DOCSLIB.ORG

On the Lagrangian Theory of Structure Formation in Relativistic Cosmology : Intrinsic Perturbation Approach and Gravitoelectromagnetism Fosca Al Roumi

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
On the Lagrangian Theory of Structure Formation in Relativistic Cosmology : Intrinsic Perturbation Approach and Gravitoelectromagnetism Fosca Al Roumi On the Lagrangian Theory of Structure Formation in Relativistic Cosmology : intrinsic Perturbation Approach and Gravitoelectromagnetism Fosca Al Roumi To cite this version: Fosca Al Roumi. On the Lagrangian Theory of Structure Formation in Relativistic Cosmology : intrinsic Perturbation Approach and Gravitoelectromagnetism. Cosmology and Extra-Galactic As- trophysics [astro-ph.CO]. Université Claude Bernard - Lyon I, 2015. English. NNT : 2015LYO10136. tel-01367703 HAL Id: tel-01367703 https://tel.archives-ouvertes.fr/tel-01367703 Submitted on 16 Sep 2016 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Thèse présentée devant l’Université Claude Bernard Lyon - I École Doctorale de Physique et d’Astrophysique pour l’obtention du DIPLÔME de DOCTORAT Spécialité : Physique Théorique / Cosmologie (arrêté du 7 août 2006) par Fosca Al Roumi Théorie Lagrangienne Relativiste de la Formation des Grandes Structures : Description Intrinsèque des Perturbations et Gravitoélectromagnétisme A soutenir publiquement le 18 Septembre 2015 devant la Commission d’Examen : Prof. P. Salati Président du jury - LAPTH, Annecy le Vieux Prof. B. Roukema Rapporteur et examinateur - Torún Centre for Astronomy, Torún Prof. R. Sussman Rapporteur et examinateur - Instituto de Ciencias Nucleares, México, D. F. Prof. R. Triay Examinateur - CPT, Marseille Prof. R. Walder Examinateur - CRAL, Lyon Prof. T. Buchert Directeur de thèse - CRAL, Lyon PHD THESIS of the UNIVERSITY of LYON Delivered by the UNIVERSITY CLAUDE BERNARD LYON 1 Subject: THEORETICAL PHYSICS / COSMOLOGY submitted by Ms FOSCA AL ROUMI for the degree of DOCTOR OF THEORETICAL PHYSICS On the Lagrangian Theory of Structure Formation in Relativistic Cosmology: Intrinsic Perturbation Approach and Gravitoelectromagnetism To be defended 18 September 2015 in front of the following Examining Committee: Prof. P. Salati President - LAPTH, Annecy le Vieux Prof. B. Roukema Reviewer and examiner - Torún Centre for Astronomy, Torún Prof. R. Sussman Reviewer and examiner - Instituto de Ciencias Nucleares, Mexico City Prof. R. Triay Examiner - CPT, Marseille Prof. R. Walder Examiner - CRAL, Lyon Prof. T. Buchert Supervisor - CRAL, Lyon Acknowlegments / Remerciements First of all I would like to thank my mentor, Thomas Buchert. It will take me many years to realize how lucky I’ve been to work under your direction. Thank you for all your scientific skills, your patience and your rigor. But most of all, thank you for your sense of humor, your creativity and for being so open-minded. I hope I took some of your qualities during these three years. I wish to thank Gilles Chabrier for his fruitful remarks during seminars and for hosting us at CRAL-ENS. My thanks to Herbert Wagner and Martin Kerscher, with whom I worked in Munich on gravitoelectromagnetism. Your help, remarks and advices have been very important for my work on this topic. This student exchange was supported by the French–Bavarian Cooperation Center, BFHZ Munich http://www.bayern-france.org/. Special thanks to Xavier Roy, who helped me a lot throughout the PhD. Thank you for the detailed answers to my questions, for all the explanations on foliation of space-time and differential geometry and for all the useful advices you gave me on the manuscript. Thank you also for all the