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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. -
On Photon Spheres and 2+1 Dimensional General Relativity
EBERHARD KARLS UNIVERSITAT¨ TUBINGEN¨ MATHEMATISCH-NATURWISSENSCHAFTLICHE FAKULTAT¨ BACHELORARBEIT DER MATHEMATIK On photon spheres and 2+1 dimensional General Relativity von Oliver Schon¨ betreut durch JProf. Dr. Carla CEDERBAUM Tubingen,¨ 3. Oktober 2017 Eigenstandigkeitserkl¨ arung¨ Ich erklare¨ hiermit, dass ich meine Bachelorarbeit selbststandig¨ und ohne Benutzung anderer als der angegebenen Hilfsmittel angefertigt habe und dass ich alle Stellen, die ich wortlich¨ oder sinngemaߨ aus Veroffentlichungen¨ entnommen habe, als solche kenntlich gemacht habe. Tubingen,¨ den 3. Oktober 2017 Oliver Schon¨ Contents Abstract4 1 Mathematical setup5 1.1 Manifolds and tensors.............................5 1.2 Spacetime, connection and the Christoffel symbols.............9 1.3 Geodesics................................... 13 1.4 Curvature and Einstein equations....................... 15 1.5 Asymptotic flatness and mass......................... 18 1.6 Submanifolds................................. 22 1.7 Conformal geometry............................. 24 1.8 The Schwarzschild solution.......................... 25 2 Photon surfaces and spheres 27 2.1 Basic definitions and properties........................ 27 2.2 Photon sphere in Schwarzschild....................... 31 2.2.1 A physical approach......................... 31 2.2.2 A mathematical approach...................... 33 2.3 Uniqueness of photon spheres........................ 36 3 Schwarzschild in (2+1) dimensions 41 3.1 Pseudo-Schwarzschild spacetime....................... 41 3.2 Submanifolds in Pseudo-Schwarzschild................... 48 3.3 Construction with Pseudo-Schwarzschild.................. 52 Bibliography 57 3 Abstract In a recent paper C. Cederbaum and G. Galloway established a uniqueness result of photon spheres in four dimensional static vacuum asymptotically flat spacetimes by adapting Bunting and Masood-ul Alam’s proof of static black hole uniqueness. In this work, we1 present all concepts necessary to understand this proof as well as give a of the proof itself. -
Review 2008 (Session 2006-2007) the Royal Society of Edinburgh Review 2008
The Royal Society of Edinburgh Review 2008 (Session 2006-2007) The Royal Society of Edinburgh Review 2008 The Royal Society of Edinburgh Printed in Great Britain by Henry Ling Limited, Dorchester, DT1 1HD ISSN 1476-4342 CONTENTS Proceedings of the Ordinary Meetings .................................... 3 Proceedings of the Statutory General Meeting ....................... 5 Trustees’ Report to 31 March 2007 ...................................... 29 Auditors’ Report and Accounts ............................................. 49 Schedule of Investments ....................................................... 51 Activities Prize Lectures ..................................................................... 79 Lectures............................................................................ 127 Conferences, Workshops, Symposia, Seminars and Discussion Forums ............................................................ 169 Publications ...................................................................... 211 The Scottish Science Advisory Committee ........................ 213 Evidence, Advice and Comment ....................................... 215 Inquiries ........................................................................... 217 Parliamentary Liaison ........................................................ 219 Events for Young People .................................................. 221 Research and Enterprise Awards ...................................... 225 Medals, Prizes and Prize Lectureships ................................ 229 -
On the Uniqueness of Kerr-Newman Black Holes
