First M87 Event Horizon Telescope Results and the Role of ALMA
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A Mathematical Derivation of the General Relativistic Schwarzschild
A Mathematical Derivation of the General Relativistic Schwarzschild Metric An Honors thesis presented to the faculty of the Departments of Physics and Mathematics East Tennessee State University In partial fulfillment of the requirements for the Honors Scholar and Honors-in-Discipline Programs for a Bachelor of Science in Physics and Mathematics by David Simpson April 2007 Robert Gardner, Ph.D. Mark Giroux, Ph.D. Keywords: differential geometry, general relativity, Schwarzschild metric, black holes ABSTRACT The Mathematical Derivation of the General Relativistic Schwarzschild Metric by David Simpson We briefly discuss some underlying principles of special and general relativity with the focus on a more geometric interpretation. We outline Einstein’s Equations which describes the geometry of spacetime due to the influence of mass, and from there derive the Schwarzschild metric. The metric relies on the curvature of spacetime to provide a means of measuring invariant spacetime intervals around an isolated, static, and spherically symmetric mass M, which could represent a star or a black hole. In the derivation, we suggest a concise mathematical line of reasoning to evaluate the large number of cumbersome equations involved which was not found elsewhere in our survey of the literature. 2 CONTENTS ABSTRACT ................................. 2 1 Introduction to Relativity ...................... 4 1.1 Minkowski Space ....................... 6 1.2 What is a black hole? ..................... 11 1.3 Geodesics and Christoffel Symbols ............. 14 2 Einstein’s Field Equations and Requirements for a Solution .17 2.1 Einstein’s Field Equations .................. 20 3 Derivation of the Schwarzschild Metric .............. 21 3.1 Evaluation of the Christoffel Symbols .......... 25 3.2 Ricci Tensor Components ................. -
Stephen Hawking: 'There Are No Black Holes' Notion of an 'Event Horizon', from Which Nothing Can Escape, Is Incompatible with Quantum Theory, Physicist Claims
NATURE | NEWS Stephen Hawking: 'There are no black holes' Notion of an 'event horizon', from which nothing can escape, is incompatible with quantum theory, physicist claims. Zeeya Merali 24 January 2014 Artist's impression VICTOR HABBICK VISIONS/SPL/Getty The defining characteristic of a black hole may have to give, if the two pillars of modern physics — general relativity and quantum theory — are both correct. Most physicists foolhardy enough to write a paper claiming that “there are no black holes” — at least not in the sense we usually imagine — would probably be dismissed as cranks. But when the call to redefine these cosmic crunchers comes from Stephen Hawking, it’s worth taking notice. In a paper posted online, the physicist, based at the University of Cambridge, UK, and one of the creators of modern black-hole theory, does away with the notion of an event horizon, the invisible boundary thought to shroud every black hole, beyond which nothing, not even light, can escape. In its stead, Hawking’s radical proposal is a much more benign “apparent horizon”, “There is no escape from which only temporarily holds matter and energy prisoner before eventually a black hole in classical releasing them, albeit in a more garbled form. theory, but quantum theory enables energy “There is no escape from a black hole in classical theory,” Hawking told Nature. Peter van den Berg/Photoshot and information to Quantum theory, however, “enables energy and information to escape from a escape.” black hole”. A full explanation of the process, the physicist admits, would require a theory that successfully merges gravity with the other fundamental forces of nature. -
RF Interference Monitoring for the Onsala Space Observatory Master of Science Thesis (Communication Engineering)
