On the Dynamics of the General Bianchi IX Spacetime Near the Singularity
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Icranet Scientific Report 2008
Early Cosmology and Fundamental General Relativity Contents 1 Topics 1215 2 Participants 1217 2.1 ICRANet participants . 1217 2.2 Past collaborations . 1217 2.3 Ongoing Collaborations . 1217 2.4 Graduate Students . 1217 3 Brief Description 1219 3.1 Highlights in Early Cosmology and Fundamental General Rel- ativity . 1219 3.1.1 Dissipative Cosmology . 1219 3.1.2 On the Jeans instability of gravitational perturbations . 1219 3.1.3 Extended Theories of Gravity . 1220 3.1.4 Coupling between Spin and Gravitational Waves . 1221 3.2 Appendix: The Generic Cosmological Solution . 1221 3.3 Appendix: Classical Mixmaster . 1221 3.4 Appendix: Interaction of neutrinos and primordial GW . 1223 3.5 Appendix: Perturbation Theory in Macroscopic Gravity . 1224 3.6 Appendix: Schouten’s Classification . 1224 3.7 Appendix: Inhomogeneous spaces and Entropy . 1225 3.8 Appendix: Polarization in GR . 1225 3.9 Appendix: Averaging Problem in Cosmology and Gravity . 1226 3.10 Appendix: Astrophysical Topics . 1227 4 Selected Publications Before 2005 1229 4.1 Early Cosmology . 1229 4.2 Fundamental General Relativity . 1233 5 Selected Publications (2005-2008) 1239 5.1 Early Cosmology . 1239 H.1Dissipative Cosmology 1245 H.2On the Jeans instability of gravitational perturbations 1251 H.3Extended Theories of Gravity 1257 1213 Contents H.4Coupling between Spin and Gravitational Waves 1261 H.5Activities 1263 H.5.1Review Work . 1263 H.5.1.1Classical and Quantum Features of the Mixmaster Sin- gularity . 1263 A.1Birth and Development of the Generic Cosmological Solution 1267 A.2Appendix: Classical Mixmaster 1271 A.2.1Chaos covariance of the Mixmaster model . 1271 A.2.2Chaos covariance of the generic cosmological solution . -
Zeldovich-100 Meeting Subatomic Particles, Nucleons, Atoms, Universe: Processes and Structure
Zeldovich-100 Meeting Subatomic particles, Nucleons, Atoms, Universe: Processes and Structure International conference in honor of Ya. B. Zeldovich 100th Anniversary March 10–14, 2014 Minsk, Belarus Yakov Borisovich Zeldovich Short biography of Ya.B. Zeldovich Born on March 8, 1914 in Minsk. Died on December 2, 1987 in Moscow. Father Zeldovich Boris Naumovich, lawyer, member of So- vier Advocate Collegia; Mother Zeldovich (Kiveliovich) Anna Petrovna, translator, member of Soviet Writers Union. Since middle of 1914 to August 1941 lived in Petrograd (later Leningrad), up to summer of 1943 in Kazan, since 1943 in Moscow. In 1924 entered secondary school right away to the 3rd form, finished the school in 1930. From autumn 1930 till May 1931 he studied at the courses and worked as a laboratory assistant at the Institute of Mechanical processing of minerals. In May 1931 became a laboratory assistant at the Institute of Chemical Physics of the Academy of Science of the USSR (ICP). He was connected with this Institute till his very last days. As he began to work in the ICF without higher education, he spend much time to self-education. From 1932 till 1934 studied as a extra-mural student at the Phys-Math department of the Leningrad State University, but didn’t recieved any degree there. Later listened lectures at the Phys-Mech department of the Poly- technical Institute. In 1934 joined ICF as a post-graduate student, in 1936 received PhD degree, in 1939 received degree of doctor of science (phys- math science). From 1938 he was a head of a laboratory at the ICF. -
Early Cosmology and Fundamental General Relativity
EARLY COSMOLOGY AND FUNDAMENTAL GENERAL RELATIVITY 734 Contents 1 Topics 737 2 Participants 738 2.1 ICRANet participants . 738 2.2 Past collaborations . 738 2.3 Ongoing Collaborations . 738 2.4 GraduateStudents . .738 3 Brief description of Early Cosmology 739 3.1 Birth and Development of the Generic Cosmological Solution . 739 3.2 Classical Mixmaster . 739 3.2.1 Chaos covariance of the Mixmaster model . 739 3.2.2 Chaos covariance of the generic cosmological solution . 740 3.2.3 Inhomogeneous inflationary models . 740 3.2.4 The Role of a Vector Field . 740 3.3 Dissipative Cosmology . 741 3.4 Extended Theories of Gravity . 741 3.5 Interaction of neutrinos and primordial GW . 742 3.6 Coupling between Spin and Gravitational Waves . 743 4 Brief Description of Fundamental General Relativity 744 4.1 Perturbation Theory in Macroscopic Gravity . 744 4.2 Schouten’s Classification . 