General relativistic null-cone evolutions with a high-order scheme

We present a high-order scheme for solving the full non-linear Einstein equations on characteristic null hypersurfaces using the framework established by Bondi and Sachs. This formalism allows asymptotically flat spaces to be represented on a finite, compactified grid, and is thus ideal for far-field studies of gravitational radiation. We have designed an algorithm based on 4th-order radial integration and finite differencing, and a spectral representation of angular components. The scheme can offer significantly more accuracy with relatively low computational cost compared to previous methods as a result of the higher-order discretization. Based on a newly implemented code, we show that the new numerical scheme remains stable and is convergent at the expected order of accuracy.Comment: 24 pages, 3 figure

Neuropsychological Deficits Are Correlated with Frontal Hypometabolism in Positron Emission Tomography Studies of Older Alcoholic Patients

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/66315/1/j.1530-0277.1993.tb00750.x.pd

The dynamics of apparent horizons in Robinson-Trautman spacetimes

We present an alternative scheme of finding apparent horizons based on spectral methods applied to Robinson-Trautman spacetimes. We have considered distinct initial data such as representing the spheroids of matter and the head-on collision of two non-rotating black holes. The evolution of the apparent horizon is presented. We have obtained in some cases a mass gap between the final Bondi and apparent horizon masses, whose implications were briefly commented in the light of the thermodynamics of black holes.Comment: 9 pages, 7 figure

Hypofractionated radiotherapy has the potential for second cancer reduction

<p>Abstract</p> <p>Background and Purpose</p> <p>A model for carcinoma and sarcoma induction was used to study the dependence of carcinogenesis after radiotherapy on fractionation.</p> <p>Materials and methods</p> <p>A cancer induction model for radiotherapy doses including fractionation was used to model carcinoma and sarcoma induction after a radiation treatment. For different fractionation schemes the dose response relationships were obtained. Tumor induction was studied as a function of dose per fraction.</p> <p>Results</p> <p>If it is assumed that the tumor is treated up to the same biologically equivalent dose it was found that large dose fractions could decrease second cancer induction. The risk decreases approximately linear with increasing fraction size and is more pronounced for sarcoma induction. Carcinoma induction decreases by around 10% per 1 Gy increase in fraction dose. Sarcoma risk is decreased by about 15% per 1 Gy increase in fractionation. It is also found that tissue which is irradiated using large dose fractions to dose levels lower than 10% of the target dose potentially develop less sarcomas when compared to tissues irradiated to all dose levels. This is not observed for carcinoma induction.</p> <p>Conclusions</p> <p>It was found that carcinoma as well as sarcoma risk decreases with increasing fractionation dose. The reduction of sarcoma risk is even more pronounced than carcinoma risk. Hypofractionation is potentially beneficial with regard to second cancer induction.</p

A correlation of the cosmic microwave sky with large scale structure

We cross correlate the large-scale cosmic microwave background (CMB) sky measured by WMAP with two probes of large-scale structure at z ~ 1. The hard X-ray background, measured by the HEAO-1 satellite, is positively correlated with the WMAP data at the 2.5-3.0 sigma level. The number counts of radio galaxies in the NVSS survey are also correlated at a slightly weaker level (2.-2.5 sigma). These correlations appear to arise from both hemispheres on the sky and are resilient to changes in the levels of masking of the Galaxy and point sources, suggesting that foregrounds are not responsible for the signal. The implication is that some of the observed CMB fluctuations arise at low redshifts. The level of the correlations is consistent with that expected for the cosmological constant (Omega_Lambda = 0.72) concordance model resulting from the integrated Sachs-Wolfe effect. Thus, we may be observing dark energy's effect on the growth of structure.Comment: 8 pages, 3 postscript figure

Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries

The article reviews the current status of a theoretical approach to the problem of the emission of gravitational waves by isolated systems in the context of general relativity. Part A of the article deals with general post-Newtonian sources. The exterior field of the source is investigated by means of a combination of analytic post-Minkowskian and multipolar approximations. The physical observables in the far-zone of the source are described by a specific set of radiative multipole moments. By matching the exterior solution to the metric of the post-Newtonian source in the near-zone we obtain the explicit expressions of the source multipole moments. The relationships between the radiative and source moments involve many non-linear multipole interactions, among them those associated with the tails (and tails-of-tails) of gravitational waves. Part B of the article is devoted to the application to compact binary systems. We present the equations of binary motion, and the associated Lagrangian and Hamiltonian, at the third post-Newtonian (3PN) order beyond the Newtonian acceleration. The gravitational-wave energy flux, taking consistently into account the relativistic corrections in the binary moments as well as the various tail effects, is derived through 3.5PN order with respect to the quadrupole formalism. The binary's orbital phase, whose prior knowledge is crucial for searching and analyzing the signals from inspiralling compact binaries, is deduced from an energy balance argument.Comment: 109 pages, 1 figure; this version is an update of the Living Review article originally published in 2002; available on-line at http://www.livingreviews.org

Breakdown of the adiabatic limit in low dimensional gapless systems

It is generally believed that a generic system can be reversibly transformed from one state into another by sufficiently slow change of parameters. A standard argument favoring this assertion is based on a possibility to expand the energy or the entropy of the system into the Taylor series in the ramp speed. Here we show that this argumentation is only valid in high enough dimensions and can break down in low-dimensional gapless systems. We identify three generic regimes of a system response to a slow ramp: (A) mean-field, (B) non-analytic, and (C) non-adiabatic. In the last regime the limits of the ramp speed going to zero and the system size going to infinity do not commute and the adiabatic process does not exist in the thermodynamic limit. We support our results by numerical simulations. Our findings can be relevant to condensed-matter, atomic physics, quantum computing, quantum optics, cosmology and others.Comment: 11 pages, 5 figures, to appear in Nature Physics (originally submitted version

Characteristic Evolution and Matching

I review the development of numerical evolution codes for general relativity based upon the characteristic initial value problem. Progress in characteristic evolution is traced from the early stage of 1D feasibility studies to 2D axisymmetric codes that accurately simulate the oscillations and gravitational collapse of relativistic stars and to current 3D codes that provide pieces of a binary black hole spacetime. Cauchy codes have now been successful at simulating all aspects of the binary black hole problem inside an artificially constructed outer boundary. A prime application of characteristic evolution is to extend such simulations to null infinity where the waveform from the binary inspiral and merger can be unambiguously computed. This has now been accomplished by Cauchy-characteristic extraction, where data for the characteristic evolution is supplied by Cauchy data on an extraction worldtube inside the artificial outer boundary. The ultimate application of characteristic evolution is to eliminate the role of this outer boundary by constructing a global solution via Cauchy-characteristic matching. Progress in this direction is discussed.Comment: New version to appear in Living Reviews 2012. arXiv admin note: updated version of arXiv:gr-qc/050809

Mass and Angular Momentum in General Relativity

We present an introduction to mass and angular momentum in General Relativity. After briefly reviewing energy-momentum for matter fields, first in the flat Minkowski case (Special Relativity) and then in curved spacetimes with or without symmetries, we focus on the discussion of energy-momentum for the gravitational field. We illustrate the difficulties rooted in the Equivalence Principle for defining a local energy-momentum density for the gravitational field. This leads to the understanding of gravitational energy-momentum and angular momentum as non-local observables that make sense, at best, for extended domains of spacetime. After introducing Komar quantities associated with spacetime symmetries, it is shown how total energy-momentum can be unambiguously defined for isolated systems, providing fundamental tests for the internal consistency of General Relativity as well as setting the conceptual basis for the understanding of energy loss by gravitational radiation. Finally, several attempts to formulate quasi-local notions of mass and angular momentum associated with extended but finite spacetime domains are presented, together with some illustrations of the relations between total and quasi-local quantities in the particular context of black hole spacetimes. This article is not intended to be a rigorous and exhaustive review of the subject, but rather an invitation to the topic for non-experts. In this sense we follow essentially the expositions in Szabados 2004, Gourgoulhon 2007, Poisson 2004 and Wald 84, and refer the reader interested in further developments to the existing literature, in particular to the excellent and comprehensive review by Szabados (2004).Comment: 41 pages. Notes based on the lecture given at the C.N.R.S. "School on Mass" (June 2008) in Orleans, France. To appear as proceedings in the book "Mass and Motion in General Relativity", eds. L. Blanchet, A. Spallicci and B. Whiting. Some comments and references added