The Royal Society of Edinburgh Review 2002

Total Page:16

File Type:pdf, Size:1020Kb

The Royal Society of Edinburgh Review 2002 The Royal Society of Edinburgh Review 2002 (Session 2000-2001) The Royal Society of Edinburgh Review 2002 CONTENTS Contents Proceedings of the Ordinary Meetings .............................................3 Proceedings of the Statutory General Meeting .................................7 General Secretary’s Report. ..............................................................7 Treasurer’s Report ......................................................................... 15 Accounts for the financial year ending 31 March 2001 ................. 21 Activities Prize Lectures .............................................................................. 41 Lectures ...................................................................................... 49 Conferences, Symposia, Workshops and Exhibitions .................. 79 Publications ............................................................................. 107 Fundraising .............................................................................. 109 Scottish Science Advisory Committee ........................................ 111 Evidence, Advice and Comment ................................................ 113 Inquiries ................................................................................... 115 Public Policy Seminars ............................................................... 117 Links with Industry ................................................................... 119 Events for Young People ........................................................... 121 Research Awards ...................................................................... 123 Medals, Prizes and Prize Lectureships ........................................ 129 Grants Committee .................................................................... 131 International Programme.......................................................... 133 Fellows’ Social Events ............................................................... 135 Grants, Sponsorship and Donations ........................................... 137 Changes in Fellowship During the Session .................................. 139 Staff ........................................................................................... 141 PROCEEDINGS OF THE ORDINARY MEETINGS See pp 41-78 for reports on lectures and prize lectures 6 November 2000 5 February 2001 Chairman Chairman Sir William Stewart FRS PRSE Sir William Stewart FRS PRSE Lecture Formal Admission to Fellowship Heterogeneous catalysis: from Professor Robert Hale. ‘black art’ to atomic understand- Award ing. Professor Gerhard Ertl, The President presented the 30th HonFRSE, of the Fritz-Haber- Award of the Gunning Victoria Institut der Max-Planck- Jubilee Prize Lectureship to Gesellschaft, Berlin. (page 49) Professor Angus Macintyre, FRS, 4 December 2000 FRSE, Professor of Mathematics at the Department of Mathematics Chairman and Statistics, University of Edin- The Rt Hon Lord Ross PC, VPRSE burgh, for his outstanding Formal Admission to Fellowship contribution to logic, model Dr Christopher Browitt theory, algebra, analysis and Lecture theoretical computer science. People Flows and Knowledge Lecture Flows: international Students and What Does Gödel’s Theorem Mean Public Policy. Professor Lalage After 70 Years? (Gunning Victoria Bown, OBE, FRSE, Chair of the Jubilee Prize Lecture). Professor Council for Education in the Angus Macintyre, FRS, FRSE. (page Commonwealth Working Group 41) on Student Mobility. (page 57) 5 March 2001 8 January 2001 Chairman Chairman Sir William Stewart FRS PRSE Sir William Stewart FRS PRSE Election of Fellows (see list on Formal Admission to Fellowship page 139) Professor Kenneth Reid Scrutineers Lecture Bishop Mario Conti and Professor The Defences of Scapa Flow: George Holmes protecting the Royal Navy’s Fleet Formal Admission to Honorary Anchorage, 1914–1945. Mr Fellowship Geoffrey Stell, Head of Architec- Professor Lawrence Markus ture at the Royal Commission on the Ancient and Historical Monu- Professor Lawrence Markus is a ments of Scotland. (page 59) distinguished mathematician who has made significant and lasting contributions, both in research and 3 Review of the Session 2000-2001 teaching, to the University of Award Minnesota-Minneapolis in the 5th Award of the BP Prize Lecture- United States of America, and to ship in the Humanities to the University of Warwick in the Dr Adrienne Scullion, from the United Kingdom. In this respect he Department of Theatre, Film and is a remarkable example of the Television Studies at the University “special relationship” between the of Glasgow, in recognition of her two countries; for the last thirty substantial contribution to Scottish years he has divided his profes- dramatic literature and contempo- sional life between the two rary performance