745 4.3 Inhomogeneous spaces and Entropy . 745 4.4 PolarizationinGR . .746 4.5 Averaging Problem in Cosmology and Gravity . 747 4.6 Astrophysical Topics . 747 5 Selected Publications 748 5.1 EarlyCosmology .........................748 5.2 Fundamental General Relativity . 754 735 6 APPENDICES 760 A Early Cosmology 761 A.1 Birth and Development of the Generic Cosmological Solution . 762 A.2 ClassicalMixmaster. .765 A.2.1 Chaos covariance of the Mixmaster model . 765 A.2.2 Chaos covariance of the generic cosmological solution . 766 A.2.3 Inhomogeneous inflationary models . 767 A.2.4 The Role of a Vector Field . 768 A.3 Dissipative Cosmology . 770 A.4 Extended Theories of Gravity . 774 A.5 Interaction of neutrinos and primordial GW . -
IRAP Phd Orizz
university of ferrara 600 YEARS OF LOOKING FORWARD. the International Relativistic Astrophysics Ph.D. Erasmus Mundus Joint Doctorate Program IRAP PhD Following the successful scientific space missions by the European Space Agency (ESA) The Faculty and the European Southern Observatory (ESO) in Chile, as well as the high energy Giovanni Amelino-Camelia SAPIENZA Università di Roma particle activities at CERN in Genève, we have initiated a Ph.D. programme dedicated Vladimir Belinski to create a pool of scientists in the field of relativistic astrophysics. After taking full SAPIENZA Università di Roma and ICRANet Carlo Luciano Bianco advantage of the observational and experimental facilities mentioned above, the SAPIENZA Università di Roma and ICRANet students of our programme are expected to lead the theoretical developments of one Donato Bini of the most active fields of research: relativistic astrophysics. CNR – Istit. per Applicaz. del Calcolo “M. Picone” Sandip Kumar Chakrabarti This program provides expertise in the most advanced topics of mathematical and Indian Centre For Space Physics, India theoretical physics, and in relativistic field theories, in the context of astronomy, Pascal Chardonnet (Erasmus Mundus Coordinator) astrophysics and cosmology. It provides the ability to model the observational data Université de Savoie received from the above laboratories. This activity is necessarily international as no Christian Cherubini single university can have a scientific expertise in such a broad range of fields. Università “Campus Biomedico” di Roma Pierre Coullet Université de Nice - Sophie Antipolis Thibault Damour We announce two calls: one with a deadline on 28 February 2011, sponsored by IHES, Bures-sur-Yvette Jaan Einasto Erasmus Mundus, and the other with a deadline on 30 September 2011. -
Spacetime Is Spinorial; New Dimensions Are Timelike
Spacetime is spinorial; new dimensions are timelike George A.J. Sparling Laboratory of Axiomatics University of Pittsburgh Pittsburgh, Pennsylvania, 15260, USA Since Pythagoras of Samos and Euclid of Alexandria1, we have known how to express the squared distance between entities as the sum of squares of displacements in perpendicular directions. Since Hermann Minkowski2 and Albert Einstein3, the squared in- terval between events has acquired a new term which represents the square of the time displacement and which comes in with a negative sign. Most higher dimensional theories, whose aim is to unify the physical interactions of nature, use space-like extra dimensions (more squares with positive signs) rather than time- like (more squares with negative signs)[4−8]. But there need be no contradiction if timelike extra dimensions are used: for exam- ple, in the seminal work of Lisa Randall and Raman Sundrum8, 2 consistency can be achieved by replacing their parameters rc and 2 Λ by −rc and −Λ, respectively. Here a new spinorial theory of physics is developed, built on Einstein’s general relativity3 and using the unifying triality concept of Elie Cartan9,10: the trial- ity links space-time with two twistor spaces[9−14]. Unification en- arXiv:gr-qc/0610068v1 13 Oct 2006 tails that space-time acquires two extra dimensions, each of which must be time-like. The experimental device known as the Large Hadron Collider, which is just now coming online, is expected to put the higher-dimensional theories and this prediction in partic- ular to the test15,16. The present theory has three key features: • A powerful new spinor transform is constructed in general relativity, the Ξ- transform, solving a forty-year old problem posed by Roger Penrose [11−14]: to find a non-local, essentially spinorial approach to fundamental physics. -