On the uniqueness of Kerr-Newman black holes Willie Wai-Yeung Wong A Dissertation Presented to the Faculty of Princeton University in Candidacy for the Degree of Doctor of Philosophy Recommended for Acceptance by the Department of Mathematics Adviser: Sergiu Klainerman June 2009 c Copyright by Willie Wai-Yeung Wong, 2009. All Rights Reserved Abstract The uniqueness of the Kerr-Newman family of black hole metrics as stationary asymp- totically flat solutions to the Einstein equations coupled to a free Maxwell field is a crucial ingredient in the study of final states of the universe in general relativity. If one imposes the additional requirement that the space-time is axial-symmetric, then said uniqueness was shown by the works of B. Carter, D.C. Robinson, G.L. Bunting, and P.O. Mazur during the 1970s and 80s. In the real-analytic category, the condi- tion of axial symmetry can be removed through S. Hawking’s Rigidity Theorem. The necessary construction used in Hawking’s proof, however, breaks down in the smooth category as it requires solving an ill-posed hyperbolic partial differential equation. The uniqueness problem of Kerr-Newman metrics in the smooth category is con- sidered here following the program initiated by A. Ionescu and S. Klainerman for uniqueness of the Kerr metrics among solutions to the Einstein vacuum equations. In this work, a space-time, tensorial characterization of the Kerr-Newman solutions is obtained, generalizing an earlier work of M. Mars. The characterization tensors are shown to obey hyperbolic partial differential equations. Using the general Carle- man inequality of Ionescu and Klainerman, the uniqueness of Kerr-Newman metrics is proven, conditional on a rigidity assumption on the bifurcate event horizon. -
Partielle Differenzialgleichungen
Partielle Differenzialgleichungen Eine Einführung in analytische und numerische Methoden Bearbeitet von Wolfgang Arendt, Karsten Urban 1. Auflage 2010. Taschenbuch. xii, 353 S. Paperback ISBN 978 3 8274 1942 2 Format (B x L): 16,8 x 24 cm Gewicht: 616 g Weitere Fachgebiete > Mathematik > Mathematische Analysis > Differentialrechnungen und -gleichungen Zu Inhaltsverzeichnis schnell und portofrei erhältlich bei Die Online-Fachbuchhandlung beck-shop.de ist spezialisiert auf Fachbücher, insbesondere Recht, Steuern und Wirtschaft. Im Sortiment finden Sie alle Medien (Bücher, Zeitschriften, CDs, eBooks, etc.) aller Verlage. Ergänzt wird das Programm durch Services wie Neuerscheinungsdienst oder Zusammenstellungen von Büchern zu Sonderpreisen. Der Shop führt mehr als 8 Millionen Produkte. 1 Modellierung oder wie man auf eine Differenzial- gleichung kommt Partielle Differenzialgleichungen beschreiben zahlreiche Vorgänge in der Natur, der Technik, der Medizin oder der Wirtschaft. In diesem ersten Kapitel wollen wir für einige prominente Beispiele die Herleitung von partiellen Differenzialglei- chungen mit Hilfe von Naturgesetzen und mathematischen Tatsachen beschrei- ben. Eine solche Herleitung nennt man (mathematische) Modellierung. Die Bei- spiele sollen auch die Vielfältigkeit der partiellen Differenzialgleichungen illus- trieren, die in diversen Anwendungen auftreten. Eine erste grobe Klassifizierung wird am Ende des Kapitels vorgenommen. Übersicht 1.1 Mathematische Modellierung ........................ 2 1.2 Transportprozesse............................. -
Atolladeros Del Pensamiento Aleatorio: Batallas En Torno De La Prueba Estadística De La Hipótesis Nula En Ciencias Sociales
Carlos Reynoso – Antropología y estadísticas Antropología y estadísticas: Batallas en torno de la Hipótesis Nula Carlos Reynoso Universidad de Buenos Aires http://carlosreynoso.com.ar Versión 04-09 – Abril de 2021 Segunda edición corregida y ampliada Atolladeros del pensamiento aleatorio: Batallas en torno de la Prueba Estadística de la Hipótesis Nula en Ciencias Sociales ................................................................................ 1 1. Introducción .............................................................................................................. 2 2. Prueba de la Hipótesis Nula – Teoría e historia ....................................................... 