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Ricci, Levi-Civita, and the Birth of General Relativity Reviewed by David E
BOOK REVIEW Einstein’s Italian Mathematicians: Ricci, Levi-Civita, and the Birth of General Relativity Reviewed by David E. Rowe Einstein’s Italian modern Italy. Nor does the author shy away from topics Mathematicians: like how Ricci developed his absolute differential calculus Ricci, Levi-Civita, and the as a generalization of E. B. Christoffel’s (1829–1900) work Birth of General Relativity on quadratic differential forms or why it served as a key By Judith R. Goodstein tool for Einstein in his efforts to generalize the special theory of relativity in order to incorporate gravitation. In This delightful little book re- like manner, she describes how Levi-Civita was able to sulted from the author’s long- give a clear geometric interpretation of curvature effects standing enchantment with Tul- in Einstein’s theory by appealing to his concept of parallel lio Levi-Civita (1873–1941), his displacement of vectors (see below). For these and other mentor Gregorio Ricci Curbastro topics, Goodstein draws on and cites a great deal of the (1853–1925), and the special AMS, 2018, 211 pp. 211 AMS, 2018, vast secondary literature produced in recent decades by the world that these and other Ital- “Einstein industry,” in particular the ongoing project that ian mathematicians occupied and helped to shape. The has produced the first 15 volumes of The Collected Papers importance of their work for Einstein’s general theory of of Albert Einstein [CPAE 1–15, 1987–2018]. relativity is one of the more celebrated topics in the history Her account proceeds in three parts spread out over of modern mathematical physics; this is told, for example, twelve chapters, the first seven of which cover episodes in [Pais 1982], the standard biography of Einstein. -
University of Groningen the Bianchi Classification of Maximal D = 8 Gauged Supergravities Bergshoeff, Eric; Gran, Ulf; Linares
University of Groningen The Bianchi classification of maximal D = 8 gauged supergravities Bergshoeff, Eric; Gran, Ulf; Linares, Román; Nielsen, Mikkel; Ortín, Tomás; Roest, Diederik Published in: Classical and Quantum Gravity IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite from it. Please check the document version below. Document Version Publisher's PDF, also known as Version of record Publication date: 2003 Link to publication in University of Groningen/UMCG research database Citation for published version (APA): Bergshoeff, E., Gran, U., Linares, R., Nielsen, M., Ortín, T., & Roest, D. (2003). The Bianchi classification of maximal D = 8 gauged supergravities. Classical and Quantum Gravity, 20, 3997-4014. Copyright Other than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons). Take-down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons the number of authors shown on this cover page is limited to 10 maximum. Download date: 24-09-2021 INSTITUTE OF PHYSICS PUBLISHING CLASSICAL AND QUANTUM GRAVITY Class. Quantum Grav. 20 (2003) 3997–4014 -
Algebraic Research Schools in Italy at the Turn of the Twentieth Century: the Cases of Rome, Palermo, and Pisa
CORE Metadata, citation and similar papers at core.ac.uk Provided by Elsevier - Publisher Connector Historia Mathematica 31 (2004) 296–309 www.elsevier.com/locate/hm Algebraic research schools in Italy at the turn of the twentieth century: the cases of Rome, Palermo, and Pisa Laura Martini Department of Mathematics, University of Virginia, PO Box 400137, Charlottesville, VA 22904-4137, USA Available online 28 January 2004 Abstract The second half of the 19th century witnessed a sudden and sustained revival of Italian mathematical research, especially in the period following the political unification of the country. Up to the end of the 19th century and well into the 20th, Italian professors—in a variety of institutional settings and with a variety of research interests— trained a number of young scholars in algebraic areas, in particular. Giuseppe Battaglini (1826–1892), Francesco Gerbaldi (1858–1934), and Luigi Bianchi (1856–1928) defined three key venues for the promotion of algebraic research in Rome, Palermo, and Pisa, respectively. This paper will consider the notion of “research school” as an analytic tool and will explore the extent to which loci of algebraic studies in Italy from the second half of the 19th century through the opening decades of the 20th century can be considered as mathematical research schools. 