Black Hole Paradoxes Mario Rabinowitz Armor Research 715 Lakemead Way Redwood City, CA 94062-3922 [email protected] Abstr
Black Hole Paradoxes Mario Rabinowitz Armor Research 715 Lakemead Way Redwood City, CA 94062-3922 [email protected] Abstract The Black Hole enigma has produced many paradoxical concepts since its introduction by John Michell in 1783. As each paradox was resolved and our understanding about black holes matured, new paradoxes arose. A consensus regarding the resolution of some conundrums such as the Naked Singularity Paradox and the Black Hole Lost Information Paradox has still not been achieved. Black hole complementarity as related to the lost information paradox (LIP) and the LIP itself are challenged by gravitational tunneling radiation. Where possible, the paradoxes will be presented in historical context presenting the interplay of competing perspectives such as those of Bekenstein, Belinski, Chandrasekar, Hawking, Maldacena, Page, Preskill, Susskind, 't Hooft, Veneziano, Wald, Winterberg, Yilmaz, and others. The average kinetic energy of emitted particles may have a feature in common with themionic emission. A broad range of topics will be covered including: Why can or can't the formation of a black hole be observed? Can one observe a naked singularity like the one clothed by a black hole? What can come out of, or seem to come out of, a black hole? What happens to the information that falls into a black hole? Doesn't the resolution of the original black hole entropy paradox introduce an equally challenging puzzle? Related anomalies in the speed of light, the speed of gravity, the speed of inflation, and Mach's principle are considered. As we shall see, these paradoxes have served as an incentive for research to sharpen our thinking, and even to promote the development of both new theoretical and experimental physics. -
Distribution Function of the Atoms of Spacetime and the Nature of Gravity
Entropy 2015, 17, 7420-7452; doi:10.3390/e17117420 OPEN ACCESS entropy ISSN 1099-4300 www.mdpi.com/journal/entropy Review Distribution Function of the Atoms of Spacetime and the Nature of Gravity Thanu Padmanabhan IUCAA, Pune University Campus, Ganeshkhind, Pune 411007, India; E-Mail: [email protected]; Tel.: +91-20-25604100; Fax: +91-20-25604699 Academic Editor: Raúl Alcaraz Martínez Received: 3 September 2015 / Accepted: 20 October 2015 / Published: 28 October 2015 Abstract: The fact that the equations of motion for matter remain invariant when a constant is added to the Lagrangian suggests postulating that the field equations of gravity should also respect this symmetry. This principle implies that: (1) the metric cannot be varied in any extremum principle to obtain the field equations; and (2) the stress-tensor of matter a b should appear in the variational principle through the combination Tabn n where na is an auxiliary null vector field, which could be varied to get the field equations. This procedure uniquely selects the Lanczos–Lovelock models of gravity in D-dimensions and Einstein’s theory in D = 4. Identifying na with the normals to the null surfaces in the spacetime in the macroscopic limit leads to a thermodynamic interpretation for gravity. Several geometrical variables and the equation describing the spacetime evolution acquire a thermodynamic interpretation. Extending these ideas one level deeper, we can obtain this variational principle from a distribution function for the “atoms of spacetime”, which counts the number of microscopic degrees of freedom of the geometry. This is based on the curious fact that the renormalized spacetime endows each event with zero volume, but finite area! Keywords: spacetime entropy; emergent gravity; cosmological constant; horizon entropy; quantum gravity; zero-point length; horizon thermodynamics 1. -
Front Matter
Cambridge University Press 978-1-107-04747-1 — The Cosmological Singularity Vladimir Belinski , Marc Henneaux Frontmatter More Information THE COSMOLOGICAL SINGULARITY Written for researchers focusing on general relativity, supergravity, and cos- mology, this is a self-contained exposition of the structure of the cosmological singularity in generic solutions of the Einstein equations, and an up-to-date mathematical derivation of the theory underlying the Belinski–Khalatnikov– Lifshitz (BKL) conjecture on this field. Part I provides a comprehensive review of the theory underlying the BKL conjecture. The generic asymptotic behavior near the cosmological singularity of the gravitational