non-scientific discussions we had. They have been crucial to me. My thanks to Alexander Wiegand for the fruitful discussions, the nice work we did together, for you time and advices. Thanks to Léo Brunswic for all the work we achieved on topology and Hodge decom- position. Your mathematical skills have been really precious for this work. I wish also to thank Alexandre Alles for the help and the useful discussions on the blackboard. My thanks to Boud Roukema for the useful discussions on topology and for his very interesting work on inhomogeneous cosmology. Thank you for your time and help! Thanks to Frank Steiner for sharing his great knowledge on cosmic topology. Martin France, thank you for all the nice discussions we had on the CMB. Thanks to Rolf Walder for the nice remarks and discussions we had during the semi- nars. I would also like to thank Roberto Sussman and Boud Roukema for having accepted to be reviewer of my thesis and spending some of your precious time on reading my thesis and writing a report. I also want to thank Pierre Salati for being the president of my examining committee, for the very interesting discussions we had on the scalar model for dark matter at the beginning of my PhD and at Cargèse last september. Thank you also for all the help gave me in my research career. iii I also want to thank Roland Triay and Rolf Walder for having accepted to be examiner of my thesis. Thanks to Jan Ostrowski for everything: from physics to beers and ping-pong. Thanks also to Pierre Mourier for the scientific discussions and the nice time we had together. Good luck with your PhD! Thanks to Thomas Buchert, Martin France, Boud Roukema, Rolf Walder, Frank Steiner, Léo Brunswick, Jan Ostrowski, Tomek Kazimierczak and Pierre Mourier for the really nice dinners we had together. It is a pleasure to talk about science or something else around a glass of wine! Je voudrais aussi remercier Stephanie Vignier, Sylvie Réa and Sylvie Flores pour avoir rendu tous les aspects administratifs bien plus simples. C’est toujours avec grand plaisir que je suis allée vous poser des questions et vous demander de l’aide. Merci pour votre patience et votre bonne humeur! Vielen Dank an Marie von München. Les quelques jours de rédaction à Munich ont étés un vrai plaisir! Merci à tous mes amis lyonnais, qui m’ont fait passer d’excellents moments pendant ces trois ans! Merci à Julien, Catherine, Martin, Elisa, Tatjana, Camille, Grégoire, Lila, Elsa, Thiago, Mariana, Mirella et Matei. Un grand merci à mes colocs adorés, Matteo et Lucy. Quel bonheur d’avoir partagé avec vous le même toit! Martin, merci aussi pour tous tes conseils sur la rédaction de la thèse! Tatjana, merci de m’avoir acceuillie après cette longue période de rédaction à Milano, la ville qui ne se couche jamais. Julien, merci de m’avoir aidée à certains moments particulièrement délicats! Merci aussi à mes amis parisiens! Julia, Fanny et Victoria, les moments que nous avons passés ensemble et les fous rires que nous avons eus ont grandement participé à mon équilibre mental. Merci aussi à Daniel, Louison, Olivier, Léo. J’espère vous voir plus souvent maintenant. Merci enfin à Mohamad et Amélie pour avoir toujours étés là pour moi. Vous m’avez beaucoup aidée. Merci aussi à mon frère Meyar pour m’avoir prêté son coffret Paradjanov. Constance, il faudrait un chapitre entier pour te remercier. Alors, je préfère le faire de vive voix dans un bon restaurant! Sans ces rencontres et ces échanges, mon travail de thèse n’aurait pas été possible. Je vous remercie donc sincèrement. iv Abstract The dynamics of structure formation in the Universe is usually described by Newto- nian