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Aspects of Black Hole Physics
Aspects of Black Hole Physics Andreas Vigand Pedersen The Niels Bohr Institute Academic Advisor: Niels Obers e-mail: [email protected] Abstract: This project examines some of the exact solutions to Einstein’s theory, the theory of linearized gravity, the Komar definition of mass and angular momentum in general relativity and some aspects of (four dimen- sional) black hole physics. The project assumes familiarity with the basics of general relativity and differential geometry, but is otherwise intended to be self contained. The project was written as a ”self-study project” under the supervision of Niels Obers in the summer of 2008. Contents Contents ..................................... 1 Contents ..................................... 1 Preface and acknowledgement ......................... 2 Units, conventions and notation ........................ 3 1 Stationary solutions to Einstein’s equation ............ 4 1.1 Introduction .............................. 4 1.2 The Schwarzschild solution ...................... 6 1.3 The Reissner-Nordstr¨om solution .................. 18 1.4 The Kerr solution ........................... 24 1.5 The Kerr-Newman solution ..................... 28 2 Mass, charge and angular momentum (stationary spacetimes) 30 2.1 Introduction .............................. 30 2.2 Linearized Gravity .......................... 30 2.3 The weak field approximation .................... 35 2.3.1 The effect of a mass distribution on spacetime ....... 37 2.3.2 The effect of a charged mass distribution on spacetime .. 39 2.3.3 The effect of a rotating mass distribution on spacetime .. 40 2.4 Conserved currents in general relativity ............... 43 2.4.1 Komar integrals ........................ 49 2.5 Energy conditions ........................... 53 3 Black holes ................................ 57 3.1 Introduction .............................. 57 3.2 Event horizons ............................ 57 3.2.1 The no-hair theorem and Hawking’s area theorem .... -
Legal "Black Hole"? Extraterritorial State Action and International Treaty Law on Civil and Political Rights
Michigan Journal of International Law Volume 26 Issue 3 2005 Legal "Black Hole"? Extraterritorial State Action and International Treaty Law on Civil and Political Rights Ralph Wilde University of London Follow this and additional works at: https://repository.law.umich.edu/mjil Part of the Human Rights Law Commons, Military, War, and Peace Commons, and the National Security Law Commons Recommended Citation Ralph Wilde, Legal "Black Hole"? Extraterritorial State Action and International Treaty Law on Civil and Political Rights, 26 MICH. J. INT'L L. 739 (2005). Available at: https://repository.law.umich.edu/mjil/vol26/iss3/1 This Article is brought to you for free and open access by the Michigan Journal of International Law at University of Michigan Law School Scholarship Repository. It has been accepted for inclusion in Michigan Journal of International Law by an authorized editor of University of Michigan Law School Scholarship Repository. For more information, please contact [email protected]. LEGAL "BLACK HOLE"? EXTRATERRITORIAL STATE ACTION AND INTERNATIONAL TREATY LAW ON CIVIL AND POLITICAL RIGHTSt Ralph Wilde* I. INTRODUCTION ......................................................................... 740 II. EXTRATERRITORIAL STATE ACTIVITIES ................................... 741 III. THE NEED FOR GREATER SCRUTINY ........................................ 752 A. Ignoring ExtraterritorialActivity ...................................... 753 B. GreaterRisks of Rights Violations in the ExtraterritorialContext .................................................... -
Germans .Britain Boosts Income Tax to New Peak^ Harbors, Airports