field, and fields describing other kinds of matter, is explained in detail. Part II focuses on the billiard reformulation of the BKL behavior. Taking a general approach, this section does not assume any simplifying symmetry con- ditions and applies to theories involving a range of matter fields and space-time dimensions, including supergravities. Overall, this book will equip theoretical and mathematical physicists with the theoretical fundamentals of the Big Bang, Big Crunch, Black Hole singularities, their billiard description, and emergent mathematical structures. Vladimir Belinski holds a permanent professor position at the Interna- tional Center for Relativistic Astrophysics Network, Italy. He is noted for his role in several key developments in theoretical physics, including the Belinski– Khalatnikov–Lifshitz conjecture on the behavior of generic solutions of Einstein equations near a cosmological singularity, the Belinski–Zakharov transform, and the “Inflationary Attractor.” He is co-author of the book Gravitational Solitons (Cambridge University Press, 2001) and has received the Landau Prize of the Russian Academy of Sciences (1974) and Marcel Grossmann Award (2012). -
Gravitation and Energy-Momentum Conservation in Nonsingular General Relativity
Gravitation and energy-momentum conservation in nonsingular general relativity N. Tsitverblit∗ School of Mechanical Engineering, Tel-Aviv University, Ramat-Aviv 69978, Israel April 14, 2018 Abstract Forced to be flat when nonsingularly described by the equations of general relativity in a synchronous frame, a region outside matter sources is recognized to fail in defining space-time curvature consistently with the material nature of the Lorentz transformation. The curvature then extends to such a region only when there is a continuous background medium there. Arising from vacuum decay in the universe, as any matter, this medium is thus capable of avoiding the singularity of gravitational collapse as well. The theory of general relativity is then suggested to stem from such a formulation of the generalized postulate of relativity as also includes the covariance of energy-momentum conservation for a macroscopically continuous material system, namely the universe. Implying identity between gravitation and inertia, this formulation does not need the principle of equiva- lence as a separate postulate. The Einstein tensor is thus interpretable as standing for the energy-momentum of the gravitational field. In terms of the background medium, its small-amplitude approximation underlain by matter dynamics and phase transitions also describes what is viewable as gravitational waves. In the framework of such a macroscopic interpretation, gravitation ought to be irrelevant to purely microscopic interactions. 1 Introduction Ever since the theory of general relativity was completed [1, 2], its commonly recognized aesthetic and conceptual appeal has been vitiated by mathematical issues whose implied po- tential resolutions have been far short of the high scientific standard otherwise suggested by this theory. -
The Thirteenth Marcel Grossmann Meeting
THE THIRTEENTH MARCEL GROSSMANN MEETING On Recent Developments in Theoretical and Experimental General Relativity, Astrophysics and Relativistic Field Theories by WSPC on 01/30/15. For personal use only. The Thirteenth Marcel Grossmann Meeting Downloaded from www.worldscientific.com 9194_9789814612180-tpV1.indd 1 3/11/14 12:57 pm July 25, 2013 17:28 WSPC - Proceedings Trim Size: 9.75in x 6.5in icmp12-master This page intentionally left blank by WSPC on 01/30/15. For personal use only. The Thirteenth Marcel Grossmann Meeting Downloaded from www.worldscientific.com PART A THE THIRTEENTH MARCEL GROSSMANN MEETING On Recent Developments in Theoretical and Experimental General Relativity, Astrophysics and Relativistic Field Theories Proceedings of the MG13 Meeting on General Relativity Stockholm University, Stockholm, Sweden 1–7 July 2012 Editors Robert T Jantzen Villanova University, USA by WSPC on 01/30/15. For personal use only. Kjell Rosquist Stockholm University, Sweden Series Editor The Thirteenth Marcel Grossmann Meeting Downloaded from www.worldscientific.com Remo Ruffini International Center for Relativistic Astrophysics Network (ICRANet), Italy University of Rome “La Sapienza”, Italy World Scientific NEW JERSEY • LONDON • SINGAPORE • BEIJING • SHANGHAI • HONG KONG • TAIPEI • CHENNAI 9194_9789814612180-tpV1.indd 2 3/11/14 12:57 pm Published by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore 596224 USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE Library of Congress Cataloging-in-Publication Data Marcel Grossmann Meeting on General Relativity (13th : 2012 : Stockholms universitet) The Thirteenth Marcel Grossmann Meeting on Recent Developments in Theoretical and Experimental General Relativity, Astrophysics, and Relativistic Field Theories : proceedings of the MG13 Meeting on General Relativity, Stockholm University, Sweden, 1–7 July 2012 / editors Kjell Rosquist (Stockholm University, Sweden), Robert T. -