RF Interference Monitoring for the Onsala Space Observatory Master of Science Thesis (Communication Engineering) SYED AMEER AHMED GILLANI Department of Earth and Space Sciences, Onsala Space Observatory, CHALMERS UNIVERSITY OF TECHNOLOGY, Göteborg, Sweden, 2010. RF INTERFERENCE MONITORING FOR ONSALA SPACE OBSERVATORY SYED AMEER AHMED GILLANI Department of Earth and Space Sciences, Onsala Space Observatory CHALMERS UNIVERSITY OF TECHNOLOGY Göteborg, Sweden 2010 ii ABSTRACT With the continuous and rapid developments in wireless services and allocation of radio frequency spectrum to these services, huge interferences have been observed in the field of radio astronomy. According to the international regulations, parts of the spectra are reserved for radio-astronomical observations. Man-made signals entering the receiver chain of a radio telescope have much higher power compared to natural or passive signals received at the radio telescopes. Passive signals received at radio telescopes are normally 60 dB below the receiver noise level. Active signals generated by man-made wireless services pollute the natural emissions by completely masking them due to high signal strength. The cosmic radiation is determined by the fundamental laws of physics, thus the frequencies are fixed and cannot be changed. So interferences created by active services lead to wrong interpretations of the astronomical data. The present thesis deals with RF interference monitoring system for the Onsala Space Observatory. As part of the thesis, a software application has been developed, which communicates with different type of digital receivers (spectrum analyzers) attached with antenna controlling hardware to control omnidirectional and steerable antennas. A steerable antenna is used to find the direction of interference source by moving the antenna in azimuth and elevation direction. -
A Precise and Accurate Determination of the Cosmic Microwave Background Temperature at Z =0.89
A&A 551, A109 (2013) Astronomy DOI: 10.1051/0004-6361/201220613 & c ESO 2013 Astrophysics A precise and accurate determination of the cosmic microwave background temperature at z =0.89 S. Muller1, A. Beelen2,J.H.Black1,S.J.Curran3,4, C. Horellou1,S.Aalto1, F. Combes5, M. Guélin6,7, and C. Henkel8,9 1 Department of Earth and Space Sciences, Chalmers University of Technology, Onsala Space Observatory, 439 92 Onsala, Sweden e-mail: [email protected] 2 Institut d’Astrophysique Spatiale, Bât. 121, Université Paris-Sud, 91405 Orsay Cedex, France 3 Sydney Institute for Astronomy, School of Physics, The University of Sydney, 2006 NSW, Australia 4 ARC Centre of Excellence for All-sky Astrophysics (CAASTRO), Australia 5 Observatoire de Paris, LERMA, CNRS, 61 Av. de l’Observatoire, 75014 Paris, France 6 Institut de Radioastronomie Millimétrique, 300 rue de la piscine, 38406 Saint-Martin d’Hères, France 7 École Normale Supérieure/LERMA, 24 rue Lhomond, 75005 Paris, France 8 Max-Planck-Institut für Radioastonomie, Auf dem Hügel 69, 53121 Bonn, Germany 9 Astron. Dept., King Abdulaziz University, PO Box 80203, Jeddah, Saudi Arabia Received 22 October 2012 / Accepted 21 December 2012 ABSTRACT Context. According to the Big Bang theory and as a consequence of adiabatic expansion of the Universe, the temperature of the cosmic microwave background (CMB) increases linearly with redshift. This relation is, however, poorly explored, and detection of any deviation would directly lead to (astro-)physics beyond the standard model. Aims. We aim to measure the temperature of the CMB with an accuracy of a few percent at z = 0.89 toward the molecular absorber in the galaxy lensing the quasar PKS 1830−211. -
Black Holes. the Universe. Today’S Lecture