numerical simulations and analytical models in the frame of the Standard Model of Cosmology. The structures are then defined on a homogeneous and isotropic background. Such a description has major drawbacks since, to be self-consistent, it entails a large amount of dark components in the content of the Universe. Different strategies are considered to solve this enigma. Particle physicists have been searching for some exotic sources of the stress-energy tensor to account for these dark components. Nevertheless, no direct evidence of these 26% of dark matter and 69% of dark energy has yet been given. Therefore, some alternative theories to General Relativity are explored. To address the problem of dark matter and dark energy, we will neither suppose that exotic sources contribute to the content of the Universe, nor that General Rela- tivity is obsolete. We will develop a more realistic description of structure formation in the frame of General Relativity and thus no longer assume that the average model is a homogeneous-isotropic solution of the Einstein equations, as claimed by the Standard Model of Cosmology. During my work under the supervision of Thomas Buchert, I contributed to the devel- opment of the perturbative formalism that enables a more realistic description of space- time dynamics. In the framework of the intrinsic Lagrangian approach, which avoids defin- ing physical quantities on a flat background, I contributed to the building of relativistic solutions to the gravitoelectric part of the Einstein equations from the generalization of the Newtonian perturbative solutions. Moreover, the gravitoelectromagnetic approach I worked with has provided a new understanding of the dynamics of the analytical solu- tions to the field equations. Finally, treating globally the spatial manifold, I used powerful mathematical tools and theorems to describe the impact of topology on the dynamics of gravitational waves. v Résumé La dynamique de formation des structures de l’Univers est habituellement décrite dans le cadre du modèle standard de Cosmologie par des simulations numériques newtoniennes et des modèles analytiques. Les structures sont alors associées à des grandeurs définies sur un fond homogène et isotrope. Cependant, pour que les observations cosmologiques soient cohérentes avec le modèle standard, il est nécessaire de supposer l’existance d’une grande proportion d’éléments de nature inconnue dans le contenu de l’Univers. Différentes stratégies sont envisagées pour déterminer la nature de ces éléments.
Load more

Recommended publications
  • Experimental Tests of Quantum Gravity and Exotic Quantum Field Theory Effects
    Advances in High Energy Physics Experimental Tests of Quantum Gravity and Exotic Quantum Field Theory Effects Guest Editors: Emil T. Akhmedov, Stephen Minter, Piero Nicolini, and Douglas Singleton Experimental Tests of Quantum Gravity and Exotic Quantum Field Theory Effects Advances in High Energy Physics Experimental Tests of Quantum Gravity and Exotic Quantum Field Theory Effects Guest Editors: Emil T. Akhmedov, Stephen Minter, Piero Nicolini, and Douglas Singleton Copyright © 2014 Hindawi Publishing Corporation. All rights reserved. This is a special issue published in “Advances in High Energy Physics.” All articles are open access articles distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Editorial Board Botio Betev, Switzerland Ian Jack, UK Neil Spooner, UK Duncan L. Carlsmith, USA Filipe R. Joaquim, Portugal Luca Stanco, Italy Kingman Cheung, Taiwan Piero Nicolini, Germany EliasC.Vagenas,Kuwait Shi-Hai Dong, Mexico Seog H. Oh, USA Nikos Varelas, USA Edmond C. Dukes, USA Sandip Pakvasa, USA Kadayam S. Viswanathan, Canada Amir H. Fatollahi, Iran Anastasios Petkou, Greece Yau W. Wah, USA Frank Filthaut, The Netherlands Alexey A. Petrov, USA Moran Wang, China Joseph Formaggio, USA Frederik Scholtz, South Africa Gongnan Xie, China Chao-Qiang Geng, Taiwan George Siopsis, USA Hong-Jian He, China Terry Sloan, UK Contents Experimental Tests of Quantum Gravity and Exotic Quantum Field Theory Effects,EmilT.Akhmedov,
