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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 .................................................... -
Choamskx Races Hessen
iI Ii - ~~~~~~~~---I I -Continuous News Serice The Weather. I I Since 1881." Clear and warmer; high in the 70's I iI i VOLUME 89, No. 35' - MITCAMBRIDGE,MASSAC:HUSETTS FRIDAY, OCTOBER 10, 1969 FIVE CENTS -- _ _- ,- - _ . .. Faculty meeting convenes i GA i to consider Oct. 15 action voces panel support - ~ ~~~~~~~-: A special faculty meeting wil C.'L. Miller, Head of the Depa#!- convene today-to consider a'-re- ment- of Civil Engineering; I. solution calling for "a convoca- 'Ross, -Headcof the Department tion of the MIT community 'at of -Chemistry;, A.H. Shapiro, 1:30 pm Wednesday, October Read of the Departinent of Me- IS." chanical Engineering; L.D. As evidence of widespread Smullin- Head of the Depast- community support for the ment of Electrical Engineering; Moratorium, the resolution cites and V.F. Wwisskopf, Head of the petition circulated' among the Department of Physics. the faculty, the vote of the Ge- neral Assembly, and the state- A similar meeting of the Har- ment approved by the Corpora- vard faculty took place Tuesday. tion. After much discussion, an amended moratorium resolution A second resolution, to be in- was- passed which states that the troduced by SA-CC, calls- for -faculty "recognizes that October completely dlosing the Institute. 15th is a day of protest against Until now, tliere has been no 'the war and, while not commit- official recognition of the Mora- ting any individual member,- torium by the, Institute. How- re-affirms its members' right to,- ever, - many -faculty members suspend classes on that day." have already canceled or resche- duled their October 15 classes. -
Ligo-India Proposal for an Interferometric Gravitational-Wave Observatory
LIGO-INDIA PROPOSAL FOR AN INTERFEROMETRIC GRAVITATIONAL-WAVE OBSERVATORY IndIGO Indian Initiative in Gravitational-wave Observations PROPOSAL FOR LIGO-INDIA !"#!$ Indian Initiative in Gravitational wave Observations http://www.gw-indigo.org II Title of the Project LIGO-INDIA Proposal of the Consortium for INDIAN INITIATIVE IN GRAVITATIONAL WAVE OBSERVATIONS IndIGO to Department of Atomic Energy & Department of Science and Technology Government of India IndIGO Consortium Institutions Chennai Mathematical Institute IISER, Kolkata IISER, Pune IISER, Thiruvananthapuram IIT Madras, Chennai IIT, Kanpur IPR, Bhatt IUCAA, Pune RRCAT, Indore University of Delhi (UD), Delhi Principal Leads Bala Iyer (RRI), Chair, IndIGO Consortium Council Tarun Souradeep (IUCAA), Spokesperson, IndIGO Consortium Council C.S. Unnikrishnan (TIFR), Coordinator Experiments, IndIGO Consortium Council Sanjeev Dhurandhar (IUCAA), Science Advisor, IndIGO Consortium Council Sendhil Raja (RRCAT) Ajai Kumar (IPR) Anand Sengupta(UD) 10 November 2011 PROPOSAL FOR LIGO-INDIA II PROPOSAL FOR LIGO-INDIA LIGO-India EXECUTIVE SUMMARY III PROPOSAL FOR LIGO-INDIA IV PROPOSAL FOR LIGO-INDIA This proposal by the IndIGO consortium is for the construction and subsequent 10- year operation of an advanced interferometric gravitational wave detector in India called LIGO-India under an international collaboration with Laser Interferometer Gravitational–wave Observatory (LIGO) Laboratory, USA. The detector is a 4-km arm-length Michelson Interferometer with Fabry-Perot enhancement arms, and aims to detect fractional changes in the arm-length smaller than 10-23 Hz-1/2 . The task of constructing this very sophisticated detector at the limits of present day technology is facilitated by the amazing opportunity offered by the LIGO Laboratory and its international partners to provide the complete design and all the key components required to build the detector as part of the collaboration. -
View Print Program (Pdf)