Physics 311 General Relativity Lecture 18: Black holes. The Universe. Today’s lecture: • Schwarzschild metric: discontinuity and singularity • Discontinuity: the event horizon • Singularity: where all matter falls • Spinning black holes •The Universe – its origin, history and fate Schwarzschild metric – a vacuum solution • Recall that we got Schwarzschild metric as a solution of Einstein field equation in vacuum – outside a spherically-symmetric, non-rotating massive body. This metric does not apply inside the mass. • Take the case of the Sun: radius = 695980 km. Thus, Schwarzschild metric will describe spacetime from r = 695980 km outwards. The whole region inside the Sun is unreachable. • Matter can take more compact forms: - white dwarf of the same mass as Sun would have r = 5000 km - neutron star of the same mass as Sun would be only r = 10km • We can explore more spacetime with such compact objects! White dwarf Black hole – the limit of Schwarzschild metric • As the massive object keeps getting more and more compact, it collapses into a black hole. It is not just a denser star, it is something completely different! • In a black hole, Schwarzschild metric applies all the way to r = 0, the black hole is vacuum all the way through! • The entire mass of a black hole is concentrated in the center, in the place called the singularity. Event horizon • Let’s look at the functional form of Schwarzschild metric again: ds2 = [1-(2m/r)]dt2 – [1-(2m/r)]-1dr2 - r2dθ2 -r2sin2θdφ2 • We want to study the radial dependence only, and at fixed time, i.e. we set dφ = dθ = dt = 0. -
Arxiv:1705.04776V1 [Astro-Ph.HE] 13 May 2017 Aaua M
White Paper on East Asian Vision for mm/submm VLBI: Toward Black Hole Astrophysics down to Angular Resolution of 1 RS Editors Asada, K.1, Kino, M.2,3, Honma, M.3, Hirota, T.3, Lu, R.-S.4,5, Inoue, M.1, Sohn, B.-W.2,6, Shen, Z.-Q.4, and Ho, P. T. P.1,7 Authors Akiyama, K.3,8, Algaba, J-C.2, An, T.4, Bower, G.1, Byun, D-Y.2, Dodson, R.9, Doi, A.10, Edwards, P.G.11, Fujisawa, K.12, Gu, M-F.4, Hada, K.3, Hagiwara, Y.13, Jaroenjittichai, P.15, Jung, T.2,6, Kawashima, T.3, Koyama, S.1,5, Lee, S-S.2, Matsushita, S.1, Nagai, H.3, Nakamura, M.1, Niinuma, K.12, Phillips, C.11, Park, J-H.15, Pu, H-Y.1, Ro, H-W.2,6, Stevens, J.11, Trippe, S.15, Wajima, K.2, Zhao, G-Y.2 1 Institute of Astronomy and Astrophysics, Academia Sinica, P.O. Box 23-141, Taipei 10617, Taiwan 2 Korea Astronomy and Space Science Institute, Daedukudae-ro 776, Yuseong-gu, Daejeon 34055, Republic of Korea 3 National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo, 181-8588, Japan 4 Shanghai Astronomical Observatory, Chinese Academy of Sciences, 80 Nandan Road, Shanghai 200030, China 5 Max-Planck-Institut f¨ur Radioastronomie, Auf dem H¨ugel 69, D-53121 Bonn, Germany 6 University of Science and Technology, 217 Gajeong-ro, Yuseong-gu, Daejeon 34113, Republic of Korea 7 East Asian Observatory, 660 N. -
CASKAR: a CASPER Concept for the SKA Phase 1 Signal Processing Sub-System
CASKAR: A CASPER concept for the SKA phase 1 Signal Processing Sub-system Francois Kapp, SKA SA Outline • Background • Technical – Architecture – Power • Cost • Schedule • Challenges/Risks • Conclusions Background CASPER Technology MeerKAT Who is CASPER? • Berkeley Wireless Research Center • Nancay Observatory • UC Berkeley Radio Astronomy Lab • Oxford University Astrophysics • UC Berkeley Space Sciences Lab • Metsähovi Radio Observatory, Helsinki University of • Karoo Array Telescope / SKA - SA Technology • NRAO - Green Bank • New Jersey Institute of Technology • NRAO - Socorro • West Virginia University Department of Physics • Allen Telescope Array • University of Iowa Department of Astronomy and • MIT Haystack Observatory Physics • Harvard-Smithsonian Center for Astrophysics • Ohio State University Electroscience Lab • Caltech • Hong Kong University Department of Electrical and Electronic Engineering • Cornell University • Hartebeesthoek Radio Astronomy Observatory • NAIC - Arecibo Observatory • INAF - Istituto di Radioastronomia, Northern Cross • UC Berkeley - Leuschner Observatory Radiotelescope • Giant Metrewave Radio Telescope • University of Manchester, Jodrell Bank Centre for • Institute of Astronomy and Astrophysics, Academia Sinica Astrophysics • National Astronomical Observatories, Chinese Academy of • Submillimeter Array Sciences • NRAO - Tucson / University of Arizona Department of • CSIRO - Australia Telescope National Facility Astronomy • Parkes Observatory • Center for Astrophysics and Supercomputing, Swinburne University -
Maser Observations with New Instruments