in the Universities, serving in research professional theatre in Scotland. and in administrative positions Lecture associated with the development Self and Nation: issues of Identity of a number of areas of mathemat- in Modern Scottish Plays by ics and control science. For many Women (BP Prize Lecture in the years he has held the much- Humanities). Professor Adrienne coveted Regent Professorship of Scullion. (page 45) Mathematics at the University of Minnesota; at the University of 9 April 2001 Warwick he has held, at various Chairman times, Nuffield and Leverhulme Sir William Stewart FRS, PRSE Chairs of Mathematics; he is now Regent Professor Emeritus at the Formal Admission to Fellowship University of Minnesota and Professor C Snape Honorary Professor of Mathematics Lecture at the University of Warwick. Cancer Research Delivers - At Last. Professor Markus is a devoted Professor Gordon McVie, Director anglophile and American patriot; General, The Cancer Research he was involved with the Manhat- Campaign. (page 65) tan Atomic Energy Project in 1943 4 June 2001 and then served in the US Navy Chairman from 1943 to 1946. He and his Sir David Carter, FRSE, VPRSE wife Lois have for many years divided their lives between the two Formal Admission to Fellowship countries, with winter and summer Professor S Blackmore, Professor J L in their apartment in Royal Leam- Brockington, Professor D Charles- ington Spa, and autumn and worth, Dr T P P Clifford, Professor spring in their home in Minneapo- D H Crawford, Professor S C lis. Garrod, Mr B G Ivory, Professor R D Jack, Professor N H Keeble, The Formal Admission to Fellowship Hon Lord MacLean, Professor R Professor Andrew Hook Morrison, Professor R E Mulvey, Professor J A Murphy, Professor A F Murray, Lord Patel of Dunkeld, 4 Proceedings of the Ordinary Meetings Professor D J Porteous, Professor I 2 July 2001 G Priede, Professor G E Rickman, Chairman Professor J F Roulston, Professor J Sir William Stewart FRS, PRSE E L Simmons, Professor K S Sorbie, Professor J K Stringer, Professor G Formal Admission to Fellowship M Teasdale, Professor A J Walton, Mr A Cubie, Professor C T H Professor A Whiten. Davies, Professor D Edwards, Professor R H Flin, Professor N A R Lecture Gow, Professor C Kuo, Professor C Health in Old Age - Dream or R McInnes, Professor M J Padgett, Reality? Professor Marion E T Professor J A Sherratt and Profes- McMurdo, Department of Medi- sor R Thompson. cine, Dundee University, Ninewells Hospital. (page 70) Lecture Knot Theory and Fluid Mechanics - A Reflection on the Work of Tait and Kelvin. Professor Keith Moffatt, FRS, FRSE, University of Cambridge. (page 72) 5 PROCEEDINGS OF THE STATUTORY GENERAL MEETING The Annual Statutory General for the 219th Session were: Meeting took place in the Socie- Professor J F Cornwell FRSE, and ty’s Wolfson Theatre on Monday Dr M A D Fluendy FRSE. The Ballot 29 October 2001 at 4.45pm. was held and papers counted. Sir William Stewart, FRS, President, The Scrutineers later reported that took the Chair. all those shown on the ballot form had been elected by an President’s Welcome overwhelming majority. The President welcomed the Fellows and then expressed General Secretary’s Report to gratitude to all the outgoing the ASM. members of Council and Commit- “The Annual Report and Accounts tees for their notable for 2001, which were included contributions to the Society. He with the papers for this meeting, mentioned especially Professor describe the main activities during Peter Wilson, outgoing General the period April 2000 to March Secretary, and Professor Bob 2001. This oral report is designed Donovan, Vice-President, who to bring the Fellowship up to date would become Chairman of the with developments since March RSE Scotland Foundation. 2001. He noted that the Scottish Since March there have been a Executive had recognised the number of activities which are Society as an independent learned breaking new ground. Our body by asking it to host the international programme contin- Scottish Science Advisory Commit- ued apace and we have made tee whose Chairman was expected excellent progress in developing to become chief advisor on and enhancing our links and science to the Scottish Executive. relations in Europe and beyond. In Europe, positive steps have been In addition the Society was being made regarding the Society proactive in initiating Inquiries obtaining membership of the All into Foot and Mouth Disease, European Academies Network. Infectious Salmon Anaemia and We will learn the outcome of that Mediation in the Health Service. in Spring next year. We have also The President was also pleased to strengthened our links with highlight the award, by HRH The European contacts - notably
Recommended publications
  • Scapa Flow Scale Site Environmental Description 2019