    [Show full text]
  • What Is Gravity and How Is Embedded in Mater Particles Giving Them Mass (Not the Higgs Field)? Stefan Mehedinteanu
    What Is Gravity and How Is Embedded in Mater Particles giving them mass (not the Higgs field)? Stefan Mehedinteanu To cite this version: Stefan Mehedinteanu. What Is Gravity and How Is Embedded in Mater Particles giving them mass (not the Higgs field)?. 2017. hal-01316929v6 HAL Id: hal-01316929 https://hal.archives-ouvertes.fr/hal-01316929v6 Preprint submitted on 23 Feb 2017 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Distributed under a Creative Commons Attribution| 4.0 International License What Is Gravity (Graviton) and How Is Embedded in Mater Particles Giving Them Mass (Not the Higgs Field)? Stefan Mehedinteanu1 1 (retired) Senior Researcher CITON-Romania; E-Mail: [email protected]; [email protected] “When Einstein was asked bout the discovery of new particles, the answer it was: firstly to clarify what is with the electron!” Abstract It will be shown how the Micro-black-holes particles produced at the horizon entry into a number of N 106162 by quantum fluctuation as virtual micro-black holes pairs like e+ e- creation, stay at the base of: the origin and evolution of Universe, the Black Holes (BH) nuclei of galaxies, of the free photons creation of near mass-less as by radiation decay that condensate later at Confinement in to the structure of gauge bosons (gluons) .
    [Show full text]
  • Non-Abelian Gravitoelectromagnetism and Applications at Finite Temperature
    Hindawi Advances in High Energy Physics Volume 2020, Article ID 5193692, 8 pages https://doi.org/10.1155/2020/5193692 Research Article Non-Abelian Gravitoelectromagnetism and Applications at Finite Temperature A. F. Santos ,1 J. Ramos,2 and Faqir C. Khanna3 1Instituto de Física, Universidade Federal de Mato Grosso, 78060-900, Cuiabá, Mato Grosso, Brazil 2Faculty of Science, Burman University, Lacombe, Alberta, Canada T4L 2E5 3Department of Physics and Astronomy, University of Victoria, BC, Canada V8P 5C2 Correspondence should be addressed to A. F. Santos; alesandroferreira@fisica.ufmt.br Received 22 January 2020; Revised 9 March 2020; Accepted 18 March 2020; Published 3 April 2020 Academic Editor: Michele Arzano Copyright © 2020 A. F. Santos et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP3. Studies about a formal analogy between the gravitational and the electromagnetic fields lead to the notion of Gravitoelectromagnetism (GEM) to describe gravitation. In fact, the GEM equations correspond to the weak-field approximation of the gravitation field. Here, a non-abelian extension of the GEM theory is considered. Using the Thermo Field Dynamics (TFD) formalism to introduce temperature effects, some interesting physical phenomena are investigated. The non-abelian GEM Stefan- Boltzmann law and the Casimir effect at zero and finite temperatures for this non-abelian field are calculated. 1. Introduction between equations for the Newton and Coulomb laws and the interest has increased with the discovery of the The Standard Model (SM) is a non-abelian gauge theory with Lense-Thirring effect, where a rotating mass generates a symmetry group Uð1Þ × SUð2Þ × SUð3Þ.
