Gravitoelectromagnetism : the Lense-Thirring Effect

Total Page:16

File Type:pdf, Size:1020Kb

Gravitoelectromagnetism : the Lense-Thirring Effect Gravitoelectromagnetism : The Lense-Thirring Effect Vasco Miguel Roldão Manteigas Extended abstract written to Obtain the Master of Science Degree in Physics Engineering Instituto Superior Técnico - Department of Physics Abstract General Relativity is the major theorical framework that explaind many gravitational phenomena in our Universe, and several experiments was planed and executed to verify the main prediction of this theory. One of lastest tests involve the measure of the Lense-Thirring effect, predicted by GR and explained naturally with a special theorical framework which use a formal analogy of electrodynamics. Using the so called GEM (Gravitoelectromagnetism) framework, it's possible ao ease the derivation and calculation of Lense-Thirring effect. Using the lastest data from Gravity Probe B, so far, the theorical prediction in GR/GEM agrees the experimental data obtained from this probe. Keywords: Gravitoelectromagnetism, Gravity Probe B, Lense-Thirring Effect. 1.Introduction: In this little introductory paper will introduce 4 h00=− the basic mathematical formulation of c2 (1) Gravitoelectromagnetism (GEM) Model, And the new gravitomagnetic potential as: which is a formal analogy of 2 A h =− i (2) Electromagnetism when applied to the 0i c2 Linearized Solution of General Relativity, as described by Mashhoon [1]. It is easy to compute explicitily the GEM potencials in terms of primary mass (M) and GEM framework is usefull to explain the their angular momentum (J). If we admit a geodesic effects recently observed by Gravity round primary (like a star or a planet), then the Probe B [2], using a nice analogy of an analog newtonian potential will value: of magnetic field around a curly source. G M =− (3) The inertial rotating source in primary will R produce a so-called gravitomagnetic force, and And the gravitomagnetic potential is just the any sattelite around the primary should be effect of angular momentum of the primary: G [L×r ] affected by this field, which acordly by RG is A= (4) R3 c no more than the non-diagonal terms of metric. Applying the equations (3) and (4) on Linear Taking the linear approximation of RG field Einstein Field Equations [3], we can derive a equations [3], we can define a newtonian gravitoelectric field (rougly a small correction potential as: of newtonian force): 1 ∂ A Returning to the RG formalism, this Larmor E =−∇ − (5) 2c ∂t precession is due to the torsion of local metric And the gravitomagnetic field: due to angular momentum of the primary [1]. 1 B = ∇ ×A (6) Any orbit around the primary will show a tiny 2 variation of the keplerian parameters, and the rate of precession can be calculated using the With this two fields (5,6) we can evaluate RG, and the re-interpreted using the GEM their own version of Maxwell's Equations of terms. GEM model: ∇⋅E=−4 G (7) Using the correct approuch, the derivation of 1 ∂ B ∇ ×E =− (8) geodesic effects of local metric are based by a c ∂t propriety in RG [5] that it called the Fermi- ∇⋅B =0 (9) Walker paralell transport, which constrains the 1 ∂ E 4 G ∇ ×B= − J (10) conservation laws of physics to the geodesic c ∂t c path of the particles in the local manifold ruled by RG. We can also dedrive the Lorentz Force of Since the gravity filed in RG is equal to a free GEM from the geodesic equation from RG: particle in a curved spacetime, then we can v F =m E 2m ×B (11) c assume the angular momentum of the satellite around the primary is a constant of motion: i 2. Derivation and Explanation of the S S =Si S =const. (12) Geodesic Effect and Lense-Thirring Effect And the covariant derivative of the angular The Geodesic Effects observed in RG can be momentum will obey the following evaluation: understond in our GEM model as an simple D S D u =u S (13) concept from the Classic Electrodynamics, the d s d s Larmor Frequency derived in many physics Which he angular momentum depends of the fields such the plasma physics. [4] velocity and position of the satellite. From the Lorentz Force (11), we can split the movement of a satellite around the primary, Taking explicity the (13) according to the with a tangential component which is the usual local metric, we obtain an equation of motion keplerian orbit, and a new axial origin vector similar to the gyroscope [5]: derived from the gravitomagnetic force which