PROGRAM November 3 - 5, 2016 Hosted by Sigma Pi Sigma, the physics honor society 2016 Quadrennial Physics Congress (PhysCon) 1 31 Our students are creating the future. They have big, bold ideas and they come to Florida Polytechnic University looking for ways to make their visions a reality. Are you the next? When you come to Florida Poly, you’ll be welcomed by students and 3D faculty who share your passion for pushing the boundaries of science, PRINTERS technology, engineering and math (STEM). Florida’s newest state university offers small classes and professors who work side-by-side with students on real-world projects in some of the most advanced technology labs available, so the possibilities are endless. FLPOLY.ORG 2 2016 Quadrennial Physics Congress (PhysCon) Contents Welcome ........................................................................................................................... 4 Unifying Fields: Science Driving Innovation .......................................................................... 7 Daily Schedules ............................................................................................................. 9-11 PhysCon Sponsors .............................................................................................................12 Planning Committee & Staff ................................................................................................13 About the Society of Physics Students and Sigma Pi Sigma ���������������������������������������������������13 Previous Sigma Pi Sigma -
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). -
Self-Guided Walking Tour of the MIT Campus
Self-Guided Walking Tour of the MIT Campus P AInformation Center MIT Museum → B Stratton Student Center → N52 C Kresge Auditorium ➔ DMIT Chapel → E Hart Nautical Galleries TECHNOLOGY Building 5 ➔ SQUARE M F Bldg. 3/Design and A Manufacturing Display S S A C GKillian Court H U HHayden Memorial S E Library Building T T S I McDermott Court A V E JTech Coop N M ➔ A U IN KAn Athena Computer E ➔→ S ➔→→ TR Cluster →→ E →→→ ET → ➔→ O L Edgerton’s Strobe T → 32 STREE Stata ➔ R VASSA Alley ➔ Center MBarker Engineering TREET AR S ➔ T SS → Library - Bldg. 10-500 VA E J E E19 Tech Coop → → R NCompton Gallery 57 T → → S T T Bldg. 10-1st floor 68 S ➔ → E Kendall M E18 T O Stata Center → A Square W35 13 ➔ ➔ B ➔ 56 E17 E25 E38 P MIT Museum ➔ Zesiger ➔ 16 → K 66 W20 ➔→→→→ ➔ → → N → Whitaker College ➔→→ Center ➔→ → ➔→→ ➔ ➔ → ➔ ➔ You are here 10 8 → ➔ → 7➔→ M 4 A → E23 Information 54 C Center L 18 → E15 MIT Medical F → D ➔ W16 I 62 64 → ➔→→W15➔ 3 4 6 McDermott E ➔ E14 Court → → 5 → E40 G ➔ ➔→→→ ➔ ➔→→→→→→ ➔→→→→→→→→→→→→→→14N ➔ 14W 14E E2 E53 1 Killian Court 2 E51 H 14S 50 E52 Gray E56 House Sloan School D O R M I T O R I E S MEMORIAL DRIVE MEMORIAL DRIVE Welcome to MIT! held at 10:00 am and names. The numbering you see a number on the route, letters of the alpha- William Barton Rogers, a problems. Today education The following suggested 2:00 pm. system might appear office doors, the first bet are used to avoid distinguished natural and research, with tour route and description confusing at first, but there number refers to the confusion with the building scientist, founded MIT to relevance to the practical should aid you in exploring We suggest that you begin is a logical explanation as building number and then numbers. -
O Nien Un Es a Is E Two New Honors Given at Yearly Awards Convocation
I I I . I ve -o nien Two new honors given at I un es a is e By Bon Frashure of the secrty after allowance Trhe yearly Awards Convocation pWThas names of the representatives estabished an Inde- for improvements. of the remang fraterriti'es were SexetResidence Development By Steve Portny field '64 for his "spirit, dedica- 3. The maxdmum. loan term antnounced last Mkght at a work- nhwhich may assist tindepen- The annual Awards Conlvocaton tion, and service" to Mffr. The will be 40 years. in meeting to implement the seon ivingid grops in improig. IRD Fund. was held last Saturday in Kresge new award came from a adexpaig 4. The minimum. rate of in- proposal by the Activities Devel- their housing fat Marshall. B. Dalton '15, Chair- Auditorium. Featured