2003 Elsevier Inc. All rights reserved. Sommario Nella seconda metà dell’Ottocento, specialmente dopo l’unificazione del paese, la ricerca matematica in Italia conobbe una vigorosa rinascita. Durante gli ultimi decenni del diciannovesimo secolo e i primi del ventesimo, matematici italiani appartenenti a diverse istituzioni e con interessi in diversi campi di ricerca, formarono giovani studiosi in vari settori dell’algebra. -
Anisotropic, Nonsingular Early Universe Model Leading to a Realistic Cosmology
This is a repository copy of Anisotropic, nonsingular early universe model leading to a realistic cosmology. White Rose Research Online URL for this paper: https://eprints.whiterose.ac.uk/85582/ Version: Accepted Version Article: Dechant, Pierre-Philippe orcid.org/0000-0002-4694-4010, Lasenby, Anthony and Hobson, Michael (2009) Anisotropic, nonsingular early universe model leading to a realistic cosmology. Physical Review D. 043524. ISSN 1550-2368 https://doi.org/10.1103/PhysRevD.79.043524 Reuse Items deposited in White Rose Research Online are protected by copyright, with all rights reserved unless indicated otherwise. They may be downloaded and/or printed for private study, or other acts as permitted by national copyright laws. The publisher or other rights holders may allow further reproduction and re-use of the full text version. This is indicated by the licence information on the White Rose Research Online record for the item. Takedown If you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing [email protected] including the URL of the record and the reason for the withdrawal request. [email protected] https://eprints.whiterose.ac.uk/ An anisotropic, non-singular early universe model leading to a realistic cosmology † ‡ Pierre-Philippe Dechant,∗ Anthony N. Lasenby, and Michael P. Hobson Astrophysics Group, Cavendish Laboratory, J J Thomson Avenue, University of Cambridge, CB3 0HE, UK (Dated: February 18, 2013) Abstract We present a novel cosmological model in which scalar field matter in a biaxial Bianchi IX geometry leads to a non-singular ‘pancaking’ solution: the hypersurface volume goes to zero instantaneously at the ‘Big Bang’, but all physical quantities, such as curvature invariants and the matter energy density remain finite, and continue smoothly through the Big Bang. -
Classification of Six-Dimensional Leibniz Algebras ${\Mathcal E} 3
Classification of six-dimensional Leibniz algebras E3 Ladislav Hlavatý∗ Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Czech Republic May 11, 2020 Abstract Leibniz algebras En were introduced as algebraic structure under- lying U-duality. Algebras E3 derived from Bianchi three-dimensional Lie algebras are classified here. Two types of algebras are obtained: Six-dimensional Lie algebras that can be considered extension of semi- Abelian four-dimensional Drinfel’d double and unique extensions of non-Abelian Bianchi algebras. For all of the algebras explicit forms of generalized frame fields are given. 1 Introduction arXiv:2003.06164v4 [hep-th] 8 May 2020 Extensions of Poisson–Lie T-dualities to non-perturbative symmetries of string theories are so called U-dualities (for review see e.g.[1]). Algebraic structures underlying U-duality were suggested in [2] and [3] as Leibniz algebras En obtained as extensions of n-dimensional Lie algebra defining non-symmetric product ◦ in [n + n(n − 1)/2]-dimensional vector space1 that satisfies Leibniz identity X ◦ (Y ◦ Z))=(X ◦ Y ) ◦ Z + Y ◦ (X ◦ Z). (1) ∗hlavaty@fjfi.cvut.cz 1for n ≤ 4 1 In those papers examples of these Leibniz algebras derived from two-dimensional and four-dimensional Lie algebras are given. Goal of the present note is to write down all algebras that can be derived from three dimensional Lie alge- bras whose classification given by Bianchi is well known. a1a2 a2a1 a1a2 Namely, let (Ta, T ), a, a1, a2 ∈ 1,...,n, T = −T is a basis of [n + n(n − 1)/2]-dimensional vector space. -