    Scapa Flow Scale Test Site – Environmental Description January 2019 Uncontrolled when printed Document History Revision Date Description Originated Reviewed Approved by by by 0.1 June 2010 Initial client accepted Xodus LF JN version of document Aurora 0.2 April 2011 Inclusion of baseline wildlife DC JN JN monitoring data 01 Dec 2013 First registered version DC JN JN 02 Jan 2019 Update of references and TJ CL CL document information Disclaimer In no event will the European Marine Energy Centre Ltd or its employees or agents, be liable to you or anyone else for any decision made or action taken in reliance on the information in this report or for any consequential, special or similar damages, even if advised of the possibility of such damages. While we have made every attempt to ensure that the information contained in the report has been obtained from reliable sources, neither the authors nor the European Marine Energy Centre Ltd accept any responsibility for and exclude all liability for damages and loss in connection with the use of the information or expressions of opinion that are contained in this report, including but not limited to any errors, inaccuracies, omissions and misleading or defamatory statements, whether direct or indirect or consequential. Whilst we believe the contents to be true and accurate as at the date of writing, we can give no assurances or warranty regarding the accuracy, currency or applicability of any of the content in relation to specific situations or particular circumstances. Title: Scapa Flow Scale Test
    [Show full text]
  • Summary As Preparation for the Final Exam
    UUnnddeerrsstatannddiinngg ththee UUnniivveerrssee Summary Lecture Volker Beckmann Joint Center for Astrophysics, University of Maryland, Baltimore County & NASA Goddard Space Flight Center, Astrophysics Science Division UMBC, December 12, 2006 OOvveerrvviieeww ● What did we learn? ● Dark night sky ● distances in the Universe ● Hubble relation ● Curved space ● Newton vs. Einstein : General Relativity ● metrics solving the EFE: Minkowski and Robertson-Walker metric ● Solving the Einstein Field Equation for an expanding/contracting Universe: the Friedmann equation Graphic: ESA / V. Beckmann OOvveerrvviieeww ● Friedmann equation ● Fluid equation ● Acceleration equation ● Equation of state ● Evolution in a single/multiple component Universe ● Cosmic microwave background ● Nucleosynthesis ● Inflation Graphic: ESA / V. Beckmann Graphic by Michael C. Wang (UCSD) The velocity- distance relation for galaxies found by Edwin Hubble. Graphic: Edwin Hubble (1929) Expansion in a steady state Universe Expansion in a non-steady-state Universe The effect of curvature The equivalent principle: You cannot distinguish whether you are in an accelerated system or in a gravitational field NNeewwtotonn vvss.. EEiinnssteteiinn Newton: - mass tells gravity how to exert a force, force tells mass how to accelerate (F = m a) Einstein: - mass-energy (E=mc²) tells space time how to curve, curved space-time tells mass-energy how to move (John Wheeler) The effect of curvature A glimpse at EinsteinThe effect’s field of equationcurvature Left side (describes the action
    [Show full text]
  • Abstract Generalized Natural Inflation and The
    ABSTRACT Title of dissertation: GENERALIZED NATURAL INFLATION AND THE QUEST FOR COSMIC SYMMETRY BREAKING PATTERS Simon Riquelme Doctor of Philosophy, 2018 Dissertation directed by: Professor Zackaria Chacko Department of Physics We present a two-field model that generalizes Natural Inflation, in which the inflaton is the pseudo-Goldstone boson of an approximate symmetry that is spon- taneously broken, and the radial mode is dynamical. Within this model, which we designate as \Generalized Natural Inflation”, we analyze how the dynamics fundamentally depends on the mass of the radial mode and determine the size of the non-Gaussianities arising from such a scenario. We also motivate ongoing research within the coset construction formalism, that aims to clarify how the spontaneous symmetry breaking pattern of spacetime, gauge, and internal symmetries may allow us to get a deeper understanding, and an actual algebraic classification in the spirit of the so-called \zoology of con- densed matter", of different possible \cosmic states", some of which may be quite relevant for model-independent statements about different phases in the evolution of our universe. The outcome of these investigations will be reported elsewhere. GENERALIZED NATURAL INFLATION AND THE QUEST FOR COSMIC SYMMETRY BREAKING PATTERNS by Simon Riquelme Dissertation submitted to the Faculty of the Graduate School of the University of Maryland, College Park in partial fulfillment of the requirements for the degree of Doctor of Philosophy 2018 Advisory Committee: Professor Zackaria Chacko, Chair/Advisor Professor Richard Wentworth, Dean's Representative Professor Theodore Jacobson Professor Rabinda Mohapatra Professor Raman Sundrum A mis padres, Kattya y Luis. ii Acknowledgments It is a pleasure to acknowledge my adviser, Dr.