was the 0 oite administrtiors officers terest vEll be three percot. presentation of the Kar Taylor opment Board. Namned in honor 5. Gifts to the IRD Fund must man of the Board of the Boston of William L. Steward Jr. '26, anounced Jast FridaY. Manufacturers Mutual Insurance Compton Awards given in reco- Fund provisins provide that the prncpal wil niition of 'outanftng contribul- the award is ~given to students not be expended, and givers must Company and -a Life Member of who have participated The IRD Flund will be an en- the MITX Corporatimn, will chair tions in promoing high standards actively in dwnnt, thie income of which permit use of the income of the of achievement and good citizen- school activities. fund for any corporate purpose both the Alumni IFC! and the Saye be used by the Corporation central ship mithinn the MIT community." Recipents of the award are: of MIT. -
The Perils of Complacency
THE PERILS OF COMPLACENCYTHE PERILS : America at a Tipping Point in Science & Engineering : America at a Tipping Point THE PERILS OF COMPLACENCY America at a Tipping Point in Science & Engineering An Update to Restoring the Foundation: The Vital Role of Research in Preserving the American Dream AMERICAN ACADEMY OF ARTS & SCIENCES AMERICAN ACADEMY THE PERILS OF COMPLACENCY America at a Tipping Point in Science & Engineering An Update to Restoring the Foundation: The Vital Role of Research in Preserving the American Dream american academy of arts & sciences Cambridge, Massachusetts This report and its supporting data were finalized in April 2020. While some new data have been released since then, the report’s findings and recommendations remain valid. Please note that Figure 1 was based on nsf analysis, which used existing oecd purchasing power parity (ppp) to convert U.S. and Chinese financial data.oecd adjusted its ppp factors in May 2020. The new factors for China affect the curves in the figure, pushing the China-U.S. crossing point toward the end of the decade. This development is addressed in Appendix D. © 2020 by the American Academy of Arts & Sciences All rights reserved. isbn: 0- 87724- 134- 1 This publication is available online at www.amacad.org/publication/perils-of-complacency. The views expressed in this report are those held by the contributors and are not necessarily those of the Officers and Members of the American Academy of Arts and Sciences. Please direct inquiries to: American Academy of Arts and Sciences 136 Irving Street Cambridge, Massachusetts 02138- 1996 Telephone: 617- 576- 5000 Email: [email protected] Website: www.amacad.org Contents Acknowledgments 5 Committee on New Models for U.S. -
Rainer Weiss, Professor of Physics Emeritus and 2017 Nobel Laureate
Giving to the Department of Physics by Erin McGrath RAINER WEISS ’55, PHD ’62 Bryce Vickmark Rai Weiss has established a fellowship in the Physics Department because he is eternally grateful to his advisor, the late Jerrold Zacharias, for all that he did for Rai, so he knows firsthand the importance of supporting graduate students. Rainer Weiss, Professor of Physics Emeritus and 2017 Nobel Laureate. Rainer “Rai” Weiss was born in Berlin, Germany in 1932. His father was a physician and his mother was an actress. His family was forced out of Germany by the Nazis since his father was Jewish and a Communist. Rai, his mother and father fled to Prague, Czecho- slovakia. In 1937 a sister was born in Prague. In 1938, after Chamberlain appeased Hitler by effectively giving him Czechoslovakia, the family was able to obtain visas to enter the United States through the Stix Family in St. Louis, who were giving bond to professional Jewish emigrants. When Rai was 21 years-old, he visited Mrs. Stix and thanked her for what she had done for his family. The family immigrated to New York City. Rai’s father had a hard time passing the medi- cal boards because of his inability to answer multiple choice exams. His mother, who Rai says “held the family together,” worked in a number of retail stores. Through the services of an immigrant relief organization Rai received a scholarship to attend the prestigious Columbia Grammar School. At the end of 1945, when Rai was 13 years old, he became fascinated with electronics and music. -