Cosmic Masers - from OH to H0 Proceedings IAU Symposium No. 287, 2012 c 2012 International Astronomical Union E. Humphreys & W. Vlemmings, eds. DOI: 00.0000/X000000000000000X Maser observations with new instruments Alwyn Wootten1 1North American ALMA Science Center, NRAOy, 520 Edgemont Rd., Charlottesville, Virginia 22903, USA email: [email protected] Abstract. The Atacama Large Millimeter/submillimeter Array (ALMA)y, and the Jansky Very Large Array (JVLA) have recently begun probing the Universe. Both provide the largest collect- ing area available at locations on a high dry site, endowing them with unparalleled potential for sensitive spectral line observations. Over the next few years, these telescopes will be joined by other telescopes to provide advances in maser science, including NOEMA and the LMT. Other instruments of note for maser science which may commence construction include the North American Array, the CCAT, and an enlarged worldwide VLB network outfitted to operate into the millimeter wavelength regime. Keywords. masers, radio lines: ISM, instrumentation: high angular resolution 1. Introduction At the last IAU Symposium on masers, construction had just begun on the Atacama Large Millimeter/Submillimeter Array (ALMA), the upgrade of the Very Large Array to the Jansky Very Large Array was being planned, and millimeter instrumentation was being introduced on the Green Bank Telescope (GBT). CARMA had just commenced its first semester of routine science and would shortly populate its more extended arrays, enabling high resolution observations, particularly well adapted to maser observations. The Submillimeter Array was forging new paths with high resolution observations up to the edge of the atmospheric windows near 700 GHz. -
Evolution of the Cosmological Horizons in a Concordance Universe
Evolution of the Cosmological Horizons in a Concordance Universe Berta Margalef–Bentabol 1 Juan Margalef–Bentabol 2;3 Jordi Cepa 1;4 [email protected] [email protected] [email protected] 1Departamento de Astrofísica, Universidad de la Laguna, E-38205 La Laguna, Tenerife, Spain: 2Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, E-28040 Madrid, Spain. 3Facultad de Ciencias Físicas, Universidad Complutense de Madrid, E-28040 Madrid, Spain. 4Instituto de Astrofísica de Canarias, E-38205 La Laguna, Tenerife, Spain. Abstract The particle and event horizons are widely known and studied concepts, but the study of their properties, in particular their evolution, have only been done so far considering a single state equation in a deceler- ating universe. This paper is the first of two where we study this problem from a general point of view. Specifically, this paper is devoted to the study of the evolution of these cosmological horizons in an accel- erated universe with two state equations, cosmological constant and dust. We have obtained closed-form expressions for the horizons, which have allowed us to compute their velocities in terms of their respective recession velocities that generalize the previous results for one state equation only. With the equations of state considered, it is proved that both velocities remain always positive. Keywords: Physics of the early universe – Dark energy theory – Cosmological simulations This is an author-created, un-copyedited version of an article accepted for publication in Journal of Cosmology and Astroparticle Physics. IOP Publishing Ltd/SISSA Medialab srl is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. -
The Third Catalog of Active Galactic Nuclei Detected by the Fermi Large Area Telescope M
The Astrophysical Journal, 810:14 (34pp), 2015 September 1 doi:10.1088/0004-637X/810/1/14 © 2015. The American Astronomical Society. All rights reserved. THE THIRD CATALOG OF ACTIVE GALACTIC NUCLEI DETECTED BY THE FERMI LARGE AREA TELESCOPE M. Ackermann1, M. Ajello2, W. B. Atwood3, L. Baldini4, J. Ballet5, G. Barbiellini6,7, D. Bastieri8,9, J. Becerra Gonzalez10,11, R. Bellazzini12, E. Bissaldi13, R. D. Blandford14, E. D. Bloom14, R. Bonino15,16, E. Bottacini14, T. J. Brandt10, J. Bregeon17, R. J. Britto18, P. Bruel19, R. Buehler1, S. Buson8,9, G. A. Caliandro14,20, R. A. Cameron14, M. Caragiulo13, P. A. Caraveo21, B. Carpenter10,22, J. M. Casandjian5, E. Cavazzuti23, C. Cecchi24,25, E. Charles14, A. Chekhtman26, C. C. Cheung27, J. Chiang14, G. Chiaro9, S. Ciprini23,24,28, R. Claus14, J. Cohen-Tanugi17, L. R. Cominsky29, J. Conrad30,31,32,70, S. Cutini23,24,28,R.D’Abrusco33,F.D’Ammando34,35, A. de