    [Show full text]
  • Extended Gravitoelectromagnetism
    sid.inpe.br/mtc-m21c/2020/12.21.15.21-RPQ EXTENDED GRAVITOELECTROMAGNETISM. III. MERCURY’S PERIHELION PRECESSION Gerson Otto Ludwig URL do documento original: <http://urlib.net/8JMKD3MGP3W34R/43QQMGL> INPE São José dos Campos 2020 PUBLICADO POR: Instituto Nacional de Pesquisas Espaciais - INPE Coordenação de Ensino, Pesquisa e Extensão (COEPE) Divisão de Biblioteca (DIBIB) CEP 12.227-010 São José dos Campos - SP - Brasil Tel.:(012) 3208-6923/7348 E-mail: [email protected] CONSELHO DE EDITORAÇÃO E PRESERVAÇÃO DA PRODUÇÃO INTELECTUAL DO INPE - CEPPII (PORTARIA No 176/2018/SEI- INPE): Presidente: Dra. Marley Cavalcante de Lima Moscati - Divisão de Modelagem Numérica do Sistema Terrestre (DIMNT) Membros: Dra. Carina Barros Mello - Coordenação de Pesquisa Aplicada e Desenvolvimento Tecnológico (COPDT) Dr. Alisson Dal Lago - Divisão de Heliofísica, Ciências Planetárias e Aeronomia (DIHPA) Dr. Evandro Albiach Branco - Divisão de Impactos, Adaptação e Vulnerabilidades (DIIAV) Dr. Evandro Marconi Rocco - Divisão de Mecânica Espacial e Controle (DIMEC) Dr. Hermann Johann Heinrich Kux - Divisão de Observação da Terra e Geoinfor- mática (DIOTG) Dra. Ieda Del Arco Sanches - Divisão de Pós-Graduação - (DIPGR) Silvia Castro Marcelino - Divisão de Biblioteca (DIBIB) BIBLIOTECA DIGITAL: Dr. Gerald Jean Francis Banon Clayton Martins Pereira - Divisão de Biblioteca (DIBIB) REVISÃO E NORMALIZAÇÃO DOCUMENTÁRIA: Simone Angélica Del Ducca Barbedo - Divisão de Biblioteca (DIBIB) André Luis Dias Fernandes - Divisão de Biblioteca (DIBIB) EDITORAÇÃO ELETRÔNICA: Ivone Martins - Divisão de Biblioteca (DIBIB) Cauê Silva Fróes - Divisão de Biblioteca (DIBIB) sid.inpe.br/mtc-m21c/2020/12.21.15.21-RPQ EXTENDED GRAVITOELECTROMAGNETISM. III. MERCURY’S PERIHELION PRECESSION Gerson Otto Ludwig URL do documento original: <http://urlib.net/8JMKD3MGP3W34R/43QQMGL> INPE São José dos Campos 2020 Esta obra foi licenciada sob uma Licença Creative Commons Atribuição-NãoComercial 3.0 Não Adaptada.
    [Show full text]
  • Gravitoelectromagnetism, Solar System Tests, and Weak-Field Solutions in F (T, B) Gravity with Observational Constraints
    universe Article Gravitoelectromagnetism, Solar System Tests, and Weak-Field Solutions in f (T, B) Gravity with Observational Constraints Gabriel Farrugia 1,2,*, Jackson Levi Said 1,2 and Andrew Finch 2 1 Institute of Space Sciences and Astronomy, University of Malta, Msida MSD 2080, Malta; [email protected] 2 Department of Physics, University of Malta, Msida MSD 2080, Malta; andrew.fi[email protected] * Correspondence: [email protected] Received: 14 December 2019; Accepted: 14 February 2020; Published: 18 February 2020 Abstract: Gravitomagnetism characterizes phenomena in the weak-field limit within the context of rotating systems. These are mainly manifested in the geodetic and Lense-Thirring effects. The geodetic effect describes the precession of the spin of a gyroscope in orbit about a massive static central object, while the Lense-Thirring effect expresses the analogous effect for the precession of the orbit about a rotating source. In this work, we explore these effects in the framework of Teleparallel Gravity and investigate how these effects may impact recent and future missions. We find that teleparallel theories of gravity may have an important impact on these effects which may constrain potential models within these theories. Keywords: gravitoelectromagnetism; geodetic; Lense-Thirring; teleparallel; f (T, B) gravity 1. Introduction General relativity (GR) has passed numerous observational tests since its inception just over a century ago, confirming its predictive power. The detection of gravitational waves in 2015 [1] agreed with the strong field predictions of GR, as does its solar system behavior [2]. However, GR requires a large portion of dark matter to explain the dynamics of galaxies [3,4] and even greater contributions from dark energy to produce current observations of cosmology [5].
