Radiation reaction in the 2.5PN waveform from inspiralling binaries in circular orbits

In this Comment we compute the contributions of the radiation reaction force in the 2.5 post-Newtonian (PN) gravitational wave polarizations for compact binaries in circular orbits. (i) We point out and correct an inconsistency in the derivation of Arun, Blanchet, Iyer, and Qusailah. (ii) We prove that all contributions from radiation reaction in the 2.5PN waveform are actually negligible since they can be absorbed into a modification of the orbital phase at the 5PN order.Comment: 7 pages, no figures, submitted to CQ

Evaluation of Sanders Associates proposal of 6/12/63 and general comments

This memorandum discusses a proposal for funding to do research on the heating of thermonuclear fuels to ignition temperatures by means of intense focused laser radiation. Technical comments are provided as to the proposal

Laser Fusion: The First Ten Years 1962-1972

This account of the beginning of the program on laser fusion at Livermore in 1962, and its subsequent development during the decade ending in 1972, was originally prepared as a contribution to the January 1991 symposium 'Achievements in Physics' honoring Professor Keith Brueckner upon his retirement from the University of San Diego at La Jolla. It is a personal recollection of work at Livermore from my vantage point as its scientific leader, and of events elsewhere that I thought significant. This period was one of rapid growth in which the technology of high-power short-pulse lasers needed to drive the implosion of thermonuclear fuel to the temperature and density needed for ignition was developed, and in which the physics of the interaction of intense light with plasmas was explored both theoretically and experimentally

Laser Fusion: The First Ten Years 1962-1972

This account of the beginning of the program on laser fusion at Livermore in 1962, and its subsequent development during the decade ending in 1972, was originally prepared as a contribution to the January 1991 symposium 'Achievements in Physics' honoring Professor Keith Brueckner upon his retirement from the University of San Diego at La Jolla. It is a personal recollection of work at Livermore from my vantage point as its scientific leader, and of events elsewhere that I thought significant. This period was one of rapid growth in which the technology of high-power short-pulse lasers needed to drive the implosion of thermonuclear fuel to the temperature and density needed for ignition was developed, and in which the physics of the interaction of intense light with plasmas was explored both theoretically and experimentally

Assessment of the safety of US nuclear weapons and related nuclear test requirements: A post-Bush Initiative update

The Nuclear Weapons Reduction Initiative announced by President Bush on September 27, 1991, is described herein as set forth in Defense Secretary Cheney`s Nuclear Arsenal Reduction Order issued September 28, 1991. The implications of the Bush Initiative for improved nuclear weapons safety are assessed in response to a request by US Senators Harkin, Kennedy, and Wirth to the Lawrence Livermore National Laboratory that the author prepare such an assessment. The author provides an estimate of the number of nuclear tests needed to accomplish a variety of specified warhead safety upgrades, then uses the results of this estimate to answer three questions posed by the Senators. These questions concern pit reuse and the number of nuclear tests needed for specified safety upgrades of those ballistic missiles not scheduled for retirement, namely the Minuteman III, C4, and D5 missiles

Evolution systems for non-linear perturbations of background geometries

The formulation of the initial value problem for the Einstein equations is at the heart of obtaining interesting new solutions using numerical relativity and still very much under theoretical and applied scrutiny. We develop a specialised background geometry approach, for systems where there is non-trivial a priori knowledge about the spacetime under study. The background three-geometry and associated connection are used to express the ADM evolution equations in terms of physical non-linear deviations from that background. Expressing the equations in first order form leads naturally to a system closely linked to the Einstein-Christoffel system, introduced by Anderson and York, and sharing its hyperbolicity properties. We illustrate the drastic alteration of the source structure of the equations, and discuss why this is likely to be numerically advantageous.Comment: 12 pages, 3 figures, Revtex v3.0. Revised version to appear in Physical Review

Solving Einstein's Equations With Dual Coordinate Frames

A method is introduced for solving Einstein's equations using two distinct coordinate systems. The coordinate basis vectors associated with one system are used to project out components of the metric and other fields, in analogy with the way fields are projected onto an orthonormal tetrad basis. These field components are then determined as functions of a second independent coordinate system. The transformation to the second coordinate system can be thought of as a mapping from the original ``inertial'' coordinate system to the computational domain. This dual-coordinate method is used to perform stable numerical evolutions of a black-hole spacetime using the generalized harmonic form of Einstein's equations in coordinates that rotate with respect to the inertial frame at infinity; such evolutions are found to be generically unstable using a single rotating coordinate frame. The dual-coordinate method is also used here to evolve binary black-hole spacetimes for several orbits. The great flexibility of this method allows comoving coordinates to be adjusted with a feedback control system that keeps the excision boundaries of the holes within their respective apparent horizons.Comment: Updated to agree with published versio

A Numerical Relativity Waveform Surrogate Model for Generically Precessing Binary Black Hole Mergers

A generic, non-eccentric binary black hole (BBH) system emits gravitational waves (GWs) that are completely described by 7 intrinsic parameters: the black hole spin vectors and the ratio of their masses. Simulating a BBH coalescence by solving Einstein's equations numerically is computationally expensive, requiring days to months of computing resources for a single set of parameter values. Since theoretical predictions of the GWs are often needed for many different source parameters, a fast and accurate model is essential. We present the first surrogate model for GWs from the coalescence of BBHs including all $7$ dimensions of the intrinsic non-eccentric parameter space. The surrogate model, which we call NRSur7dq2, is built from the results of $744$ numerical relativity simulations. NRSur7dq2 covers spin magnitudes up to $0.8$ and mass ratios up to $2$, includes all $\ell \leq 4$ modes, begins about $20$ orbits before merger, and can be evaluated in $\sim~50\,\mathrm{ms}$. We find the largest NRSur7dq2 errors to be comparable to the largest errors in the numerical relativity simulations, and more than an order of magnitude smaller than the errors of other waveform models. Our model, and more broadly the methods developed here, will enable studies that would otherwise require millions of numerical relativity waveforms, such as parameter inference and tests of general relativity with GW observations.Comment: 10 pages, 5 figures; Added report numbe

Hyperboloidal evolution of test fields in three spatial dimensions

We present the numerical implementation of a clean solution to the outer boundary and radiation extraction problems within the 3+1 formalism for hyperbolic partial differential equations on a given background. Our approach is based on compactification at null infinity in hyperboloidal scri fixing coordinates. We report numerical tests for the particular example of a scalar wave equation on Minkowski and Schwarzschild backgrounds. We address issues related to the implementation of the hyperboloidal approach for the Einstein equations, such as nonlinear source functions, matching, and evaluation of formally singular terms at null infinity.Comment: 10 pages, 8 figure

Einstein boundary conditions for the 3+1 Einstein equations

In the 3+1 framework of the Einstein equations for the case of vanishing shift vector and arbitrary lapse, we calculate explicitly the four boundary equations arising from the vanishing of the projection of the Einstein tensor along the normal to the boundary surface of the initial-boundary value problem. Such conditions take the form of evolution equations along (as opposed to across) the boundary for certain components of the extrinsic curvature and for certain space-derivatives of the intrinsic metric. We argue that, in general, such boundary conditions do not follow necessarily from the evolution equations and the initial data, but need to be imposed on the boundary values of the fundamental variables. Using the Einstein-Christoffel formulation, which is strongly hyperbolic, we show how three of the boundary equations should be used to prescribe the values of some incoming characteristic fields. Additionally, we show that the fourth one imposes conditions on some outgoing fields.Comment: Revtex 4, 6 pages, text and references added, typos corrected, to appear in Phys. Rev.