\ UeilDAr.}T)LTII.tM« ..im r i M L v s '■’Vi flatirftfstnr Etiratno 3SrndIk Average Dally Cirealetlea Far tha Moath at Jama. l$ i . The regular meatlng af Mlaato- Mra Herbert Sargent and tv-f 4 The Weather While working on the new town Dr. Edward F. Krtksclun of Chi Pr. and Mrs. A. A. Friahalt o f M Edward Harris, ■7ST Maary Mrs. Joi^^hina Ptow4k Hills, Elwood street are taking a vaca street, was sersiiaded ftmdey. by noraoh TTlbe No. BB, I. O. ft. M., children, Alice Jeen and Herbert roraeaat af O. S. WaaUur Bmi who U oondudUng a summer art dump several men of the Love cago, ni., one of the successful wUl ha held In the Sports Center Kilby, have left for Weymouth HitTawn Lane W. P. A. project have been tion until August 2, and enjoying tha siOvatlon Army Band. X f. 6,429 course in Rodm 10 of ManehooUr candidates In the state dental sViaon WellsTT vgam ,^ streetv tonight at el^ t Nova Scotia, where they will epenf / affected by^tHrlUtlon of the skin short trips to nsarby places of in HarriA wbo is a member o f thr High school, has changsd the in exams Is a nephew of Peter Staum terest band'haa been confined to bed adth shiu’p. the remainder of the summer. Maatbar af tha Aadit / struction hours, by request, frops from polpcmlng. None of the cases of 89 W. Middle Turnpike. He 1s a heart aliment for the past six BnieM o f Otienlotlono ^ srsji BMtriM AnoM. -
Mapping Prostitution: Sex, Space, Taxonomy in the Fin- De-Siècle French Novel
Mapping Prostitution: Sex, Space, Taxonomy in the Fin- de-Siècle French Novel The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters Citation Tanner, Jessica Leigh. 2013. Mapping Prostitution: Sex, Space, Taxonomy in the Fin-de-Siècle French Novel. Doctoral dissertation, Harvard University. Citable link http://nrs.harvard.edu/urn-3:HUL.InstRepos:10947429 Terms of Use This article was downloaded from Harvard University’s DASH repository, WARNING: This file should NOT have been available for downloading from Harvard University’s DASH repository. Mapping Prostitution: Sex, Space, Taxonomy in the Fin-de-siècle French Novel A dissertation presented by Jessica Leigh Tanner to The Department of Romance Languages and Literatures in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the subject of Romance Languages and Literatures Harvard University Cambridge, Massachusetts May 2013 © 2013 – Jessica Leigh Tanner All rights reserved. Dissertation Advisor: Professor Janet Beizer Jessica Leigh Tanner Mapping Prostitution: Sex, Space, Taxonomy in the Fin-de-siècle French Novel Abstract This dissertation examines representations of prostitution in male-authored French novels from the later nineteenth century. It proposes that prostitution has a map, and that realist and naturalist authors appropriate this cartography in the Second Empire and early Third Republic to make sense of a shifting and overhauled Paris perceived to resist mimetic literary inscription. Though always significant in realist and naturalist narrative, space is uniquely complicit in the novel of prostitution due to the contemporary policy of reglementarism, whose primary instrument was the mise en carte: an official registration that subjected prostitutes to moral and hygienic surveillance, but also “put them on the map,” classifying them according to their space of practice (such as the brothel or the boulevard). -
Top Flite Models Inc
Product Support (Do Not Remove From Department) INTRODUCTION TOP FLITE MODELS, INC. is proud to introduce the new Elder 40. This design is a direct result of popular demand after the great little Elder 20 was introduc- ed. Modelers loved the design, still do, but wanted something "larger" and "while you're at it, give it ailerons." So, here it is and does it ever fly nice'. The Elder 40 was designed and sized expressly for .40 engines and this includes the popular .40- .45 and .49 engines. The design turns in great performance with the four-stroke power plants and there is plenty of power margin left over for the aerobatic- minded pilot. However, the real "kick" of this design, like its smaller brother, is the the design with 4-cycle engines is an absolute delight. realistic, slow-speed flights that allow you to actually Give it a try in your Elder 40. Note that the motor mount see the airplane instead of just a blur. we have provided in the kit may not fit some 4-cycle The design lends itself to all kinds of detailing, if you're engines and it may be necessary to visit your local retail so inclined. For the beginner, nothing fancy is needed; hobby shop to get the right one for your engine. go out and fly it. The Elder 40 makes a remarkably good training aircraft with gentle and totally honest flying IMPORTANT NOTE: characteristics. A big bonus here is that your trainer is TOP FLITE MODELS, INC. would certainly recommend just not going to look like everyone else's high-wing, the Elder 40 as a first R/C powered aircraft. -
