Papers by richard matzner
Physical Review D, 2003
An orbiting black hole binary will generate strong gravitational radiation signatures, making the... more An orbiting black hole binary will generate strong gravitational radiation signatures, making these binaries important candidates for detection in gravitational wave observatories. The gravitational radiation is characterized by the orbital parameters, including the frequency and separation at the innermost stable circular orbit (ISCO). One approach to estimating these parameters relies on a sequence of initial data slices that attempt to capture the physics of the inspiral. Using calculations of the binding energy, several authors have estimated the ISCO parameters using initial data constructed with various algorithms. In this paper we examine this problem using conformally Kerr-Schild initial data. We present convergence results for our initial data solutions, and give data from numerical solutions of the constraint equations representing a range of physical configurations. In a first attempt to understand the physical content of the initial data, we find that the Newtonian binding energy is contained in the superposed Kerr-Schild background before the constraints are solved. We examine some deficiencies with the initial data approach to orbiting binaries, especially touching on the effects of prior motion and spin-orbital coupling of the angular momenta. Making rough estimates of these effects, we find that they are not insignificant compared to the binding energy, leaving some doubt of the utility of using initial data to predict ISCO parameters. In computations of specific initial-data configurations we find spin-specific effects that are consistent with analytical estimates.
General Relativity and Gravitation, 2009
It is a well known analytic result in general relativity that the 2-dimensional area of the appar... more It is a well known analytic result in general relativity that the 2-dimensional area of the apparent horizon of a black hole remains invariant regardless of the motion of the observer, and in fact is independent of the t = constant slice, which can be quite arbitrary in general relativity. Nonetheless the explicit computation of horizon area is often substantially more difficult in some frames (complicated by the coordinate form of the metric), than in other frames. Here we give an explicit demonstration for very restricted metric forms of (Schwarzschild and Kerr) vacuum black holes. In the Kerr-Schild coordinate expression for these spacetimes they have an explicit Lorentz-invariant form. We consider boosted versions with the black hole moving through the coordinate system.
Classical and Quantum Gravity, 2011
It is now widely accepted that the universe as we understand it is accelerating in expansion and ... more It is now widely accepted that the universe as we understand it is accelerating in expansion and fits the de Sitter model rather well. As such, a realistic assumption of black holes must place them on a de Sitter background and not Minkowski as is typically done in General Relativity. The most astrophysically relevant black hole is the uncharged, rotating Kerr solution, a member of the more general Kerr-Newman metrics. A generalization of the rotating Kerr black hole to a solution of the Einstein's equation with a cosmological constant Λ was discovered by Carter [1]. It is typically referred to as the Kerr-de Sitter spacetime. Here, we discuss the horizon structure of this spacetime and its dependence on Λ. We recall that in a Λ > 0 universe, the term 'extremal black hole' refers to a black hole with angular momentum J > M 2. We obtain explicit numerical results for the black hole's maximal spin value and get a distribution of admissible Kerr holes in the (Λ, spin) parameter space. We look at the conformal structure of the extended spacetime and the embedding of the 3-geometry of the spatial hypersurfaces. In analogy with Reissner-Nordström-de Sitter spacetime, in particular by considering the Kerr-de Sitter causal structure as a distortion of the Reissner-Nordström-de Sitter one, we show that spatial sections of the extended spacetime are 3-spheres containing 2-dimensional topologically spherical sections of the horizons of Kerr holes at the poles. Depending on how a t = constant 3-space is defined these holes may be seen as black or white holes (four possible combinations).
Physical Review D, 2002
We describe a finite-difference method for locating apparent horizons in generic spacetimes and i... more We describe a finite-difference method for locating apparent horizons in generic spacetimes and illustrate its capabilities on boosted Kerr and Schwarzschild black holes. Our model spacetime is given by the Kerr-Schild metric. We apply a Lorentz boost to this spacetime metric and then carry out a 3ϩ1 decomposition. The result is a slicing of Kerr-Schwarzschild spacetime in which the black hole is propagated and Lorentz contracted. We show that our method can locate distorted apparent horizons efficiently and accurately.
Physical Review D, 2003
This work establishes critical phenomena in the topological transition of black hole coalescence.... more This work establishes critical phenomena in the topological transition of black hole coalescence. We describe and validate a computational front tracking event horizon solver, developed for generic studies of the black hole coalescence problem. We then apply this to the Kastor-Traschen axisymmetric analytic solution of the extremal Maxwell-Einstein black hole merger with cosmological constant. The surprising result of this computational analysis is a power law scaling of the minimal throat proportional to time. The minimal throat connecting the two holes obeys this power law during a short time immediately at the beginning of merger. We also confirm the behavior analytically. Thus, at least in one axisymmetric situation a critical phenomenon exists. We give arguments for a broader universality class than the restricted requirements of the Kastor-Traschen solution.
