A Festschrift for Thomas Erber
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The Emergence of Gravitational Wave Science: 100 Years of Development of Mathematical Theory, Detectors, Numerical Algorithms, and Data Analysis Tools
BULLETIN (New Series) OF THE AMERICAN MATHEMATICAL SOCIETY Volume 53, Number 4, October 2016, Pages 513–554 http://dx.doi.org/10.1090/bull/1544 Article electronically published on August 2, 2016 THE EMERGENCE OF GRAVITATIONAL WAVE SCIENCE: 100 YEARS OF DEVELOPMENT OF MATHEMATICAL THEORY, DETECTORS, NUMERICAL ALGORITHMS, AND DATA ANALYSIS TOOLS MICHAEL HOLST, OLIVIER SARBACH, MANUEL TIGLIO, AND MICHELE VALLISNERI In memory of Sergio Dain Abstract. On September 14, 2015, the newly upgraded Laser Interferometer Gravitational-wave Observatory (LIGO) recorded a loud gravitational-wave (GW) signal, emitted a billion light-years away by a coalescing binary of two stellar-mass black holes. The detection was announced in February 2016, in time for the hundredth anniversary of Einstein’s prediction of GWs within the theory of general relativity (GR). The signal represents the first direct detec- tion of GWs, the first observation of a black-hole binary, and the first test of GR in its strong-field, high-velocity, nonlinear regime. In the remainder of its first observing run, LIGO observed two more signals from black-hole bina- ries, one moderately loud, another at the boundary of statistical significance. The detections mark the end of a decades-long quest and the beginning of GW astronomy: finally, we are able to probe the unseen, electromagnetically dark Universe by listening to it. In this article, we present a short historical overview of GW science: this young discipline combines GR, arguably the crowning achievement of classical physics, with record-setting, ultra-low-noise laser interferometry, and with some of the most powerful developments in the theory of differential geometry, partial differential equations, high-performance computation, numerical analysis, signal processing, statistical inference, and data science. -
Generalizations of the Kerr-Newman Solution
Generalizations of the Kerr-Newman solution Contents 1 Topics 1035 1.1 ICRANetParticipants. 1035 1.2 Ongoingcollaborations. 1035 1.3 Students ............................... 1035 2 Brief description 1037 3 Introduction 1039 4 Thegeneralstaticvacuumsolution 1041 4.1 Line element and field equations . 1041 4.2 Staticsolution ............................ 1043 5 Stationary generalization 1045 5.1 Ernst representation . 1045 5.2 Representation as a nonlinear sigma model . 1046 5.3 Representation as a generalized harmonic map . 1048 5.4 Dimensional extension . 1052 5.5 Thegeneralsolution . 1055 6 Tidal indicators in the spacetime of a rotating deformed mass 1059 6.1 Introduction ............................. 1059 6.2 The gravitational field of a rotating deformed mass . 1060 6.2.1 Limitingcases. 1062 6.3 Circularorbitsonthesymmetryplane . 1064 6.4 Tidalindicators ........................... 1065 6.4.1 Super-energy density and super-Poynting vector . 1067 6.4.2 Discussion.......................... 1068 6.4.3 Limit of slow rotation and small deformation . 1069 6.5 Multipole moments, tidal Love numbers and Post-Newtonian theory................................. 1076 6.6 Concludingremarks . 1077 7 Neutrino oscillations in the field of a rotating deformed mass 1081 7.1 Introduction ............................. 1081 7.2 Stationary axisymmetric spacetimes and neutrino oscillation . 1082 7.2.1 Geodesics .......................... 1083 1033 Contents 7.2.2 Neutrinooscillations . 1084 7.3 Neutrino oscillations in the Hartle-Thorne metric . 1085 7.4 Concludingremarks . 1088 8 Gravitational field of compact objects in general relativity 1091 8.1 Introduction ............................. 1091 8.2 The Hartle-Thorne metrics . 1094 8.2.1 The interior solution . 1094 8.2.2 The Exterior Solution . 1096 8.3 The Fock’s approach . 1097 8.3.1 The interior solution . -
Arxiv:Gr-Qc/0112028V3 28 May 2002