Angelis36, R. Desiante6,37, S. W. Digel14, L. Di Venere38, P. S. Drell14, C. Favuzzi13,38, S. J. Fegan19, E. C. Ferrara10, J. Finke27, W. B. Focke14, A. Franckowiak14, L. Fuhrmann39, Y. Fukazawa40, A. K. Furniss14, P. Fusco13,38, F. Gargano13, D. Gasparrini23,24,28, N. Giglietto13,38, P. Giommi23, F. Giordano13,38, M. Giroletti34, T. Glanzman14, G. Godfrey14, I. A. Grenier5, J. E. Grove27, S. Guiriec10,2,71, J. W. Hewitt41,42, A. B. Hill14,43,68, D. Horan19, R. Itoh40, G. Jóhannesson44, A. S. Johnson14, W. N. Johnson27, J. Kataoka45,T.Kawano40, F. Krauss46, M. Kuss12, G. La Mura9,47, S. Larsson30,31,48, L. -
Cutting-Edge Engineering for the World's Largest Radio Telescope
SKAO Cutting-edge engineering for the world’s largest radio telescope Cutting-edge engineering for the world’s largest radio telescope Approaching a technological challenge on the scale of the SKA is formidable... while building on 60 years of radio- astronomy developments, the huge increase in scale from existing facilities demands a revolutionary break from traditional radio telescope design and radical developments in processing, computer speeds and the supporting technological infrastructure. To answer this challenge the SKA has been broken down into various elements that will form the final SKA telescope. Each element is managed by an international consortium comprising world leading experts in their fields. The SKA Office, staffed with engineering domain experts, systems engineers, scientists and managers, centralises the project management and system design. SKAO The design work was awarded through the SKA Office to these Consortia, made up of over 100 of some of the world’s top research institutions and companies, drawn primarily from the SKA Member countries but also beyond. Following the delivery of a detailed design package in 2016, in 2018 nine consortia are having their Critical Design Reviews (CDR) to deliver the final design documentation to prepare a construction proposal for government approval. The other three consortia are part of the SKA’s Advanced Instrumentation Programme, which develops future instrumention for the SKA. The 2018 SKA CalenDaR aims to recognise the immense work conducted by these hundreds of dedicated engineers and project managers from around the world over the past five years. Without their crucial work, the SKA’s ambitious science programme would not be possible. -
Counting Gamma Rays in the Directions of Galaxy Clusters
A&A 567, A93 (2014) Astronomy DOI: 10.1051/0004-6361/201322454 & c ESO 2014 Astrophysics Counting gamma rays in the directions of galaxy clusters D. A. Prokhorov1 and E. M. Churazov1,2 1 Max Planck Institute for Astrophysics, Karl-Schwarzschild-Strasse 1, 85741 Garching, Germany e-mail: [email protected] 2 Space Research Institute (IKI), Profsouznaya 84/32, 117997 Moscow, Russia Received 6 August 2013 / Accepted 19 May 2014 ABSTRACT Emission from active galactic nuclei (AGNs) and from neutral pion decay are the two most natural mechanisms that could establish a galaxy cluster as a source of gamma rays in the GeV regime. We revisit this problem by using 52.5 months of Fermi-LAT data above 10 GeV and stacking 55 clusters from the HIFLUCGS sample of the X-ray brightest clusters. The choice of >10 GeV photons is optimal from the point of view of angular resolution, while the sample selection optimizes the chances of detecting signatures of neutral pion decay, arising from hadronic interactions of relativistic protons with an intracluster medium, which scale with the X-ray flux. In the stacked data we detected a signal for the central 0.25 deg circle at the level of 4.3σ. Evidence for a spatial extent of the signal is marginal. A subsample of cool-core clusters has a higher count rate of 1.9 ± 0.3 per cluster compared to the subsample of non-cool core clusters at 1.3 ± 0.2. Several independent arguments suggest that the contribution of AGNs to the observed signal is substantial, if not dominant.