A relativistic deep space positioning system has been proposed using four or more pulsars with st... more A relativistic deep space positioning system has been proposed using four or more pulsars with stable repetition rates. (Each pulsar emits pulses at a fixed repetition period in its rest frame.) The positioning system uses the fact that an event in spacetime can be fully described by emission coordinates: the proper emission time of each pulse measured at the event. The proper emission time of each pulse from four different pulsars---interpolated as necessary---provides the four spacetime coordinates of the reception event in the emission coordinate system. If more than four pulsars are available, the redundancy can improve the accuracy of the determination and/or resolve degeneracies resulting from special geometrical arrangements of the sources and the event. We introduce a robust numerical approach to measure the emission coordinates of an event in any arbitrary spacetime geometry. Our approach uses a continuous solution of the eikonal equation describing the backward null cone f...
Physical Review D, 1998
We present here an alternative approach to data setting for spacetimes with multiple moving black... more We present here an alternative approach to data setting for spacetimes with multiple moving black holes generalizing the Kerr-Schild form for rotating or non-rotating single black holes to multiple moving holes. Because this scheme preserves the Kerr-Schild form near the holes, it selects out the behaviour of null rays near the holes, may simplify horizon tracking, and may prove useful in computational applications. For computational evolution, a discussion of coordinates (lapse function and shift vector) is given which preserves some of the properties of the single-hole Kerr-Schild form.
Physical Review D, 2011
A relativistic deep space positioning system has been proposed using four or more pulsars with st... more A relativistic deep space positioning system has been proposed using four or more pulsars with stable repetition rates. (Each pulsar emits pulses at a fixed repetition period in its rest frame.) The positioning system uses the fact that an event in spacetime can be fully described by emission coordinates: the proper emission time of each pulse measured at the event. The proper emission time of each pulse from four different pulsars—interpolated as necessary—provides the four spacetime coordinates of the reception event in the emission coordinate system. If more than four pulsars are available, the redundancy can improve the accuracy of the determination and/or resolve degeneracies resulting from special geometrical arrangements of the sources and the event. We introduce a robust numerical approach to measure the emission coordinates of an event in any arbitrary spacetime geometry. Our approach uses a continuous solution of the eikonal equation describing the backward null cone from ...
Physical Review Letters, Mar 2, 1998
We present a method for extracting gravitational radiation from a three-dimensional numerical rel... more We present a method for extracting gravitational radiation from a three-dimensional numerical relativity simulation and, using the extracted data, to provide outer boundary conditions. The method treats dynamical gravitational variables as nonspherical perturbations of Schwarzschild geometry. We discuss a code which implements this method and present results of tests which have been performed with a three-dimensional numerical relativity code.[S0031-9007 (98) 05380-0]
Introduction to Gravitational Waves
Astrophysics and Space Science Library, 2010
Testing relativity in the desert: The Texas-Mauritania eclipse expedition
The Physics Teacher, 1975
Low-frequency limit of gravitational scattering
Physical Review D, 1977
We consider the low-frequency limit of cross sections for massless scalar, electromagnetic, and g... more We consider the low-frequency limit of cross sections for massless scalar, electromagnetic, and gravitational waves scattering on a Schwarzschild black hole. Explicit results are found for the scattering amplitudes, which differ from the Born approximation results.
Inhomogeneous nucleosynthesis with neutron diffusion
Physical Review D, 1988
It was recently proposed that a critical, i.e., closure, baryon density could be compatible with ... more It was recently proposed that a critical, i.e., closure, baryon density could be compatible with helium and deuterium observations, if this baryon density were suitably inhomogeneous during cosmic nucleosynthesis. In this scenario, neutrons would diffuse out of the high-density regions, which would lead to a nonstandard nucleosynthesis, with reduced helium production and improved deuterium survival, and could restore the agreement
Books [reviews of "A First Course in Computational Physics, 2nd ed. (DeVries, P. and Hasbun, J.; 2010) and "Numerical Relativity (Baumgarte, T.W. and Shapiro, S.L.; 2010)]
Computing in Science & Engineering, 2000
Cosmological spatial curvature probed by microwave polarization
Physical Review D, 1982
Inhomogeneous inflation: The initial-value problem
Physical Review D, 1991
... VOLUME 44, NUMBER 10 Inhomogeneous inflation: The initial-value problem Pablo Laguna Theoreti... more ... VOLUME 44, NUMBER 10 Inhomogeneous inflation: The initial-value problem Pablo Laguna Theoretical Division, Los Alamos National Laboratory, Los ... a derivation of the 3 + 1-dimensional version of these formulas, see Choquet-Bruhat, DeWitt-Morette, and Dillard-Bleick [20 ...
Nonlinear wave solutions to the planar vacuum Einstein equations
Physical Review D, 1991
Nonlinear solutions for initial data in the vacuum Einstein equations in plane symmetry
Physical Review D, 1989
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Papers by richard matzner