Sergiu Vacaru and Panayiotis Stavrinos SPINORS and SPACE–TIME ANISOTROPY arXiv:gr-qc/0112028v3 28 May 2002 University of Athens, 2002 ————————————————— c Sergiu Vacaru and Panyiotis Stavrinos ii ... iii ABOUT THE BOOK This is the first monograph on the geometry of anisotropic spinor spaces and its applications in modern physics. The main subjects are the theory of grav- ity and matter fields in spaces provided with off–diagonal metrics and asso- ciated anholonomic frames and nonlinear connection structures, the algebra and geometry of distinguished anisotropic Clifford and spinor spaces, their extension to spaces of higher order anisotropy and the geometry of gravity and gauge theories with anisotropic spinor variables. The book summarizes the authors’ results and can be also considered as a pedagogical survey on the mentioned subjects. iv - v ABOUT THE AUTHORS Sergiu Ion Vacaru was born in 1958 in the Republic of Moldova. He was educated at the Universities of the former URSS (in Tomsk, Moscow, Dubna and Kiev) and reveived his PhD in theoretical physics in 1994 at ”Al. I. Cuza” University, Ia¸si, Romania. He was employed as principal senior researcher, as- sociate and full professor and obtained a number of NATO/UNESCO grants and fellowships at various academic institutions in R. Moldova, Romania, Germany, United Kingdom, Italy, Portugal and USA. He has published in English two scientific monographs, a university text–book and more than hundred scientific works (in English, Russian and Romanian) on (super) gravity and string theories, extra–dimension and brane gravity, black hole physics and cosmolgy, exact solutions of Einstein equations, spinors and twistors, anistoropic stochastic and kinetic processes and thermodynamics in curved spaces, generalized Finsler (super) geometry and gauge gravity, quantum field and geometric methods in condensed matter physics. -
Memories of Julian Schwinger
Memories of Julian Schwinger Edward Gerjuoy* ABSTRACT The career and accomplishments of Julian Schwinger, who shared the Nobel Prize for physics in 1965, have been reviewed in numerous books and articles. For this reason these Memories, which seek to convey a sense of Schwinger’s remarkable talents as a physicist, concentrate primarily (though not entirely) on heretofore unpuBlished pertinent recollections of the youthful Schwinger by this writer, who first encountered Schwinger in 1934 when they both were undergraduates at the City College of New York. *University of Pittsburgh Dept. of Physics and Astronomy, Pittsburgh, PA 15260. 1 Memories of Julian Schwinger Julian Seymour Schwinger, who shared the 1965 Nobel prize in physics with Richard Feynman and Sin-itiro Tomonaga, died in Los Angeles on July 16, 1994 at the age of 76. He was a remarkably talented theoretical physicist, who—through his own publications and through the students he trained—had an enormous influence on the evolution of physics after World War II. Accordingly, his life and work have been reviewed in a number of publications [1-3, inter alia]. There also have been numerous published obituaries, of course [4-5, e.g.] These Memories largely are the text of the Schwinger portion of a colloquium talk, “Recollections of Oppenheimer and Schwinger”, which the writer has given at a number of universities, and which can be found on the web [6]. The portion of the talk devoted to J. Robert Oppenheimer—who is enduringly famous as director of the Los Alamos laboratory during World War II—has been published [7], but the portion devoted to Julian is essentially unpublished; references 7-9 describe the basically trivial exceptions to this last assertion. -
Center for History of Physics Newsletter, Spring 2008
One Physics Ellipse, College Park, MD 20740-3843, CENTER FOR HISTORY OF PHYSICS NIELS BOHR LIBRARY & ARCHIVES Tel. 301-209-3165 Vol. XL, Number 1 Spring 2008 AAS Working Group Acts to Preserve Astronomical Heritage By Stephen McCluskey mong the physical sciences, astronomy has a long tradition A of constructing centers of teaching and research–in a word, observatories. The heritage of these centers survives in their physical structures and instruments; in the scientific data recorded in their observing logs, photographic plates, and instrumental records of various kinds; and more commonly in the published and unpublished records of astronomers and of the observatories at which they worked. These records have continuing value for both historical and scientific research. In January 2007 the