    [Show full text]
  • West Sept-Dec 2015 Parent and Carer Support Booklet
    Programmes, Activities and Groups for parents and carers in West Edinburgh Sept-Dec 2015 1 Contents Page New services – Childcare for eligible two year olds. Fox Covert Early Years Centre. 4 Parenting Programmes Mellow Bumps 5 Peep 6-7 The Psychology of Parenting Project (PoPP) : The Incredible Years / Triple P 8-9 Raising Children with Confidence 10 Raising Teens with Confidence 11 Teen Triple P 12 Parent and Child Activities Adult and child swim sessions 13 Baby Massage 13 Bookbug 13-14 Buggy Walks 14 Cooking with kids 15 Craft Fridays 15 Diggers and Dreamers 15 Early Years Group 15 Family Forest Schools 15 Family Learning 16 Family Swim Sessions 16 Funky Fridays 16 Get Going (weight management) 17 Homework Club 17 Parent and Child Workshops 17 Play, Stay and Read 17 Play@Home 18 Storytime 18 The Drop-In 18 Us Together Activity Group 18 2 Parent Groups The Cool Club 19 Dads’ Club 19 Foster Carers’ Group 19 JUNO 19 People First Parents’ Group 19 English for Speakers of Other Languages 21 (ESOL) Support and Advice (NHS and City Edinburgh Coucil) Ante Natal Classes / Parent craft classes 22 New Parents’ Group 22 New Baby Groups 22-23 Breastfeeding and Weaning Advice 23 Parent Information Points and drop-in 24 Support and Advice - Organisations Crossreach – postnatal depression 25 Children 1st - family support 25 Dads Rock – counselling 25 Families Need Fathers 25 First Hand 26 Home Start – family support 26 Making it Work for lone parents (employment 27 One Parent Families Scotland 27 The Edinburgh Lone Fathers Project 27 Playgroups 28 Activities for all ages 29 Early Years Centres and Hubs 30 Contacts 32 3 New Service Early learning and childcare for eligible two year olds Certain children are entitled to receive up to 600 hours of free early learning and childcare during school terms.
    [Show full text]
  • Scapa Flow & Basking Sharks Sept 19 - 29, 2019
    Scotland Scapa Flow & Basking Sharks Sept 19 - 29, 2019 Blue Green Expeditions is headed to Scotland. We are combining two epic experiences in one amazing package! Come snorkel with us with one of the largest sharks in the world, Basking Sharks. This is one of the biggest hotspots in the world to see them! Basking sharks typically range from 20 - 26 feet long but no worries, they eat plankton and are harmless! Then journey with us to the premier wreck diving jewel of the world, Scapa Flow. The area teems of history that spans the centuries with more than 150 wrecks that are scattered across the seabed from 18th century sailing ships to more recent fishing vessels. We plan to dive on the wrecks of the German fleet including the SMS Coln, Brummer, Dresden, Markgraf, Konig, and others. The massive hulking wrecks are truly amazing with so much to explore. The un-salvaged vessels of the German High Sea Fleet offer some of the greatest wreck diving the world has to offer. Truly a bucket list trip for any wreck diver! We will be staying aboard the Valhalla, a newly refurbished live-aboard diving vessel. This is one adventure you will not want to miss! Price Includes: • All meals aboard the Valhalla • 2-3 dives per day in Scapa Flow • Weights and 104cf tanks • Nitrox fills • Transfers from ferry or airport in Kirkwall • Lodge accommodations for Basking Sharks • Boat and transfers from ferry for Basking sharks Not included: • Double tanks, stage bottles or O2 for deco • Sorb for rebreathers • Airfare • Dive Insurance (required) • Trip Insurance (highly recommended) • Extra hotel nights due to flight schedules • Alcoholic beverages • Meals during Basking Shark trip • Crew gratuities Pricing: $3299 per person, standard cabin Non refundable deposit of $1500 Balance due - June 1st, 2019 For more information contact: Faith Ortins [email protected] 619.363.2408 Paul Holbrook [email protected] 619.363.2408 www.bluegreenexpeditions.com .