5 3. El discurso del método ........................................................................................... 13 4. El lado oscuro de la inferencia inductiva................................................................ 17 5. El surgimiento de la crítica ..................................................................................... 24 6. Errores de tipo I y II ............................................................................................... 30 7. Significancia y significado ..................................................................................... 36 8. El elusivo significado de la hipótesis nula.............................................................. 43 9. Los valores de p ...................................................................................................... 49 10. El arte de la interpretación -
Wheeler, Tiomno E a Fısica Brasileira
426 Jos´e Maria Filardo Bassalo e Olival Freire Junior Wheeler, Tiomno e a F´ısica Brasileira (Wheeler, Tiomno, and Brazilian Physics) Jos´e Maria Filardo Bassalo∗ Departamento de F´ısica da UFPA, 66075-900, Bel´em, Par´a, Brasil Olival Freire Junior† Instituto de F´ısica da UFBA, 40210-340, Salvador, BA, Brasil Recebido em 01 Outubro, 2003. Aceito em 31 de outubro, 2003. Este artigo examina as relac¸˜oes do f´ısico norte-americano John Archibald Wheeler com o f´ısico brasileiro Jayme Tiomno. A imagem de Tiomno como um dos f´ısicos te´oricos mais brilhantes de sua gerac¸˜ao emerge amplifi- cada; mas fica claro, tamb´em, que os preju´ızos causados pelo regime militar (1964-1985) ao desenvolvimento da ciˆencia brasileira foram ainda maiores do que os que usualmente se reconhece. This paper analyzes the relationships between the American physicist, John Archibald Wheeler, and the Brazil- ian physicist Jayme Tiomno. It enlarges Tiomno’s image as one of the most gifted theoretical physicist of his generation and it reveals that the losses of the Brazilian science, due to the military government (1964-1985), were more meaningful than what one usually admits. 1 Introduc¸ao˜ reconhecemos. I always think of Tiomno as one of the most unappreciated of physicists. His work on muon decay and capture in 1947-1949 was pathbreaking and would 2 Wheeler: uma vida entre still merit recognition by some suitable award. J. A. Wheeler, 1998. part´ıculas, campos e informac¸ao˜ Wheeler nasceu em Jacksonville, Fl´orida, no dia 9 de julho Neste artigo, examinaremos as relac¸˜oes do f´ısico norte- de 1911. -
Istoria Matematicii
IstoriaMatematicii file:///C:/Programele%20Mele/IstoriaMatematicii/IstoriaMatematicii.html Istoria Matematicii Cuprins: Introducere Numere și reprezentarea lor Aritmetică Algebră Geometrie Analiză matematică Logică Matematică aplicată Matematică computațională Programarea calculatoarelor Repere istorice Introducere Din totdeauna, matematica a făcut apanajul potentaților vremii, a fost un instrument cu ajutorul căruia oamenii și-au măsurat bogăția, strălucirea sau puterea. Acest material nu își propune o înșiruire de date istorice sau nume ale unor matematicieni aranjate cronologic, ci mai degrabă o călătorie în timp prin universul matematicii, pentru a redescoperi ordinea în care s-au formulat principalele probleme și soluțiile lor. Dintre personalitățile matematicii, atenția se va abate mai mult asupra celor care au avut ceva de socotit, decât asupra acelora care au făcut socotelile. Oricare dintre realizările lor poate fi astăzi un bun exercițiu pentru scrie proiectul cu mijloace moderne, sau pentru calculul necesarului. Cel care poate alcătui proiectul și caietul de sarcini pentru Piramida lui Keops, sau pentru Zidul Chinezesc, va putea proiecta mai ușor o locuință modernă sau o anexă. Poate fi un exercițiu bun și calculația pentru un proiect ce utilizează doar tehnologia și resursele existente la vremea respectivă. Fiecare dintre subiectele propuse poate face subiectul unei disertații, al unui eseu sau al unei ore de curs facultativ. Nedorind a amalgama prea mult noțiunile și așa destul de complexe, șirul povestirii este deșirat în mai multe capitole, structurate pentru diferitele ramuri ale matematicii. Textul nu are caracter didactic dar poate inspira viitorii profesori de matematică. Este bun un pretext pentru o călătorie în timp, un fel de temă de casă a unui elev mai întârziat ca vârstă. -
