Second post-Newtonian gravitational radiation reaction for two-body systems: Nonspinning bodies

Starting from the recently obtained 2PN accurate forms of the energy and angular momentum fluxes from inspiralling compact binaries, we deduce the gravitational radiation reaction to 2PN order beyond the quadrupole approximation - 4.5PN terms in the equation of motion - using the refined balance method proposed by Iyer and Will. We explore critically the features of their construction and illustrate them by contrast to other possible variants. The equations of motion are valid for general binary orbits and for a class of coordinate gauges. The limiting cases of circular orbits and radial infall are also discussed.Comment: 38 pages, REVTeX, no figures, to appear in Phys. Rev.

Eccentricity content of binary black hole initial data

Using a post-Newtonian diagnostic tool developed by Mora and Will, we examine numerically generated quasiequilibrium initial data sets that have been used in recently successful numerical evolutions of binary black holes through plunge, merger and ringdown. We show that a small but significant orbital eccentricity is required to match post-Newtonian and quasiequilibrium calculations. If this proves to be a real eccentricity, it could affect the fine details of the subsequent numerical evolutions and the predicted gravitational waveforms.Comment: 5 pages, 5 figures, clarifications and minor corrections; version submitted to Phys. Rev.

Cumulative Dragging - An Intrinsic Characteristic of Stationary Axisymmetric Spacetime

The Cumulative Drag Index defined recently by Prasanna has been generalised to include the centrifugal acceleration. We have studied the behaviour of the drag index for the Kerr metric and the Neugebauer-Meinel metric representing a self-gravitating rotating disk and their Newtonian approximations. The similarity of the behaviour of the index for a given set of parameters both in the full and approximated forms, suggests that the index characterises an intrinsic property of spacetime with rotation. Analysing the index for a given set of parameters shows possible constraints on them.Comment: Discussion of Neugebauer-Meinel rotating disk and clarifications adde

A post-Newtonian diagnosis of quasiequilibrium configurations of neutron star-neutron star and neutron star-black hole binaries

We use a post-Newtonian diagnostic tool to examine numerically generated quasiequilibrium initial data sets for non-spinning double neutron star and neutron star-black hole binary systems. The PN equations include the effects of tidal interactions, parametrized by the compactness of the neutron stars and by suitable values of ``apsidal'' constants, which measure the degree of distortion of stars subjected to tidal forces. We find that the post-Newtonian diagnostic agrees well with the double neutron star initial data, typically to better than half a percent except where tidal distortions are becoming extreme. We show that the differences could be interpreted as representing small residual eccentricity in the initial orbits. In comparing the diagnostic with preliminary numerical data on neutron star-black hole binaries, we find less agreement.Comment: 17 pages, 6 tables, 8 figure

Centrifugal Force and Ellipticity behaviour of a slowly rotating ultra compact object

Using the optical reference geometry approach, we have derived in the following, a general expression for the ellipticity of a slowly rotating fluid configuration using Newtonian force balance equation in the conformally projected absolute 3-space, in the realm of general relativity. Further with the help of Hartle-Thorne (H-T) metric for a slowly rotating compact object, we have evaluated the centrifugal force acting on a fluid element and also evaluated the ellipticity and found that the centrifugal reversal occurs at around $R/R_s \approx 1.45$, and the ellipticity maximum at around $R/R_s \approx 2.75$. The result has been compared with that of Chandrasekhar and Miller which was obtained in the full 4-spacetime formalism

SPEAR : Semi-supervised Data Programming in Python

We present SPEAR, an open-source python library for data programming with semi supervision. The package implements several recent data programming approaches including facility to programmatically label and build training data. SPEAR facilitates weak supervision in the form of heuristics (or rules) and association of noisy labels to the training dataset. These noisy labels are aggregated to assign labels to the unlabeled data for downstream tasks. We have implemented several label aggregation approaches that aggregate the noisy labels and then train using the noisily labeled set in a cascaded manner. Our implementation also includes other approaches that jointly aggregate and train the model for text classification tasks. Thus, in our python package, we integrate several cascade and joint data-programming approaches while also providing the facility of data programming by letting the user define labeling functions or rules. The code and tutorial notebooks are available at https://github.com/decile-team/spear. Further, extensive documentation can be found at https://spear-decile.readthedocs.io/. Video tutorials demonstrating the usage of our package are available here. We also present some real-world use cases of SPEAR.Comment: EMNLP Demonstrations - 202

Computational Relativistic Astrophysics With Adaptive Mesh Refinement: Testbeds

We have carried out numerical simulations of strongly gravitating systems based on the Einstein equations coupled to the relativistic hydrodynamic equations using adaptive mesh refinement (AMR) techniques. We show AMR simulations of NS binary inspiral and coalescence carried out on a workstation having an accuracy equivalent to that of a $1025^3$ regular unigrid simulation, which is, to the best of our knowledge, larger than all previous simulations of similar NS systems on supercomputers. We believe the capability opens new possibilities in general relativistic simulations.Comment: 7 pages, 16 figure