    [Show full text]
  • Fundamental Geometrodynamic Justification of Gravitomagnetism
    Issue 2 (October) PROGRESS IN PHYSICS Volume 16 (2020) Fundamental Geometrodynamic Justification of Gravitomagnetism (I) G. G. Nyambuya National University of Science and Technology, Faculty of Applied Sciences – Department of Applied Physics, Fundamental Theoretical and Astrophysics Group, P.O. Box 939, Ascot, Bulawayo, Republic of Zimbabwe. E-mail: [email protected] At a most fundamental level, gravitomagnetism is generally assumed to emerge from the General Theory of Relativity (GTR) as a first order approximation and not as an exact physical phenomenon. This is despite the fact that one can justify its existence from the Law of Conservation of Mass-Energy-Momentum in much the same manner one can justify Maxwell’s Theory of Electrodynamics. The major reason for this is that in the widely accepted GTR, Einstein cast gravitation as a geometric phenomenon to be understood from the vantage point of the dynamics of the metric of spacetime. In the literature, nowhere has it been demonstrated that one can harness the Maxwell Equa- tions applicable to the case of gravitation – i.e. equations that describe the gravitational phenomenon as having a magnetic-like component just as happens in Maxwellian Elec- trodynamics. Herein, we show that – under certain acceptable conditions where Weyl’s conformal scalar [1] is assumed to be a new kind of pseudo-scalar and the metric of spacetime is decomposed as gµν = AµAν so that it is a direct product of the components of a four-vector Aµ – gravitomagnetism can be given an exact description from within Weyl’s beautiful but supposedly failed geometry. My work always tried to unite the Truth with the Beautiful, consistent mathematical framework that has a direct corre- but when I had to choose one or the other, I usually chose the spondence with physical and natural reality as we know it.
    [Show full text]
  • Quantum Wave Mechanics 3Rd Ed
    Geometrical description of photons, electrons and composite particles. Dimensional analysis of electrical charge. Quantum gravity, gravitational frequency spectrum, mass oscillator synchronization, spectral energy density modulation and phase conjugation. Origin of charge, fine structure constant and inertia. Prospects for wave-based EM propulsion. Quantum Wave Mechanics by Larry Reed Order the complete book from the publisher Booklocker.com https://www.booklocker.com/p/books/10176.html?s=pdf or from your favorite neighborhood or online bookstore. To my parents who never knew the result of their great experiment Copyright © 2019, 2020 by Larry J. Reed All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, recording or otherwise, without the prior written permission of the author. Printed on acid-free paper. Library of Congress Control Number: 2018901065 ISBN: 978-1-63492-964-6 paperback To order additional copies of this book, contact: www.booklocker.com CONTENTS Preface ........................................................................................................................... ix SECTION 1 – LIGHT 1. Photon model ................................................................................................................. 1 2. Quantum vacuum ......................................................................................................... 13 3. Electromagnetic 4-Potential .......................................................................................
    [Show full text]
  • About Gravitomagnetism
    About Gravitomagnetism Behrooz Malekolkalami∗ and Mehrdad Farhoudi† Department of Physics, Shahid Beheshti University, G. C., Evin, Tehran 19839, Iran September 2, 2008 Abstract The gravitomagnetic field is the force exerted by a moving body on the basis of the intriguing interplay between geometry and dynamics which is the analog to the magnetic field of a moving charged body in electromagnetism. The existence of such a field has been demonstrated based on special relativity approach and also by special relativity plus the gravitational time dilation for two different cases, a moving infinite line and a uniformly moving point mass, respectively. We treat these two approaches when the applied cases are switched while appropriate key points are employed. Thus, we demonstrate that the strength of the resulted gravitomagnetic field in the latter approach is twice the former. Then, we also discuss the full linearized general relativity and show that it should give the same strength for gravitomagnetic field as the latter approach. Hence, through an exact analogy with the elec- trodynamic equations, we present an argument in order to indicate the best definition amongst those considered in this issue in the literature. Finally, we investigate the gravitomagnetic effects and consequences of different definitions on the geodesic equation including the second order approximation terms. arXiv:gr-qc/0610095v2 13 Nov 2009 PACS number: 03.30. + p ; 04.20. q − Keywords: Gravitomagnetism; Special Relativity; Linearized General Relativity. 1 Introduction The analogous idea of the electric theory and the Newtonian gravita- tional theory inspiring a Maxwell–type gravitational theory is dated back to the second half of the nineteenth century [1]–[4].