Historia Teorii Względności
Historia TeoriiW zglêdnoœci Ciekawewyniki po1955 Zbigniew Osiak 05 Linki do moich publikacji naukowych i popularnonaukowych, e-booków oraz audycji telewizyjnych i radiowych są dostępne w bazie ORCID pod adresem internetowym: http://orcid.org/0000-0002-5007-306X (Tekst) Zbigniew Osiak HISTORIA TEORII WZGLĘDOŚCI Ciekawe wyniki po 1955 (Ilustracje) Małgorzata Osiak © Copyright 2015 by Zbigniew Osiak (text) and Małgorzata Osiak (illustrations) Wszelkie prawa zastrzeżone. Rozpowszechnianie i kopiowanie całości lub części publikacji zabronione bez pisemnej zgody autora tekstu i autorki ilustracji. Portret autora zamieszczony na okładkach przedniej i tylnej Rafał Pudło Wydawnictwo: Self Publishing ISBN: 978-83-272-4479-6 e-mail: [email protected] Wstęp 5 “Historia Teorii Względności – Ciekawe wyniki po 1955” jest piątym z pięciu tomów pomocniczych materiałów do prowadzonego przeze mnie seminarium dla słuchaczy Uniwersytetu Trzeciego Wieku w Uniwersytecie Wrocławskim. Szczegółowe informacje dotyczące sygnalizowanych tam zagadnień zainteresowani Czytelnicy znajdą w innych moich eBookach: Z. Osiak: Szczególna Teoria Względności. Self Publishing (2012). Z. Osiak: Ogólna Teoria Względności. Self Publishing (2012). Z. Osiak: Antygrawitacja . Self Publishing (2012). Z. Osiak: Energia w Szczególnej Teorii Względności. SP (2012). Z. Osiak: Giganci Teorii Względności. Self Publishing (2012). Z. Osiak: Teoria Względności – Prekursorzy. Self Publishing (2012). Z. Osiak: Teoria Względności – Twórcy. Self Publishing (2013). Z. Osiak: Teoria Względności – Kulisy. Self Publishing (2012). Z. Osiak: Teoria Względności – Kalendarium. SP (2013). Wstęp 6 Zapis wszystkich pomocniczych materiałów zgrupowanych w pięciu tomach zostanie zamieszczony w internecie w postaci eBooków. Z. Osiak: Historia Teorii Względności – Od Kopernika do ewtona Z. Osiak: Historia Teorii Względności – Od ewtona do Maxwella Z. Osiak: Historia Teorii Względności – Od Maxwella do Einsteina Z. -
MARTIN DAVID KRUSKAL Martin David Kruskal, One of the Most Insightful and Innovative of Applied Mathematicians and Theoretical Physicists, Died on 26 December 2006
MARTIN DAVID KRUSKAL Martin David Kruskal, one of the most insightful and innovative of applied mathematicians and theoretical physicists, died on 26 December 2006. During his long active career, largely at Princeton, then latterly at Rutgers University, his many honours included the National Medal of Science in 1993, the Gibbs Lectureship and the 2006 Steele Prize for Seminal Contribution to Research (both from the American Mathematical Society) and the Maxwell Prize from the International Congress on Industrial and Applied Mathematics. He was a member of the National Academy of Sciences (1980), foreign member of the Royal Society of London (1997) and of the Russian Academy of Sciences (2000) and a Honorary Fellow of the RSE (2001). Born in New York City on 28 September 1925, he grew up in New Rochelle, New York, with two brothers destined also to become well-known mathematicians. He received his BS in mathematics from the University of Chicago in 1945, then moving to New York University for his MS and PhD under Richard Courant (a neighbour of his parents) and Bernard Friedman on `The bridge theorem for minimal surfaces'. His first employment, from 1951, was on the (classified) Project Matterhorn which aimed to use controlled nuclear fusion as a clean, safe energy source. Under the project's director Lyman Spitzer, he supplied the expertise in mathematical modelling and analysis crucial in laying down the theoretical foundations for controlled fusion and the yet undeveloped field of plasma physics. After declassification, the project became the Princeton Plasma Physics Laboratory, where Kruskal became successively Associate Head of the Theoretical Division, then Senior Research Associate, while combining his sophisticated knowledge of mathematics with strong physical intuition to develop important results both in mathematical technique and for physical application. -