Physics of LIGO Lecture 4
Physics of LIGO Lecture 4 40KG § Advanced LIGO SAPPHIRE, 31.4CMf SILICA, HERAEUS SV 35CMf INPUT MODE SILICA, LIGO I GRADE § LIGO Data analysis CLEANER ~26CMf ACTIVE THERMAL CORRECTION T=0.5% 125W 830KW LASER MOD. BS PRM ITM ETM time T~6% SRM T=7% OUTPUT MODE CLEANER PD Ringdowns GW READOUT Broadband Background Bursts frequency CW (quasi-periodic) Chirps LIGO-G000165-00-R AJW, Caltech, LIGO Project 1 Initial LIGO Þ Advanced LIGO schedule 1995 NSF Funding secured ($360M) 1996 Construction Underway (mostly civil) 1997 Facility Construction (vacuum system) 1998 Interferometer Construction (complete facilities) 1999 Construction Complete (interferometers in vacuum) 2000 Detector Installation (commissioning subsystems) 2001 Commission Interferometers (first coincidences) 2002 Sensitivity studies (initiate LIGO I Science Run) 2003+ Initial LIGO data run (one year integrated data at h ~ 10-21) 2007 Begin Advanced LIGO installation 2008 Advanced LIGO science run (2.5 hours ~ 1 year of Initial LIGO) LIGO-G000165-00-R AJW, Caltech, LIGO Project 2 Advanced LIGO incremental improvements § Reduce shot noise: higher power CW-laser: 12 watts Þ120 watts § Reduce shot noise: Advanced optical configuration: signal recycling mirror (7th suspended optic) to tune shot-noise response in frequency § Reduce seismic noise: Advanced (active) seismic isolation. Seismic wall moved from 40 Hz Þ ~ 12 Hz. § Reduce seismic and suspension noise: Quadrupal pendulum suspensions to filter environmental noise in stages. § Reduce suspension noise: Fused silica fibers, silica welds. § Reduce test mass thermal noise: Last pendulum stage (test mass) is controlled via electrostatic or photonic forces (no magnets). § Reduce test mass thermal noise: High-Q material (40 kg sapphire). -
National Science Foundation LIGO FACTSHEET NSF and the Laser Interferometer Gravitational-Wave Observatory
e National Science Foundation LIGO FACTSHEET NSF and the Laser Interferometer Gravitational-Wave Observatory In 1916, Albert What is LIGO? Einstein published the LIGO consists of two widely separated laser paper that predicted interferometers located within the United States – one gravitational waves – in Hanford, Washington, and the other in Livingston, ripples in the fabric of Louisiana – each housed inside an L-shaped, ultra-high space-time resulting vacuum tunnel. The twin LIGO detectors operate in from the most violent unison to detect gravitational waves. Caltech and MIT phenomena in our led the design, construction and operation of the NSF- universe, from funded facilities. supernovae explosions to the collision of black What are gravitational waves? holes. For 100 years, Gravitational waves are distortions of the space and that prediction has time which emit when any object that possesses mass stimulated scientists accelerates. This can be compared in some ways to how around the world who accelerating charges create electromagnetic fields (e.g. have been seeking light and radio waves) that antennae detect. To generate to directly detect gravitational waves that can be detected by LIGO, the gravitational waves. objects must be highly compact and very massive, such as neutron stars and black holes. Gravitational-wave In the 1970s, the National Science Foundation (NSF) detectors act as a “receiver.” Gravitational waves travel joined this quest and began funding the science to Earth much like ripples travel outward across a pond. and technological innovations behind the Laser However, these ripples in the fabric of space-time carry Interferometer Gravitational-Wave Observatory (LIGO), information about their violent origins and about the the instruments that would ultimately yield a direct nature of gravity – information that cannot be obtained detection of gravitational waves.