    [Show full text]
  • Degree in Mathematics
    Degree in Mathematics Title: Singularities and qualitative study in LQC Author: Llibert Aresté Saló Advisor: Jaume Amorós Torrent, Jaume Haro Cases Department: Departament de Matemàtiques Academic year: 2017 Universitat Polit`ecnicade Catalunya Facultat de Matem`atiquesi Estad´ıstica Degree in Mathematics Bachelor's Degree Thesis Singularities and qualitative study in LQC Llibert Arest´eSal´o Supervised by: Jaume Amor´osTorrent, Jaume Haro Cases January, 2017 Singularities and qualitative study in LQC Abstract We will perform a detailed analysis of singularities in Einstein Cosmology and in LQC (Loop Quantum Cosmology). We will obtain explicit analytical expressions for the energy density and the Hubble constant for a given set of possible Equations of State. We will also consider the case when the background is driven by a single scalar field, obtaining analytical expressions for the corresponding potential. And, in a given particular case, we will perform a qualitative study of the orbits in the associated phase space of the scalar field. Keywords Quantum cosmology, Equation of State, cosmic singularity, scalar field. 1 Contents 1 Introduction 3 2 Einstein Cosmology 5 2.1 Friedmann Equations . .5 2.2 Analysis of the singularities . .7 2.3 Reconstruction method . .9 2.4 Dynamics for the linear case . 12 3 Loop Quantum Cosmology 16 3.1 Modified Friedmann equations . 16 3.2 Analysis of the singularities . 18 3.3 Reconstruction method . 21 3.4 Dynamics for the linear case . 23 4 Conclusions 32 2 Singularities and qualitative study in LQC 1. Introduction In 1915, Albert Einstein published his field equations of General Relativity [1], giving birth to a new conception of gravity, which would now be understood as the curvature of space-time.
    [Show full text]
  • 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.
    [Show full text]
  • Annual Review 2018 – 19
    ANNUAL REVIEW 2018 – 19 “Sport has the power to change the world. It has the power to inspire. It has the power to unite people in a way that little else does. It speaks to youth in a language they understand. Sport can create hope where once there was only despair” - Nelson Mandela - 2 Foreword… 2018-19 was a year of self-reflection for the Active Schools team, having completed the Insights Personality test. Understanding others and appreciating our differences was one of the key learnings. This programme helped us build valuable working relationships and a network of partners, allowing Active Schools to make the impact they have made this year. The Active Schools team continue to work with and nurture senior pupils who officiate, coach, organise competitions, become Young Ambassadors who are our decision makers. Gaining relevant sports qualifications and valuable experience in delivery, the young people are able to Jude Salmon develop their employability skills. Active Schools Manager In today’s world we are affected by factors including stress, mental health, obesity and poverty. Taking part in sport and physical activity truly does make a difference to our lives and I hope that some of the stories you are about to read will illustrate this to you. The phrase, ‘healthy body, healthy mind’ says it all. Our bodies were designed to move and when we keep them healthy, we have a better outlook on life, and on learning. The most wonderful part of keeping fit and healthy is that it is fun, but as this annual review shows, it can also open doors into future careers through volunteering and coaching.