Bianchi, Luigi.Pdf 141KB
Centro Archivistico BIANCHI, LUIGI Elenco sommario del fondo 1 Indice generale Introduzione.....................................................................................................................................................2 Carteggio (1880-1923)......................................................................................................................................2 Carteggio Saverio Bianchi (1936 – 1954; 1975)................................................................................................4 Manoscritti didattico scientifici........................................................................................................................5 Fascicoli............................................................................................................................................................6 Introduzione Il fondo è pervenuto alla Biblioteca della Scuola Normale Superiore di Pisa per donazione degli eredi nel 1994-1995; si tratta probabilmente solo di una parte della documentazione raccolta da Bianchi negli anni di ricerca e insegnamento. Il fondo era corredato di un elenco dattiloscritto a cura di Paola Piazza, in cui venivano indicati sommariamente i contenuti delle cartelle. Il materiale è stato ordinato e descritto da Sara Moscardini e Manuel Rossi nel giugno 2014. Carteggio (1880-1923) La corrispondenza presenta oltre 100 lettere indirizzate a L. B. dal 1880 al 1923, da illustri studiosi del XIX-XX secolo come Eugenio Beltrami, Enrico Betti, A. von Brill, Francesco Brioschi, -
Dynamics of Bianchi Spacetimes
Dynamics of Bianchi spacetimes Fran¸coisB´eguin Universit´eParis-Sud 11 & ENS´ Febuary 9th, 2012 Raisons d'^etre: I natural finite dimensional class of spacetimes ; I BKL conjecture : generic spacetimes \behave like" spatially homogeneous spacetimes close to their initial singularity. Bianchi cosmological models : presentation Bianchi spacetimes are spatially homogeneous (not isotropic) cosmological models. Bianchi cosmological models : presentation Bianchi spacetimes are spatially homogeneous (not isotropic) cosmological models. Raisons d'^etre: I natural finite dimensional class of spacetimes ; I BKL conjecture : generic spacetimes \behave like" spatially homogeneous spacetimes close to their initial singularity. I A Bianchi spacetime is a spacetime (M; g) with 2 M ' I × G g = −dt + ht where I = (t−; t+) ⊂ R, G is 3-dimensional Lie group, ht is a left-invariant riemannian metric on G. I A Bianchi spacetime amounts to a one-parameter family of left-invariant metrics (ht )t2I on a 3-dimensional Lie group G. Bianchi cosmological models : definitions I A Bianchi spacetime is a globally hyperbolic spatially homogeneous (but not isotropic) spacetime. I A Bianchi spacetime amounts to a one-parameter family of left-invariant metrics (ht )t2I on a 3-dimensional Lie group G. Bianchi cosmological models : definitions I A Bianchi spacetime is a globally hyperbolic spatially homogeneous (but not isotropic) spacetime. I A Bianchi spacetime is a spacetime (M; g) with 2 M ' I × G g = −dt + ht where I = (t−; t+) ⊂ R, G is 3-dimensional Lie group, ht is a left-invariant riemannian metric on G. Bianchi cosmological models : definitions I A Bianchi spacetime is a globally hyperbolic spatially homogeneous (but not isotropic) spacetime. -
On the Energy of Homogeneous Cosmologies