d S⃗ =Ω⃗˙ ×S⃗ (14) will cause a Larmor-type precession of the d s keplerian orbit. Where the derivative of the Larmor-type frequency of the (14) is equal to: This means that it's possible to derive a ˙ 1 d ⃗v 1 theorical evalution that should be agree if the Ω⃗ =− ⃗v× +⃗v×∇ ϕ− (∇×A⃗ ) (15) 2 d t 2 c RG is correct at the GEM model approximation. By splitting (15) into three terms, we obtain the Thomas Precession (due to kinematics), the For a low orbit satelitte, the average value of De Sitter or geodesic precession and the geodesic precession (De Sitter) would be: Lense-Thirring precession. [5] 3/ 2 3(G M ) 9 R 2 〈Ω 〉= 1− J (19) G 2c2 r 5/ 2 [ 8 2( r ) ] Since the Thomas Precession is irrelevant in And the Lense-Thirring precession would be: many non-relativistic bound systems (inertial 2π G M R2 219 R 2 〈Ω 〉= 1− J (20) frames, for example), the other two factors of LT 5c2 r 3T [ 392 2( r ) ] (15) can be simplified in our toy model: Let's assume the source's primary Taking the numerical orbital values of GP-B gravitational filed have a spherical symmetry [2] into (19,20), we get: with some multi-polar expantion corrections. 〈ΩG〉=6,606arc/ yr (21) The multi-polar expantion is needed to some 〈ΩLT 〉=39,2marc / yr (22) precision tests like the Graviy Probe B [2], We talk the experimental results after later in since it's orbit is a low altitude type, and the next setion, to introduce first the GP-B setup. quadrupolar terms of gravitiational field 3. The Gravity Probe B Setup and Brief cannot be ignored. Experimental Results Taking this constraints seriously, the De Sitter Precession rate of a low-orbit satelitte will be: The Gravity Probe B experiment can be ⃗ 3G 3 3 ΩG= M− I (⃗r ×⃗v)+ ( I ⃗r ×⃗v) (16) traced back to early 1960 when two Ph.D. in 2r 3 [( r 2 ) r 2 ] Physics publish a paper, “Possible New And the Lense-Thirring Precession will be: Experimental Test of General Relativity” in ⃗ 2G I 3 ΩLT = (−ω⃗ + (ω⃗⋅⃗r )⃗r ) (17) “Physical Review Letters”, which propose the r 3 r 2 use of a gyroscope in space to measure the geodesic effects predicted by RG. The “I” term in (16) and (17) is the inertial The project gain momentum when it's momentum of the primary. Ignoring oblate sponsered by NASA in the transition form factors of the curvate of the Earth, the inertial 1960's to 1970's, specially in the brand new momentum of a sphere is: space technology and better high precision 2 2 I = M r (18) 5 manufacturing technics. The main prototype of GP-B was designed in 1984, which consists a highlly round sphere Bibliography (to reduce oblatness), a telescope, a helium cooling device and the measurements [1] Bahram Mashhoon : arXiv:gr- hardware support. qc/0011014v1, 3/11/2000, To avoid complications in harmonics analysis, “Gravitoelectromagnetism”. the gyro's sphere should be perfectly smooth (and the final sphere was a oblatness less that [2] “Gravity Probe B in a nutshell”, “The 40 nm in 10 cm of sphere radius!), and this Gravity Probe B Experiment” : Stanford achivement was awarded by the Guiness Book University, Lockhead Martin, NASA official of Records! [2] presentation. The satellite telescope are used to maintain the satellite aligned to a distant star, whose [3] Sean M.Carrol , “Lecture Notes on General relative movement in celestial sphere can be Relativity”. ignored without jeopardize the measurements. (This means the distant star is an “perfect” [4] John David Jackson, “Classical inertial frame in the short period of the GP-B Electrodynamics”, 1962, John Wiley & Sons, mission when collects data.) Inc. After several years of internal development, [5] Ignazio Ciufolini, David Lucchesi, the GP-B was finally launched in 2004, and Francesco Vespe, Federico Chieppa : arXiv:gr- the main mission occured between 2005 and qc/9704065v1, 23/4/1997, “Detection of 2007, however the data analisys will take Lense-Thirring Effect Due to Earth's Spin”. several years to account. In 2012 [6], the experimental results of [6] C. W. F. Everitt, D. B. DeBra, B. W. geodesic effect and frame-dragging was Parkinson et all: arXiv:1105.3456v1 [gr-qc], publish by NASA, and the values are: 17/5/2011, “Gravity Probe B: Final Results of 〈ΩG〉exp=6,6018±0,0183arc/ yr (23) a Space Experiment to Test General 〈ΩLT 〉exp=37,2±7,2marc/ yr (24) Relativity” This means the first high precison test of RG show that the gravity is a space-time metric effect, and the results appart of statistical flutuations, are consistent with the prediction of RG..