    [Show full text]
  • USF Honors Graduates, Bishop at Commencement
    50¢ May 13, 2007 Volume 81, No. 19 www.diocesefwsb.org/TODAY Serving the Diocese of Fort Wayne-South Bend TTODAYODAY’’SS CCATHOLICATHOLIC Mothers are USF honors graduates, special to all Area mothers profiled bishop at commencement Pages 10-12 BY DON CLEMMER Stem-cell benefits FORT WAYNE — Gathering at the Allen County War Cord blood donations Memorial Coliseum for its annual commencement exercises, the University of Saint Francis (USF) used for research bestowed degrees on its graduates and made Bishop Page 4 John M. D’Arcy an honorary member of the class of 2007 by giving him an honorary degree. Sister M. Elise Kriss, OSF, president of the univer- sity, welcomed those gathered and, after a short invo- cation by graduate Brittani Lusch, introduced Dr. Young Adults Esperanca Camara, an art history professor at USF and the recipient of the Teaching Excellence and Campus Don’t underestimate Leadership Award for 2007. After Dr. Camara’s remarks, Sister Elise spoke of your value some of the accomplishments of Bishop D’Arcy’s time Page 19 in Fort Wayne-South Bend before introducing him in his other capacity at the May 5 ceremony, commence- ment speaker. Bishop D’Arcy, who had celebrated the Baccalaureate Mass with the USF community earlier The tournaments in the day, first noted how touched he had been by Dr. Camara’s speaking of her mother leaving her home on CYO and ICCL look ahead an island near Portugal for the United States so that her Page 20 children would receive a better education. Bishop D’Arcy reflected on the experiences of his own Irish immigrant parents and appealed for openness to pres- ent-day immigrants before proceeding with his address.
    [Show full text]
  • Wreck of the Edindoune (BF1118), Scapa Flow, Orkney. Final Report
    Wreck of the Edindoune (BF1118), Scapa Flow, Orkney. Final Report Submitted to: Historic Environment Scotland - Philip Robertson Contact: Kevin Heath SULA Diving Old Academy Stromness Orkney KW16 3AW Tel. 01856 850 285 E-mail. [email protected] Approved for release by M. Thomson (Director): Document history Version: State Prepared by: Date: 02 Final M. Thomson/K. Heath 26th March 2018 01 Draft M. Thomson/K. Heath 22nd March 2018 CONTENTS PAGE ACKNOWLEDGEMENTS…………………………………………………………………………………………………. ii SUMMARY………………......................................................................................................... iii 1. INTRODUCTION……………................................................................................................ 1 2. METHODS....................................................................................................................... 2 2.1 Side scan sonar………………………………………………………………………………………………... 2 2.2 Diving……………………………………………………………………………………………….……………... 2 3. RESULTS.......................................................................................................................... 3 3.1 Side scan sonar...................................................................................................... 3 3.2 Diving………………….................................................................................................. 3 4. DISCUSSION.................................................................................................................... 17 REFERENCES & BIBLIOGRAPHY..........................................................................................
    [Show full text]
  • 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.
    [Show full text]
  • Observational Cosmology - 30H Course 218.163.109.230 Et Al
    Observational cosmology - 30h course 218.163.109.230 et al. (2004–2014) PDF generated using the open source mwlib toolkit. See http://code.pediapress.com/ for more information. PDF generated at: Thu, 31 Oct 2013 03:42:03 UTC Contents Articles Observational cosmology 1 Observations: expansion, nucleosynthesis, CMB 5 Redshift 5 Hubble's law 19 Metric expansion of space 29 Big Bang nucleosynthesis 41 Cosmic microwave background 47 Hot big bang model 58 Friedmann equations 58 Friedmann–Lemaître–Robertson–Walker metric 62 Distance measures (cosmology) 68 Observations: up to 10 Gpc/h 71 Observable universe 71 Structure formation 82 Galaxy formation and evolution 88 Quasar 93 Active galactic nucleus 99 Galaxy filament 106 Phenomenological model: LambdaCDM + MOND 111 Lambda-CDM model 111 Inflation (cosmology) 116 Modified Newtonian dynamics 129 Towards a physical model 137 Shape of the universe 137 Inhomogeneous cosmology 143 Back-reaction 144 References Article Sources and Contributors 145 Image Sources, Licenses and Contributors 148 Article Licenses License 150 Observational cosmology 1 Observational cosmology Observational cosmology is the study of the structure, the evolution and the origin of the universe through observation, using instruments such as telescopes and cosmic ray detectors. Early observations The science of physical cosmology as it is practiced today had its subject material defined in the years following the Shapley-Curtis debate when it was determined that the universe had a larger scale than the Milky Way galaxy. This was precipitated by observations that established the size and the dynamics of the cosmos that could be explained by Einstein's General Theory of Relativity.
    [Show full text]