    [Show full text]
  • Calculation of the Gravitoelectromagnetism Force for Cylindrically Symmetric Spacetime
    U.P.B. Sci. Bull., Series A, Vol. 76, Iss. 3, 2014 ISSN 1223-7027 CALCULATION OF THE GRAVITOELECTROMAGNETISM FORCE FOR CYLINDRICALLY SYMMETRIC SPACETIME Morteza Yavari1 Keywords: Threading formalism, cylindrically symmetric spacetime, gravito- electromagnetism force Using 1+3 splitting concepts of a spacetime, we first discuss the gravito- electromagnetism force in terms of the gravitoelectric and gravitomagnetic fields. By applying the Hamilton-Jacobi method, the trajectory of a moving test particle in the cylindrically symmetric spacetime is calculated. Finally, the gravitoelectro- magnetism force and the corresponding potential function are determined. 1. Introduction As is well known [1], theory of general relativity discussed the motion of Mercury perihelion in terms of a relativistic gravitoelectric field correction to the Newtonian gravitational potential of the Sun. Also it contains a gravitomagnetic field due to proper rotation of the Sun and this field influence on planetary orbits, [2-4]. The gravitomagnetic field is much smaller than the gravitoelectric one. Theory of gravitoelectromagnetism1 that assumes a perfect isomorphism between gravitation and electromagnetism has been established by Heaviside [6] and Jefimenko, [7]. In the same way that a magnetic field is created when a charged object rotates, a gravitomagnetic field is created when a massive body rotates and this effect is too small. The gravitomagnetic field plays an important role in some astrophysical scenarios such as neutron stars [8-10] and rotating black holes. To detect this field, it is necessary to examine a very massive object or build an instrument that is very sensitive. The gravitomagnetic field of Earth can be measured by studying the motion of satellites LAGEOS2, [11,12].
    [Show full text]
  • Lorentz-Violating Gravitoelectromagnetism
    Physics & Astronomy - Prescott College of Arts & Sciences 9-13-2010 Lorentz-Violating Gravitoelectromagnetism Quentin G. Bailey Embry-Riddle Aeronautical University, [email protected] Follow this and additional works at: https://commons.erau.edu/pr-physics Part of the Elementary Particles and Fields and String Theory Commons Scholarly Commons Citation Bailey, Q. G. (2010). Lorentz-Violating Gravitoelectromagnetism. Physical Review D, 82(6). https://doi.org/ 10.1103/PhysRevD.82.065012 © 2010 American Physical Society. This article is also available from the publisher at https://doi.org/ 10.1103/ PhysRevD.82.065012 This Article is brought to you for free and open access by the College of Arts & Sciences at Scholarly Commons. It has been accepted for inclusion in Physics & Astronomy - Prescott by an authorized administrator of Scholarly Commons. For more information, please contact [email protected]. PHYSICAL REVIEW D 82, 065012 (2010) Lorentz-violating gravitoelectromagnetism Quentin G. Bailey* Physics Department, Embry-Riddle Aeronautical University, 3700 Willow Creek Road, Prescott, Arizona 86301, USA (Received 16 May 2010; published 13 September 2010) The well-known analogy between a special limit of general relativity and electromagnetism is explored in the context of the Lorentz-violating standard-model extension. An analogy is developed for the minimal standard-model extension that connects a limit of the CPT-even component of the electromagnetic sector to the gravitational sector. We show that components of the post-Newtonian metric can be directly obtained from solutions to the electromagnetic sector. The method is illustrated with specific examples including static and rotating sources. Some unconventional effects that arise for Lorentz-violating electrostatics and magnetostatics have an analog in Lorentz-violating post-Newtonian gravity.