On the energy of homogeneous cosmologies James M. Nester Department of Physics, National Central University, Chungli 32054, Taiwan Department of Physics and Institute of Astronomy, National Central University, Chungli 32054, Taiwan. [email protected] Lau Loi So1 Department of Physics, National Central University, Chungli 32054, Taiwan [email protected] T. Vargas2 Instituto de Fisica Teorica, Universidade Estadual Paulista, Rua Pamplona 145, 01405-900 Sao Paulo SP, Brazil. [email protected] Received ; accepted 1present address:Department of physics, Tamkang University, Tamsui 251, Taiwan. 2present address:Department of Physics, National Central University, Chungli 32054, Tai- wan. – 2 – ABSTRACT We investigate the quasi-local energy of all the homogeneous cosmological models. More specifically using the standard natural prescription we find the quasi-local energy-momentum for a large class of gravity theories with a tetrad description for all 9 Bianchi types with general gravitational sources. Using ideas related to a Hamiltonian approach we find that, with homogeneous boundary conditions, the quasi-local energy vanishes for all regions in all Bianchi class A models, and it does not vanish for any class B model. This is so not only for Einstein’s general relativity but, moreover, for the whole 3-parameter class of tetrad-teleparallel theories. For the physically favored one parameter subclass, which includes the teleparallel equivalent of Einstein’s theory as an important special case, the quasi-local energy for all class B models is positive. PACS 04.20.Cv, 04.20.Fy, 98.80.Jk 2006-12-19jmn 1. Introduction Energy has been one of the most useful physical concepts, no less so in gravitating systems—one need only recall its utility in the Newtonian Kepler problem. -
Rotating Dust Solutions of Einstein's Equations with 3-Dimensional Symmetry Groups. I. Two Killing Fields Spanned on U and W
Rotating dust solutions of Einstein’s equations with 3-dimensional symmetry groups. I. Two Killing fields spanned on ua and wa Andrzej Krasin´ski N. Copernicus Astronomical Center and College of Science, Polish Academy of Sciences, Bartycka 18, 00 716 Warszawa, Poland ~Received 14 May 1997; accepted for publication 7 July 1997! For a rotating dust with a 3-dimensional symmetry group all possible metric forms can be classified and, within each class, explicitly written out. This is made possible by the formalism of Pleban´ski based on the Darboux theorem. In the resulting coordinates, the Killing vector fields ~if any exist! assume a special form. Each Killing vector field may be either spanned on the fields of velocity and rotation or linearly independent of them. By considering all such cases one arrives at the classification. With respect to the structures of the groups, this is just the Bianchi classification, but with all possible orientations of the orbits taken into account. In this paper, which is part 1 of a 3-part series, all solutions are considered for which two Killing fields are spanned on velocity and rotation. The solutions of Lanczos and Go¨del are identified as special cases, and their new invariant definitions are provided. In addition, a new invariant definition is given of the Ozsvath class III solution. © 1998 American Institute of Physics. @S0022-2488~97!03112-5# I. INTRODUCTION AND SUMMARY The theorem of Darboux presented in Sec. II allows one to introduce invariantly defined coordinates in which the velocity field of a fluid ~not assumed to be perfect! acquires a ‘‘canoni- cal’’ form. -
Bianchi 121 Bianchi
BIANCHI BIANCHI interpretation of quantum-theory foundations . He Upon his return to Italy in 1881, Bianchi was initiated and was elected chairman of the inter- appointed professor at the Scuola Normale Superiore national scientific conference in Warsaw (1938) where of Pisa, and after having taught differential geometry this problem was discussed by many famous theorists . at the University of Pisa, in 1886 he was appointed During World War 11, Biaaobrzeski prepared a three- extraordinary professor of projective geometry on the volume work to be entitled Podstawy poznawcze fizvki basis of a competitive examination . During the same twiala atomowego ("Epistemological Foundations of year he was also made professor of analytic geometry, the Physics of the Atomic World"), in which he a post he held for the rest of his life . By special developed his philosophical interpretation of the appointment Bianchi also taught higher mathematics quantum theory . Unfortunately, the manuscripts of and analysis. After 1918 he was director of the Scuola the first two volumes were burned during the Warsaw Normale Superiore . He was a member of many Ital- Insurrection (1944) . After the war Biajobrzeski re- ian and foreign academies, and a senator of the king- turned to Warsaw University and started to recon- dom of Italy . struct the book . The work, limited to one volume, was Bianchi concentrated on studies and research in finished in 1951 and published in 1956 . metric differential geometry. Among his major results was his discovery of all the geometries of Riemann that allow for a continuous group of movements, that BIBLIOGRAPHY is, those in which a figure may move continuously without undergoing any deformation . -