On the Uniqueness of Kerr-Newman Black Holes
On the uniqueness of Kerr-Newman black holes Willie Wai-Yeung Wong A Dissertation Presented to the Faculty of Princeton University in Candidacy for the Degree of Doctor of Philosophy Recommended for Acceptance by the Department of Mathematics Adviser: Sergiu Klainerman June 2009 c Copyright by Willie Wai-Yeung Wong, 2010. All Rights Reserved Abstract The uniqueness of the Kerr-Newman family of black hole metrics as stationary asymp- totically flat solutions to the Einstein equations coupled to a free Maxwell field is a crucial ingredient in the study of final states of the universe in general relativity. If one imposes the additional requirement that the space-time is axial-symmetric, then said uniqueness was shown by the works of B. Carter, D.C. Robinson, G.L. Bunting, and P.O. Mazur during the 1970s and 80s. In the real-analytic category, the condi- tion of axial symmetry can be removed through S. Hawking’s Rigidity Theorem. The necessary construction used in Hawking’s proof, however, breaks down in the smooth category as it requires solving an ill-posed hyperbolic partial differential equation. The uniqueness problem of Kerr-Newman metrics in the smooth category is con- sidered here following the program initiated by A. Ionescu and S. Klainerman for uniqueness of the Kerr metrics among solutions to the Einstein vacuum equations. In this work, a space-time, tensorial characterization of the Kerr-Newman solutions is obtained, generalizing an earlier work of M. Mars. The characterization tensors are shown to obey hyperbolic partial differential equations. Using the general Carle- man inequality of Ionescu and Klainerman, the uniqueness of Kerr-Newman metrics is proven, conditional on a rigidity assumption on the bifurcate event horizon. -
Wheeler, Tiomno E a Física Brasileira1
CBPF-CS-001/04 WHEELER, TIOMNO E A FÍSICA BRASILEIRA1 JOSÉ MARIA FILARDO BASSALO Departamento de Física da UFPA ([email protected]) OLIVAL FREIRE JUNIOR Instituto de Física da UFBA ([email protected]) I always think of Tiomno as one of the most unappreciated of physicists. His work on muon decay and capture in 1947-1949 was pathbreaking and would still merit recognition by some suitable award. J. A. Wheeler, 1998. Introdução Neste artigo, examinaremos as relações do físico norte-americano John Archibald Wheeler com o físico brasileiro Jayme Tiomno, e com a Física Brasileira, tendo como pano de fundo uma apresentação das principais idéias e conceitos físicos formulados por Wheeler ao longo de sua carreira de pesquisador. Tomamos como ponto de partida a autobiografia de Wheeler, a qual nos fornece um panorama de sua trajetória intelectual [1], marcada por uma permanente inconformidade com as idéias já estabelecidas na ciência, além de um interessante quadro da Física e de seu contexto, ao longo de um vasto período entre 1930 e 1990. O livro revela também um fragmento da história da física brasileira, com um expressivo depoimento a propósito da carreira científica de Tiomno. A consulta aos arquivos pessoais de Wheeler permite ampliar significativamente a informação sobre as relações entre Wheeler e a Física Brasileira, e sugere uma interessante reflexão tanto sobre a pujança intelectual quanto sobre as vicissitudes características da nossa ciência [2]. A imagem de Tiomno como um dos físicos teóricos mais brilhantes de sua geração emerge amplificada desse estudo; mas fica claro, também, que os prejuízos causados pelo regime militar ao desenvolvimento da ciência brasileira foram ainda maiores do que os que usualmente reconhecemos.