    [Show full text]
  • Gravitoelectromagnetism.Pdf
    GRAVITOELECTROMAGNETISM BAHRAM MASHHOON Department of Physics and Astronomy University of Missouri-Columbia Columbia, Missouri 65211, USA E-mail: [email protected] Gravitoelectromagnetism is briefly reviewed and some recent developments in this topic are discussed. The stress-energy content of the gravitoelectromagnetic field is described from different standpoints. In particular, the gravitational Poynting flux is analyzed and it is shown that there exists a steady flow of gravitational energy circulating around a rotating mass. 1 Introduction Gravitoelectromagnetism (GEM) is based upon the close formal analogy be- tween Newton’s law of gravitation and Coulomb’s law of electricity. The New- tonian theory of gravitation may thus be interpreted in terms of a gravito- electric field. Any field theory that would bring Newtonian gravitation and Lorentz invariance together in a consistent framework would necessarily con- tain a gravitomagnetic field as well. In general relativity, the non-Newtonian gravitomagentic field is due to mass current and has interesting physical prop- erties that are now becoming amenable to experimental observation. Developments in electrodynamics in the second half of the nineteenth cen- tury led Holzm¨uller [1] and Tisserand [2] to postulate a gravitomagnetic com- ponent for the gravitational influence of the Sun on the motion of planets. The magnitude of this ad hoc component could be adjusted so as to account for the excess perihelion motion of Mercury. However, Einstein’s general relativ- arXiv:gr-qc/0011014v1 3 Nov 2000 ity successfully accounted for the perihelion precession of Mercury by means of a post-Newtonian correction to the gravitoelectric influence of the Sun. The general relativistic effect of the rotation of the Sun on planetary orbits was first calculated by de Sitter [3] and later more generally by Thirring and Lense [4].
    [Show full text]
  • A Gravito-Electromagnetic Analogy Based on Tidal Tensors
    A gravito-electromagnetic analogy based on tidal tensors L. Filipe Costa and Carlos A. R. Herdeiro ∗ Departamento de F´ısica e Centro de F´ısica do Porto Faculdade de Ciˆencias da Universidade do Porto Rua do Campo Alegre, 687, 4169-007 Porto, Portugal May 2007 Abstract We propose a new approach to a physical analogy between General Relativity and Electro- magnetism, based on tidal tensors of both theories. Using this approach we write a covariant form for the gravitational analogues of the Maxwell equations. The following realisations of the analogy are given. The first one matches linearised gravitational tidal tensors to exact electromagnetic tidal tensors in Minkwoski spacetime. The second one matches exact mag- netic gravitational tidal tensors for ultra-stationary metrics to exact magnetic tidal tensors of electromagnetism in curved spaces. In the third we show that our approach leads to two-step exact derivation of the Papapetrou force on a gyroscope. We then establish a new proof for a class of tensor identities that define invariants of the type E~ 2 B~ 2 and E~ B~ , and we exhibit − · the invariants built from tidal tensors in both gravity and electromagnetism. We contrast our approach with the two gravito-electromagnetic analogies commonly found in the literature, and argue that it sheds light on the debate about the limit of validity of one of the analogies, and clarifies issues concerning the physical interpretation of the other. arXiv:gr-qc/0612140v2 21 May 2007 ∗ Email addresses: fi[email protected], [email protected] 1 Contents 1 Introduction 2 1.1 The need for a new, physically transparent approach .
    [Show full text]