Recommended publications
  • Toy Models for Black Hole Evaporation
    UCSBTH-92-36 hep-th/9209113 Toy Models for Black Hole Evaporation∗ Steven B. Giddings† Department of Physics University of California Santa Barbara, CA 93106-9530 Abstract These notes first present a brief summary of the puzzle of information loss to black holes, of its proposed resolutions, and of the flaws in the proposed resolutions. There follows a review of recent attempts to attack this problem, and other issues in black hole physics, using two-dimensional dilaton gravity theories as toy models. These toy models contain collapsing black holes and have for the first time enabled an explicit semiclassical treatment of the backreaction of the Hawking radiation on the geometry of an evaporating black hole. However, a complete answer to the information conundrum seems to require physics beyond the semiclassical approximation. Preliminary attempts to make progress arXiv:hep-th/9209113v2 11 Nov 1992 in this direction, using connections to conformal field theory, are described. *To appear in the proceedings of the International Workshop of Theoretical Physics, 6th Session, String Quantum Gravity and Physics at the Planck Energy Scale, 21 – 28 June 1992, Erice, Italy. † Email addresses: [email protected], [email protected]. Since the discovery of black holes, physicists have been faced with the possibility that they engender a breakdown of predictability. At the classical level this breakdown arises at the singularity. Classically we do not know how to evolve past it. Inclusion of quantum effects may serve as a remedy, allowing predictable evolution, by smoothing out the singularities of general relativity. However, as suggested by Hawking [1,2], quantum effects also present another sharp challenge to predictability through the mechanism of Hawking evaporation.
    [Show full text]
  • Quantum Vacuum Energy Density and Unifying Perspectives Between Gravity and Quantum Behaviour of Matter
    Annales de la Fondation Louis de Broglie, Volume 42, numéro 2, 2017 251 Quantum vacuum energy density and unifying perspectives between gravity and quantum behaviour of matter Davide Fiscalettia, Amrit Sorlib aSpaceLife Institute, S. Lorenzo in Campo (PU), Italy corresponding author, email: [email protected] bSpaceLife Institute, S. Lorenzo in Campo (PU), Italy Foundations of Physics Institute, Idrija, Slovenia email: [email protected] ABSTRACT. A model of a three-dimensional quantum vacuum based on Planck energy density as a universal property of a granular space is suggested. This model introduces the possibility to interpret gravity and the quantum behaviour of matter as two different aspects of the same origin. The change of the quantum vacuum energy density can be considered as the fundamental medium which determines a bridge between gravity and the quantum behaviour, leading to new interest- ing perspectives about the problem of unifying gravity with quantum theory. PACS numbers: 04. ; 04.20-q ; 04.50.Kd ; 04.60.-m. Key words: general relativity, three-dimensional space, quantum vac- uum energy density, quantum mechanics, generalized Klein-Gordon equation for the quantum vacuum energy density, generalized Dirac equation for the quantum vacuum energy density. 1 Introduction The standard interpretation of phenomena in gravitational fields is in terms of a fundamentally curved space-time. However, this approach leads to well known problems if one aims to find a unifying picture which takes into account some basic aspects of the quantum theory. For this reason, several authors advocated different ways in order to treat gravitational interaction, in which the space-time manifold can be considered as an emergence of the deepest processes situated at the fundamental level of quantum gravity.
    [Show full text]
  • 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]
  • Spacetime Geometry from Graviton Condensation: a New Perspective on Black Holes
    Spacetime Geometry from Graviton Condensation: A new Perspective on Black Holes Sophia Zielinski née Müller München 2015 Spacetime Geometry from Graviton Condensation: A new Perspective on Black Holes Sophia Zielinski née Müller Dissertation an der Fakultät für Physik der Ludwig–Maximilians–Universität München vorgelegt von Sophia Zielinski geb. Müller aus Stuttgart München, den 18. Dezember 2015 Erstgutachter: Prof. Dr. Stefan Hofmann Zweitgutachter: Prof. Dr. Georgi Dvali Tag der mündlichen Prüfung: 13. April 2016 Contents Zusammenfassung ix Abstract xi Introduction 1 Naturalness problems . .1 The hierarchy problem . .1 The strong CP problem . .2 The cosmological constant problem . .3 Problems of gravity ... .3 ... in the UV . .4 ... in the IR and in general . .5 Outline . .7 I The classical description of spacetime geometry 9 1 The problem of singularities 11 1.1 Singularities in GR vs. other gauge theories . 11 1.2 Defining spacetime singularities . 12 1.3 On the singularity theorems . 13 1.3.1 Energy conditions and the Raychaudhuri equation . 13 1.3.2 Causality conditions . 15 1.3.3 Initial and boundary conditions . 16 1.3.4 Outlining the proof of the Hawking-Penrose theorem . 16 1.3.5 Discussion on the Hawking-Penrose theorem . 17 1.4 Limitations of singularity forecasts . 17 2 Towards a quantum theoretical probing of classical black holes 19 2.1 Defining quantum mechanical singularities . 19 2.1.1 Checking for quantum mechanical singularities in an example spacetime . 21 2.2 Extending the singularity analysis to quantum field theory . 22 2.2.1 Schrödinger representation of quantum field theory . 23 2.2.2 Quantum field probes of black hole singularities .