An Annotated List of Fantasy Novels Incorporating Tarot (1990-2005)
Volume 38 Number 2 Article 12 5-15-2020 An Annotated List of Fantasy Novels Incorporating Tarot (1990-2005) Emily E. Auger Independent Scholar Follow this and additional works at: https://dc.swosu.edu/mythlore Part of the Children's and Young Adult Literature Commons Recommended Citation Auger, Emily E. (2020) "An Annotated List of Fantasy Novels Incorporating Tarot (1990-2005)," Mythlore: A Journal of J.R.R. Tolkien, C.S. Lewis, Charles Williams, and Mythopoeic Literature: Vol. 38 : No. 2 , Article 12. Available at: https://dc.swosu.edu/mythlore/vol38/iss2/12 This Notes and Letters is brought to you for free and open access by the Mythopoeic Society at SWOSU Digital Commons. It has been accepted for inclusion in Mythlore: A Journal of J.R.R. Tolkien, C.S. Lewis, Charles Williams, and Mythopoeic Literature by an authorized editor of SWOSU Digital Commons. An ADA compliant document is available upon request. For more information, please contact [email protected]. To join the Mythopoeic Society go to: http://www.mythsoc.org/join.htm Mythcon 51: A VIRTUAL “HALFLING” MYTHCON July 31 - August 1, 2021 (Saturday and Sunday) http://www.mythsoc.org/mythcon/mythcon-51.htm Mythcon 52: The Mythic, the Fantastic, and the Alien Albuquerque, New Mexico; July 29 - August 1, 2022 http://www.mythsoc.org/mythcon/mythcon-52.htm Abstract This annotated list of books from 1990 through 2005 continues the bibliography in Mythlore 36.2 (Spring- Summer 2018) and includes abstracts for each novel or series and some card layout diagrams. Additional Keywords Fantasy literature—Bibliography; Tarot in literature This notes and letters is available in Mythlore: A Journal of J.R.R. -
Y A-T-Il Encore De La Place En Bas ? Le Paysage Contemporain Des Nanosciences Et Des Nanotechnologies
Philosophia Scientiæ Travaux d'histoire et de philosophie des sciences 23-1 | 2019 Y a-t-il encore de la place en bas ? Le paysage contemporain des nanosciences et des nanotechnologies Jonathan Simon et Bernadette Bensaude-Vincent (dir.) Édition électronique URL : http://journals.openedition.org/philosophiascientiae/1693 DOI : 10.4000/philosophiascientiae.1693 ISSN : 1775-4283 Éditeur Éditions Kimé Édition imprimée Date de publication : 18 février 2019 ISSN : 1281-2463 Référence électronique Jonathan Simon et Bernadette Bensaude-Vincent (dir.), Philosophia Scientiæ, 23-1 | 2019, « Y a-t-il encore de la place en bas ? » [En ligne], mis en ligne le 01 janvier 2021, consulté le 30 mars 2021. URL : http://journals.openedition.org/philosophiascientiae/1693 ; DOI : https://doi.org/10.4000/ philosophiascientiae.1693 Tous droits réservés Y a-t-il encore de la place en bas ? Le paysage contemporain des nanosciences et des nanotechnologies Introduction. Nanotechnoscience: The End of the Beginning Bernadette Bensaude-Vincent Université Paris 1 Panthéon-Sorbonne (France) Jonathan Simon Archives Henri-Poincaré – Philosophie et Recherches sur les Sciences et les Technologies (AHP-PReST), Université de Lorraine, Université de Strasbourg, CNRS, Nancy (France) Is there still room at the bottom? The question providing the theme for the present issue of Philosophia Scientiæ is, of course, adapted from Richard Feynman’s well-known speech at the 1959 meeting of the American Physical Society. On this occasion he attracted physicists’ attention to the vast potential of working at the scale of the nanometre if not the ångström, using the catchy title: “Plenty of Room at the Bottom” [Feynman 1959]. This hookline from a famous Nobel laureate physicist served as a motto for the emerging field of nanoscience and nanotechnology (which we will here abbreviate to nanoresearch) in the early 2000s. -
Unusual Attitudes and the Aerodynamics of Maneuvering Flight Author’S Note to Flightlab Students
