action for two masses, which mixes instantaneous interaction terms (described by a usual Hamiltonian) with a (time-symmetric) nonlocal-in-time interaction.

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arXiv2013

Dimensional regularization of local singularities in the 4th post-Newtonian two-point-mass Hamiltonian

The article delivers the only still unknown coefficient in the 4th post-Newtonian energy expression for binary point masses on circular orbits as function of orbital angular frequency. Apart from a single coefficient, which is known solely numerically, all the coefficients are given as exact numbers. The shown Hamiltonian is presented in the center-of-mass frame and out of its 57 coefficients 51 are given fully explicitly. Those coefficients are six coefficients more than previously achieved [Jaranowski/Schäfer, Phys. Rev. D 86, 061503(R) (2012)]. The local divergences in the point-mass model are uniquely controlled by the method of dimensional regularization. As application, the last stable circular orbit is determined as function of the symmetric-mass-ratio parameter.

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arXiv2012

Towards the 4th post-Newtonian Hamiltonian for two-point-mass systems

The article presents the conservative dynamics of gravitationally interacting two-point-mass systems up to the eight order in the inverse power of the velocity of light, i.e.\ 4th post-Newtonian (4PN) order, and up to quadratic order in Newton's gravitational constant. Additionally, all logarithmic terms at the 4PN order are given as well as terms describing the test-mass limit. With the aid of the Poincaré algebra additional terms are obtained. The dynamics is presented in form of an autonomous Hamiltonian derived within the formalism of Arnowitt, Deser and Misner. Out of the 57 different terms of the 4PN Hamiltonian in the center-of-mass frame, the coefficients of 45 of them are derived. Reduction of the obtained results to circular orbits is performed resulting in the 4PN-accurate formula for energy expressed in terms of angular frequency in which two coefficients are obtained for the first time.

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arXiv2010

Banks of templates for directed searches of gravitational waves from spinning neutron stars

We construct efficient banks of templates suitable for directed searches of almost monochromatic gravitational waves originating from spinning nuetron stars in our Galaxy in data being collected by currently operating interferometric detectors. We thus assume that the position of the gravitational-wave source in the sky is known, but we do not assume that the wave's frequency and its derivatives are a priori known. In the construction we employ simplified model of the signal with constant amplitude and phase which is a polynomial function of time. All our template banks enable usage of the fast Fourier transform algorithm in the computation of the maximum-likelihood F-statistic for nodes of the grids defining the bank. We study and employ the dependence of the grid's construction on the choice of the position of the observational interval with respect to the origin of time axis. We also study the usage of the fast Fourier transform algorithms with non-standard frequency resolutions achieved by zero padding or folding the data. In the case of the gravitational-wave signal with one spindown parameter included we have found grids with covering thicknesses which are only 0.1%--16% larger than the thickness of the optimal two-dimensional hexagonal covering.

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arXiv2010

Searching for gravitational waves from known pulsars using the $\mathcal{F}$ and $\mathcal{G}$ statistics

In searches for gravitational waves emitted by known isolated pulsars in data collected by a detector one can assume that the frequency of the wave, its spindown parameters, and the position of the source in the sky are known, so the almost monochromatic gravitational-wave signal we are looking for depends on at most four parameters: overall amplitude, initial phase, polarization angle, and inclination angle of the pulsar's rotation axis with respect to the line of sight. We derive two statistics by means of which one can test whether data contains such gravitational-wave signal: the $\mathcal{G}$-statistic for signals which depend on only two unknown parameters (overall amplitude and initial phase), and the $\mathcal{F}$-statistic for signals depending on all four parameters. We study, by means of the Fisher matrix, the theoretical accuracy of the maximum-likelihood estimators of the signal's parameters and we present the results of the Monte Carlo simulations we performed to test the accuracy of these estimators.

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arXiv2010

Data analysis of gravitational-wave signals from spinning neutron stars. V. A narrow-band all-sky search

We present theory and algorithms to perform an all-sky coherent search for periodic signals of gravitational waves in narrow-band data of a detector. Our search is based on a statistic, commonly called the $\mathcal{F}$-statistic, derived from the maximum-likelihood principle in Paper I of this series. We briefly review the response of a ground-based detector to the gravitational-wave signal from a rotating neuron star and the derivation of the $\mathcal{F}$-statistic. We present several algorithms to calculate efficiently this statistic. In particular our algorithms are such that one can take advantage of the speed of fast Fourier transform (FFT) in calculation of the $\mathcal{F}$-statistic. We construct a grid in the parameter space such that the nodes of the grid coincide with the Fourier frequencies. We present interpolation methods that approximately convert the two integrals in the $\mathcal{F}$-statistic into Fourier transforms so that the FFT algorithm can be applied in their evaluation. We have implemented our methods and algorithms into computer codes and we present results of the Monte Carlo simulations performed to test these codes.

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arXiv2008

Hamiltonian of two spinning compact bodies with next-to-leading order gravitational spin-orbit coupling

A Hamiltonian formulation is given for the gravitational dynamics of two spinning compact bodies to next-to-leading order ($G/c^4$ and $G^2/c^4$) in the spin-orbit interaction. We use a novel approach (valid to linear order in the spins), which starts from the second-post-Newtonian metric (in ADM coordinates) generated by two spinless bodies, and computes the next-to-leading order precession, in this metric, of suitably redefined ``constant-magnitude'' 3-dimensional spin vectors ${\bf S}_1$, ${\bf S}_2$. We prove the Poincaré invariance of our Hamiltonian by explicitly constructing ten phase-space generators realizing the Poincaré algebra. A remarkable feature of our approach is that it allows one to derive the {\it orbital} equations of motion of spinning binaries to next-to-leading order in spin-orbit coupling without having to solve Einstein's field equations with a spin-dependent stress tensor. We show that our Hamiltonian (orbital and spin) dynamics is equivalent to the dynamics recently obtained by Faye, Blanchet, and Buonanno, by solving Einstein's equations in harmonic coordinates.

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