A CRITICAL EVALUATION of MODERN PHYSICS by Claudio Voarino
A CRITICAL EVALUATION OF MODERN PHYSICS By Claudio Voarino A Few Words of Introduction In his article, Science and the Mountain Peak, Professor Isaac Asimov wrote: “There has been at least one occasion in history, when Greek secular and rational thought bowed to the mystical aspect of Christianity, and what followed was a Dark Age. We can’t afford another!” I don’t think I am exaggerating when I say that, when it comes to Modern Physics (also known as New Physics), we have indeed been in some sort of intellectual dark age, whether we can afford it or not. In fact, we have been in it since the end of the 19 th Century; and this is when Classical Physics started to be substituted with Modern Physics. This despite the fact there were lots of instances that clearly show the absurdity and science-fictional character of most of the theories of this kind of physics, which I will be discussing in details further on in this article. But for now, the following few examples should prove the correctness of my opinion on this topic. Incidentally, for the purpose of this article, the word ‘physics’ means mostly ‘astrophysics’. Also, whenever referring to modern physicists, I think it is more accurate to add the adjective ‘theoretical’ before the word ‘physicists’. I am saying that because I just cannot associate the main tenets of Relativity and Quantum Physics theories with physical reality. The following example should attest the truth of my statement. Back on September 10, 1989, the Australian newspaper Sunday Telegraph carried the following bizarre article entitled Keep Looking or the Moon May Vanish. -
The First Period: 1888 - 1904
The first period: 1888 - 1904 The members of the editorial board: 1891: Henri Poincaré entered to belong to “direttivo” of Circolo. (In that way the Rendiconti is the first mathematical journal with an international editorial board: the Acta’s one was only inter scandinavian) 1894: Gösta Mittag-Leffler entered to belong to “direttivo” of Circolo . 1888: New Constitution Art. 2: [Il Circolo] potrà istituire concorsi a premi e farsi promotore di congress scientifici nelle varie città del regno. [Il Circolo] may establish prize competitions and become a promoter of scientific congress in different cities of the kingdom. Art 17: Editorial Board 20 members (five residents and 15 non residents) Art. 18: elections with a system that guarantees the secrety of the vote. 1888: New Editorial Board 5 from Palermo: Giuseppe and Michele Albeggiani; Francesco Caldarera; Michele Gebbia; Giovan Battista Guccia 3 from Pavia: Eugenio Beltrami; Eugenio Bertini; Felice Casorati; 3 from Pisa: Enrico Betti; Riccardo De Paolis; Vito Volterra 2 from Napoli: Giuseppe Battaglini; Pasquale Del Pezzo 2 from Milano: Francesco Brioschi; Giuseppe Jung 2 from Roma: Valentino Cerruti; Luigi Cremona 2 from Torino: Enrico D’Ovidio; Corrado Segre 1 from Bologna: Salvatore Pincherle A very well distributed arrangement of the best Italian mathematicians! The most important absence is that of the university of Padova: Giuseppe Veronese had joined the Circolo in 1888, Gregorio Ricci will never be a member of it Ulisse Dini and Luigi Bianchi in Pisa will join the Circolo respectively in 1900 and in 1893. The first and the second issue of the Rendiconti Some papers by Palermitan scholars and papers by Eugène Charles Catalan, Thomas Archer Hirst, Pieter Hendrik Schoute, Corrado Segre (first issue, 1887) and Enrico Betti, George Henri Halphen, Ernest de Jonquières, Camille Jordan, Giuseppe Peano, Henri Poincaré, Corrado Segre, Alexis Starkov, Vito Volterra (second issue, 1888).