American Astronomical Society (AAS) formed a working group to develop and disseminate procedures, criteria, and priorities for identifying, designating, and preserving structures, instruments, and records so that they will continue to be available for astronomical and historical research, for the teaching of astronomy, and for outreach to the general public. The scope of this charge is quite broad, encompassing astronomical structures ranging from archaeoastronomical sites to modern observatories; papers of individual astronomers, observatories and professional journals; observing records; and astronomical instruments themselves. Reflecting this wide scope, the members of the working group include historians of astronomy, practicing astronomers and observatory directors, and specialists Oak Ridge National Laboratory; Santa encounters tight security during in astronomical instruments, archives, and archaeology. a wartime visit to Oak Ridge. Many more images recently donated by the Digital Photo Archive, Department of Energy appear on page 13 and The first item on the working group’s agenda was to determine through out this newsletter. -
Physics and Feynman's Diagrams » American Scientist 6/3/10 12:09 PM
Physics and Feynman's Diagrams » American Scientist 6/3/10 12:09 PM FEATURE ARTICLE Physics and Feynman's Diagrams In the hands of a postwar generation, a tool intended to lead quantum electrodynamics out of a decades-long morass helped transform physics David Kaiser George Gamow, the wisecracking theoretical physicist who helped invent the Big Bang model of the universe, was fond of explaining what he liked best about his line of work: He could lie down on a couch and close his eyes, and no one would be able to tell whether he was working or not. A fine gag, but a bad model for thinking about the day-to-day work that theoretical physicists do. For too long, physicists, historians and philosophers took Gamow's joke quite seriously. Research in theory, we were told, concerns abstract thought wholly separated from anything like labor, activity or skill. Theories, worldviews or paradigms seemed the appropriate units of analysis, and the challenge lay in charting the birth and conceptual development of particular ideas. In the accounts that resulted from such studies, the skilled manipulation of tools played little role. Ideas, embodied in texts, traveled easily from theorist to theorist, shorn of the material constraints that encumbered experimental physicists (tied as they were to their electron microscopes, accelerators or bubble chambers). The age-old trope of minds versus hands has been at play in our account of progress in physics, which pictures a purely cognitive realm of ideas separated from a manual realm of action. This depiction of what theorists do, I am convinced, obscures a great deal more than it clarifies. -
Axisymmetric Spacetimes in Relativity
9, tr' Axisymmetric Spacetimes in Relativity S. P. Drake Department of Physics and Mathematical Physics îåäi,î31 tÏfåi" Australia 22 July 1998 ACKNO\MTEDGEMENTS It is an unfortunate fact that only my name Soes on this thesis' This is not the work of one person, it is an accumulation of the labor of many' AII those who have helped me in ways that none of us could image should be acknowledged, but how. None of this would have been possible were it not for the wisdom and guidance of my supervisor Peter Szekeres. I have often pondered over the difficulty of supervising students. It must be heart-bleaking to watch as students make necessary mistakes. Patience I'm sure must be the key' So for his wisdom, patience and kindness I am deeply indebted to Peter Szekeres. Without the love and support of my family this thesis would never have begun, much less been completed, to them I owe my life, and all that comes with it. It would take too long to write the names of all those I wish to thank. Those who are special to me, have helped me through so much over the years will receive the thanks in Person. I would like to the department of physics here at Adelaide where most of my thesis work was done. I would like to thank the department of physics at Melbourne university, where I did my undergraduate degree and began my PhD. I would like to thank the university of Padova for there hospitality dur- ing my stay there. -