Schwarzschild Metric - Wikipedia, the Free Encyclopedia Page 1 of 7
Schwarzschild metric - Wikipedia, the free encyclopedia Page 1 of 7 Schwarzschild metric From Wikipedia, the free encyclopedia In Einstein's theory of general relativity, the Schwarzschild solution General relativity (or the Schwarzschild vacuum ) describes the gravitational field Introduction outside a spherical, uncharged, non-rotating mass such as a (non- Mathematical formulation rotating) star, planet, or black hole. It is also a good approximation to the gravitational field of a slowly rotating body like the Earth or Sun. Resources The cosmological constant is assumed to equal zero. Fundamental concepts According to Birkhoff's theorem, the Schwarzschild solution is the most Special relativity general spherically symmetric, vacuum solution of the Einstein field Equivalence principle equations. A Schwarzschild black hole or static black hole is a black World line · Riemannian hole that has no charge or angular momentum. A Schwarzschild black geometry hole has a Schwarzschild metric, and cannot be distinguished from any other Schwarzschild black hole except by its mass. Phenomena Kepler problem · Lenses · The Schwarzschild black hole is characterized by a surrounding Waves spherical surface, called the event horizon, which is situated at the Frame-dragging · Geodetic Schwarzschild radius, often called the radius of a black hole. Any non- rotating and non-charged mass that is smaller than its Schwarzschild effect radius forms a black hole. The solution of the Einstein field equations is Event horizon · Singularity valid for any mass M, so in principle (according to general relativity Black hole theory) a Schwarzschild black hole of any mass could exist if conditions became sufficiently favorable to allow for its formation. -
Conservative Relativity Principle: Logical Ground and Analysis of Relevant Experiments
Conservative relativity principle: Logical ground and analysis of relevant experiments Alexander Kholmetskii1, Tolga Yarman2, and Oleg Missevitch3 1Department of Physics, Belarus State University, Minsk, Belarus, e-mail: [email protected] 2Okan University, Istanbul, Turkey & Savronik, Eskisehir, Turkey 3Institute for Nuclear Problems, Minsk, Belarus Abstract. We suggest a new relativity principle, which asserts the impossibility to distinguish the state of rest and the state of motion at the constant velocity of a system, if no work is done to the system in question during its motion. We suggest calling this new rule as “conservative rela- tivity principle” (CRP). In the case of an empty space, CRP is reduced to the Einstein special rel- ativity principle. We also show that CRP is compatible with the general relativity principle. One of important implications of CRP is the dependence of the proper time of a charged particle on the electric potential at its location. In the present paper we consider the relevant experimental facts gathered up to now, where the latter effect can be revealed. We show that in atomic physics the introduction of this effect furnishes a better convergence between theory and experiment than that provided by the standard approach. Finally, we reanalyze the Mössbauer experiments in ro- tating systems and show that the obtained recently puzzling deviation of the relative energy shift between emission and absorption lines from the relativistic prediction can be explained by the CRP. 1 Introduction Nowadays, modern physics accepts two relativity principles: the special relativity principle (SRP) asserting that fundamental physical equations do not change (they are form-invariant) un- der transformations between inertial reference frames in an empty space, and the general relativi- ty principle (GRP) stating that fundamental physical equations do not change their form (they are covariant) under transformations between any frames of reference.