    [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]
  • Black Holes and Gravitational Waves in Models of Minicharged Dark Matter
    Home Search Collections Journals About Contact us My IOPscience Black holes and gravitational waves in models of minicharged dark matter This content has been downloaded from IOPscience. Please scroll down to see the full text. JCAP05(2016)054 (http://iopscience.iop.org/1475-7516/2016/05/054) View the table of contents for this issue, or go to the journal homepage for more Download details: IP Address: 62.210.105.116 This content was downloaded on 28/06/2016 at 17:13 Please note that terms and conditions apply. ournal of Cosmology and Astroparticle Physics JAn IOP and SISSA journal Black holes and gravitational waves in models of minicharged dark matter JCAP05(2016)054 Vitor Cardoso,a;b Caio F.B. Macedo,a Paolo Pania;c and Valeria Ferraric aCENTRA, Departamento de F´ısica,Instituto Superior T´ecnico| IST, Universidade de Lisboa | UL, Avenida Rovisco Pais 1, 1049 Lisboa, Portugal bPerimeter Institute for Theoretical Physics, 31 Caroline Street North Waterloo, Ontario N2L 2Y5, Canada cDipartimento di Fisica, \Sapienza" Universit`adi Roma and Sezione INFN Roma1, Piazzale A. Moro 5, 00185, Roma, Italy E-mail: [email protected], [email protected], [email protected], [email protected] Received April 29, 2016 Revised May 16, 2016 Accepted May 17, 2016 Published May 23, 2016 Abstract. In viable models of minicharged dark matter, astrophysical black holes might be charged under a hidden U(1) symmetry and are formally described by the same Kerr- Newman solution of Einstein-Maxwell theory. These objects are unique probes of minicharged dark matter and dark photons.
    [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]
  • Asymptotically Flat Boundary Conditions for the U(1)3 Model for Euclidean Quantum Gravity
    universe Article Asymptotically Flat Boundary Conditions for the U(1)3 Model for Euclidean Quantum Gravity Sepideh Bakhoda 1,2,* , Hossein Shojaie 1 and Thomas Thiemann 2,* 1 Department of Physics, Shahid Beheshti University, Tehran 1983969411, Iran; [email protected] 2 Institute for Quantum Gravity, FAU Erlangen—Nürnberg, Staudtstraße 7, 91058 Erlangen, Germany * Correspondence: [email protected] (S.B.); [email protected] (T.T.) 3 Abstract: A generally covariant U(1) gauge theory describing the GN ! 0 limit of Euclidean general relativity is an interesting test laboratory for general relativity, specially because the algebra of the Hamiltonian and diffeomorphism constraints of this limit is isomorphic to the algebra of the corresponding constraints in general relativity. In the present work, we the study boundary conditions and asymptotic symmetries of the U(1)3 model and show that while asymptotic spacetime translations admit well-defined generators, boosts and rotations do not. Comparing with Euclidean general relativity, one finds that the non-Abelian part of the SU(2) Gauss constraint, which is absent in the U(1)3 model, plays a crucial role in obtaining boost and rotation generators. Keywords: asymptotically flat boundary conditions; classical and quantum gravity; U(1)3 model; asymptotic charges Citation: Bakhoda, S.; Shojaie, H.; 1. Introduction Thiemann, T. Asymptotically Flat In the framework of the Ashtekar variables in terms of which General Relativity (GR) Boundary Conditions for the U(1)3 is formulated as a SU(2) gauge theory [1–3], attempts to find an operator corresponding to Model for Euclidean Quantum the Hamiltonian constraint of the Lorentzian vacuum canonical GR led to the result [4] that Gravity.
    [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]