GR15 Workshop A3---Mathematical Studies of Field Equations---A Report
GR15 Workshop A3 Mathematical Studies of Field Equations A report Piotr T. Chru´sciel D´epartement de Math´ematiques, Facult´edes Sciences, Parc de Grandmont, F–37200 Tours, France September 25, 2018 1 Introduction In this report I have tried to describe the main streams of research presented at the workshop. Occasionally I have described some contributions which were presented in poster form, whenever they were directly related to the subjects presented in the talks. This paper is, essentially, a patchwork of various people description of their work, which I have edited in an attempt to obtain some uniformity in style, and to produce a report of finite length. Much to my regret, I had to cut or shorten a lot of material because of length constraints. I wish to thank all those who have sent me a contribution. arXiv:gr-qc/9803008v1 2 Mar 1998 2 The Riemannian Penrose Inequality In 1972, Penrose [89] gave a heuristic argument to establish the geometric in- equality mADM (M) ≥ |N|/16π (2.1) q for a time-reversible initial data set (M,g), where |N| is the area of a marginally trapped surface bounding M. We refer to (2.1) as the Riemannian Penrose inequality, because throughout this section it is assumed that the initial data have vanishing extrinsic curvature, Kij = 0. Penrose’s argument relies on knowledge of the future evolution of M, including the Hawking area monotonicity of the (suitably differentiable) event horizon. Therefore, Penrose suggested that (2.1) can be seen as a Riemannian test for the standard picture of black hole formation, particularly the Weak Cosmic Censorship Hypothesis. -
Arxiv:1608.03021V1 [Gr-Qc]
Ernst formulation of axisymmetric fields in f(R) gravity: applications to neutron stars and gravitational waves Arthur George Suvorov∗ and Andrew Melatos† School of Physics, University of Melbourne, Parkville VIC 3010, Australia (Dated: October 30, 2018) The Ernst formulation of the Einstein equations is generalised to accommodate f(R) theories of gravity. It is shown that, as in general relativity, the axisymmetric f(R) field equations for a vacuum spacetime that is either stationary or cylindrically symmetric reduce to a single, non-linear differential equation for a complex-valued scalar function. As a worked example, we apply the generalised Ernst equations to derive a f(R) generalisation of the Zipoy-Voorhees metric, which may be used to describe the gravitational field outside of an ellipsoidal neutron star. We also apply the theory to investigate the phase speed of large-amplitude gravitational waves in f(R) gravity in the context of soliton-like solutions that display shock-wave behaviour across the causal boundary. PACS numbers: 04.20.Jb, 04.30.Nk, 04.50.Kd, 04.70.Bw I. INTRODUCTION function f and its derivatives, as well as the Ricci scalar R and its derivatives. Since their initial presentation, the Einstein equations There are two flavours of Ernst equation that we gen- have been rewritten in many different ways [1, 2]. For sta- eralise here to the f(R) theory of gravity: stationary, tionary and axisymmetric spacetimes, the Ernst formula- and cylindrically symmetric. Stationary spacetimes arise tion has proved to be an especially useful representation in numerous physically important contexts; for example, [3]. -
Gravitational and Electromagnetic Potentials of the Stationary Einstein
Gravitational and electromagnetic potentials of the stationary Einstein-Maxwell field equations by Thaddeus Charles Jones A thesis submitted in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY in Physics Montana State University © Copyright by Thaddeus Charles Jones (1979) Abstract: Associated with the stationary Einstein-Maxwell field equations is an infinite hierarchy of potentials. The basic characteristics of these potentials are examined in general and then in greater detail for the particular case of the Reissner-Nordstrom metric. Their essential utility in the process of solution generation is elucidated and the necessary equations for solution generation are developed. Appropriate generating functions, which contain the complete infinite hierarchy of potentials, are