Unusual Attitudes and the Aerodynamics of Maneuvering Flight Author’s Note to Flightlab Students The collection of documents assembled here, under the general title “Unusual Attitudes and the Aerodynamics of Maneuvering Flight,” covers a lot of ground. That’s because unusual-attitude training is the perfect occasion for aerodynamics training, and in turn depends on aerodynamics training for success. I don’t expect a pilot new to the subject to absorb everything here in one gulp. That’s not necessary; in fact, it would be beyond the call of duty for most—aspiring test pilots aside. But do give the contents a quick initial pass, if only to get the measure of what’s available and how it’s organized. Your flights will be more productive if you know where to go in the texts for additional background. Before we fly together, I suggest that you read the section called “Axes and Derivatives.” This will introduce you to the concept of the velocity vector and to the basic aircraft response modes. If you pick up a head of steam, go on to read “Two-Dimensional Aerodynamics.” This is mostly about how pressure patterns form over the surface of a wing during the generation of lift, and begins to suggest how changes in those patterns, visible to us through our wing tufts, affect control. If you catch any typos, or statements that you think are either unclear or simply preposterous, please let me know. Thanks. Bill Crawford ii Bill Crawford: WWW.FLIGHTLAB.NET Unusual Attitudes and the Aerodynamics of Maneuvering Flight © Flight Emergency & Advanced Maneuvers Training, Inc. -
On the Hunt for Excited States
INTERNATIONAL JOURNAL OF HIGH-ENERGY PHYSICS CERN COURIER VOLUME 45 NUMBER 10 DECEMBER 2005 On the hunt for excited states HOMESTAKE DARK MATTER SNOWMASS Future assured for Galactic gamma rays US workshop gets underground lab p5 may hold the key p 17 ready for the ILC p24 www.vectorfields.comi Music to your ears 2D & 3D electromagnetic modellinj If you're aiming for design excellence, demanding models. As a result millions you'll be pleased to hear that OPERA, of elements can be solved in minutes, the industry standard for electromagnetic leaving you to focus on creating modelling, gives you the most powerful outstanding designs. Electron trajectories through a TEM tools for engineering and scientific focussing stack analysis. Fast, accurate model analysis • Actuators and sensors - including Designed for parameterisation and position and NDT customisation, OPERA is incredibly easy • Magnets - ppm accuracy using TOSCA to use and has an extensive toolset, making • Electron devices - space charge analysis it ideal for a wide range of applications. including emission models What's more, its high performance analysis • RF Cavities - eigen modes and single modules work at exceptional levels of speed, frequency response accuracy and stability, even with the most • Motors - dynamic analysis including motion Don't take our word for it - order your free trial and check out OPERA yourself. B-field in a PMDC motor Vector Fields Ltd Culham Science Centre, Abingdon, Oxon, 0X14 3ED, U.K. Tel: +44 (0)1865 370151 Fax: +44 (0)1865 370277 Email: [email protected] Vector Fields Inc 1700 North Famsworth Avenue, Aurora, IL, 60505. -
West Copper River Delta Landscape Assessment Cordova Ranger District Chugach National Forest 03/18/2003 Updated 04/19/2007
West Copper River Delta Landscape Assessment Cordova Ranger District Chugach National Forest 03/18/2003 updated 04/19/2007 Copper River Delta – circa 1932 – photo courtesy of Perry Davis Team: Susan Kesti - Team Leader, writer-editor, vegetation Milo Burcham – Wildlife resources, Subsistence Bruce Campbell – Lands, Special Uses Dean Davidson – Soils, Geology Rob DeVelice – Succession, Ecology Carol Huber – Minerals, Geology, Mining Tim Joyce – Fish subsistence Dirk Lang – Fisheries Bill MacFarlane – Hydrology, Water Quality Dixon Sherman – Recreation Linda Yarborough – Heritage Resources Table of Contents Executive Summary...........................................................................................vi Chapter 1 – Introduction ....................................................................................1 