developed and analyzed. Particular attention is paid to the inherent gauge freedom of these generating functions. Two methods of solution generation, which yield asymptotically flat solutions in vacuum, are generalized to include electromagnetism. One method, using potentials consistent with the Harrison transformation and the Reissner-Nordstrom metric, is discussed in detail and its resultant difficulties explored. GRAVITATIONAL AND ELECTROMAGNETIC POTENTIALS OF THE STATIONARY EINSTEIN-MAXWELL FIELD EQUATIONS by THADDEUS CHARLES JONES A thesis submitted in partial fulfillment of the requirements for the degree . o* DOCTOR OF PHILOSOPHY in Physics Approved: MONTANA STATE UNIVERSITY Bozeman, Montana June, 1979 iii ACKNOWLEDGMENTS I have but one person to thank for the most chal lenging and exciting intellectual period of my life. Dr. William Kinnersley. I express my gratitude for his continued faith in me during times when I had almost lost my own. I also gratefully acknowledge the many hours of clarifying discussion with Dr. -
Fundamental Equations for Hypersurfaces
Appendix A Fundamental Equations for Hypersurfaces In this appendix we consider submanifolds with codimension 1 of a pseudo- Riemannian manifold and derive, among other things, the important equations of Gauss and Codazzi–Mainardi. These have many useful applications, in particular for 3 + 1 splittings of Einstein’s equations (see Sect. 3.9). For definiteness, we consider a spacelike hypersurface Σ of a Lorentz manifold (M, g). Other situations, e.g., timelike hypersurfaces can be treated in the same way, with sign changes here and there. The formulation can also be generalized to sub- manifolds of codimension larger than 1 of arbitrary pseudo-Riemannian manifolds (see, for instance, [51]), a situation that occurs for instance in string theory. Let ι : Σ −→ M denote the embedding and let g¯ = ι∗g be the induced metric on Σ. The pair (Σ, g)¯ is a three-dimensional Riemannian manifold. Other quanti- ties which belong to Σ will often be indicated by a bar. The basic results of this appendix are most efficiently derived with the help of adapted moving frames and the structure equations of Cartan. So let {eμ} be an orthonormal frame on an open region of M, with the property that the ei ,fori = 1, 2, 3, at points of Σ are tangent μ to Σ. The dual basis of {eμ} is denoted by {θ }.OnΣ the {ei} can be regarded as a triad of Σ that is dual to the restrictions θ¯i := θ j |TΣ(i.e., the restrictions to tangent vectors of Σ). Indices for objects on Σ always refer to this pair of dual basis. -
Of the Annual
Institute for Advanced Study IASInstitute for Advanced Study Report for 2013–2014 INSTITUTE FOR ADVANCED STUDY EINSTEIN DRIVE PRINCETON, NEW JERSEY 08540 (609) 734-8000 www.ias.edu Report for the Academic Year 2013–2014 Table of Contents DAN DAN KING Reports of the Chairman and the Director 4 The Institute for Advanced Study 6 School of Historical Studies 10 School of Mathematics 20 School of Natural Sciences 30 School of Social Science 42 Special Programs and Outreach 50 Record of Events 58 79 Acknowledgments 87 Founders, Trustees, and Officers of the Board and of the Corporation 88 Administration 89 Present and Past Directors and Faculty 91 Independent Auditors’ Report CLIFF COMPTON REPORT OF THE CHAIRMAN I feel incredibly fortunate to directly experience the Institute’s original Faculty members, retired from the Board and were excitement and wonder and to encourage broad-based support elected Trustees Emeriti. We have been profoundly enriched by for this most vital of institutions. Since 1930, the Institute for their dedication and astute guidance. Advanced Study has been committed to providing scholars with The Institute’s mission depends crucially on our financial the freedom and independence to pursue curiosity-driven research independence, particularly our endowment, which provides in the sciences and humanities, the original, often speculative 70 percent of the Institute’s income; we provide stipends to thinking that leads to the highest levels of understanding. our Members and do not receive tuition or fees. We are The Board of Trustees is privileged to support this vital immensely grateful for generous financial contributions from work.