Purpose.............................................................................................................1 The Analysis Area .............................................................................................1 Legislative History .............................................................................................3 Relationship to the revised Chugach Land and Resource Management Plan...4 Chapter 2 – Analysis Area Description .............................................................7 Physical Characteristics ....................................................................................7 Location .........................................................................................................7 -
)-4*********************************************** * Reproductions Supplied by EDRS Are the Best That Can Be Made from the Original Document
DOCUMENT RESUME ED 369 531 PS 022 279 AUTHOR Charney, Ruth Sidney TITLE Teaching Children to Care: Management in the Responsive Classroom. INSTITUTION Northeast Foundation for Children, Greenfield, MA. REPORT NO ISBN-0-9618636-1-7 PUB DATE 93 NOTE 306p. AVAILABLE FROMNortheast Foundation for Children, 71 Montague City Road, Greenfield, MA 01301 ($22.50, plus shipping. Discount on quantity orders). PUB TYPE Guides Classroom Use Teaching Guides (For Teacher) (052) Books (010) EDRS PRICE MF01/PC13 Plus Postage. DESCRIPTORS Classroom Communication; Classroom Environment; *Classroom Techniques; Conflict Resolution; *Discipline; Elementary Education; Language; Peer Relationship; Problem Solving; *Prosocial Behavior; *Self Control; Teacher Student Relationship; Timeout; *Values; *Values Education IDENTIFIERS Classroom Thoughtfulness; School Rules ABSTRACT This book is about managing a responsive classroom and teaching children to care. The aim of every chapter and technique is the creation of self-controls and community, defined as the capacity to care about oneself, others, and the world. The 16 chapter topics are:(1) goals of self-control and community;(2) techniques of the first 6 weeks of school and their extension through the rest of the year;(3) basic classroom rules and how children can be involved in their creation;(4) a system of logical consequences for children's actions;(5) problem-solving class meetings; (6) a time-out procedure;(7) approaches to children who engage in power struggles;(8) ways to approach problem-solving with individuals -
Search in the Patience Game 'Black Hole'
1 Search in the Patience Game ‘Black Hole’ Ian P. Gent a, Chris Jefferson b, Tom Kelsey a, InˆesLynce c, Ian Miguel a, Peter Nightingale a, Barbara M. Smith d and S. Armagan Tarim d a School of Computer Science, University of St Andrews, KY16 9SX, UK E-mail: {ipg,tom,ianm,pn}@dcs.st-and.ac.uk b Computing Laboratory, University of Oxford, UK E-mail:Chris.Jeff[email protected] c IST/INESC-ID, Technical University of Lisbon, Portugal E-mail:[email protected] d Cork Constraint Computation Centre, University College Cork, Ireland E-mail: {b.smith,at}@4c.ucc.ie We present an evaluation of different AI search paradigms applied to a natural planning problem. The problem we investigate is a particular card game for one player called Black Hole. For paradigms such as SAT and Constraint Programming, the game has the particular advantage that all solutions are the same length. We show that a general version of Black Hole is NP-complete. Then we report on the application of a number of AI paradigms to the problem, namely Planning, Constraint Programming, SAT, Mixed-Integer Programming and a specialised solver. An important feature of Black Hole is the presence of symmetries which arise during the search process. We show that tackling these can improve search dramatically, as can caching states that occur during search. Our implementations as SAT, Constraint Programming and Planning problems are efficient and competitive, allowing detailed empirical evaluation of the strengths and weaknesses of each methodology. Our empirical evaluation shows that Black Hole is winnable approximately 87% of the time, and that given instances can be trivially solved, easy to solve, hard to solve and even intractable, depending on the AI methodology used to obtain solutions.