Special Issue "Rotation Effects in Relativity"

A special issue of Universe (ISSN 2218-1997).

Deadline for manuscript submissions: closed (15 December 2019).

Special Issue Editor

Dr. Matteo Luca Ruggiero
Website
Guest Editor
Department of Applied Science and Technology, Politecnico di Torino, 10129 Torino, Italy
Interests: rotation effects in relativity; gravitomagnetic effects in general relativity; rotating observers in special relativity; gravitational theories with torsion (Einstein–Cartan theory); relativistic theories of gravity and experimental tests; gravitational waves; relativistic positioning systems
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Special Issue Information

Dear Colleagues,

Rotation and circular motion have always played a peculiar role in the development of scientific thought. While in the context of Aristotelian physics, circular motion was thought of as perfect and incorruptible, and the whole universe was represented as an ensemble of concentric rotating spheres, the peculiarity of rotation was recognized on experimental grounds, and not only as a philosophical speculation, at the beginning of the modern scientific era. In fact, in the framework of Newtonian physics, Foucault's pendulum provided spectacular evidence of the absolute character of rotation. Subsequently, in the context of the theory of relativity, the absolute character of rotation was emphasized by the Sagnac effect, which also stimulated a long and interesting debate on the foundations of relativity. Further peculiarities are shown by the solutions of Einstein's equations for the gravitational field of a rotating source: Lense and Thirring proved a fascinating similarity between the gravitational field of a distribution of mass and the electromagnetic field of a distribution of charge. Just like charge currents produce a magnetic field, mass currents produce a field that, by analogy, is called a gravito-magnetic field; the latter has an important role in the debate on the origin of inertia, according to the general relativistic interpretation of Mach's ideas. Even if it does not appear to be viable due to observational constraints, the Gödel model of a rotating universe is important for the implications on closed time-like curves, causality and the meaning of time. Eventually, rotating solutions are very important in astrophysics and, in particular, in the study of black holes.

Rotation effects in relativity are indeed quite ubiquitous: they are important not only from a theoretical viewpoint, but it is worth mentioning that they have an impact on everyday life, since it is well known that the global positioning system would not have the same accuracy if it neglected the relativistic effects due to the rotation of the Earth. 

This Special Issue will focus on what we know about rotation effects in relativity and, more in general, on relativistic theories of gravity, one hundred years after the birth of Einstein's theory. We encourage contributions that encompass fundamental issues, theoretical problems and experimental proposals, both on a purely classical background and at the interface between classical and quantum physics. As a result, we do expect to provide a useful reference for those who, now and in the future, have an interest in this field.

Dr. Matteo Luca Ruggiero
Guest Editor

Manuscript Submission Information

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Keywords

  • rotation in relativity
  • rotation in alternative theories of gravity
  • rotating observers
  • rotating reference frames
  • rotating sources
  • spinning particles
  • spin
  • torsion
  • gravitomagnetism
  • rotating solutions
  • measurements in space–time

Published Papers (19 papers)

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Editorial

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Open AccessEditorial
Rotation Effects in Relativity
Universe 2020, 6(12), 224; https://doi.org/10.3390/universe6120224 - 27 Nov 2020
Abstract
Rotation has always been a central thread in physics and has influenced its development [...] Full article
(This article belongs to the Special Issue Rotation Effects in Relativity)

Research

Jump to: Editorial, Review

Open AccessArticle
Generalised Uncertainty Relations for Angular Momentum and Spin in Quantum Geometry
Universe 2020, 6(4), 56; https://doi.org/10.3390/universe6040056 - 19 Apr 2020
Cited by 5
Abstract
We derive generalised uncertainty relations (GURs) for orbital angular momentum and spin in the recently proposed smeared-space model of quantum geometry. The model implements a minimum length and a minimum linear momentum and recovers both the generalised uncertainty principle (GUP) and extended uncertainty [...] Read more.
We derive generalised uncertainty relations (GURs) for orbital angular momentum and spin in the recently proposed smeared-space model of quantum geometry. The model implements a minimum length and a minimum linear momentum and recovers both the generalised uncertainty principle (GUP) and extended uncertainty principle (EUP), previously proposed in the quantum gravity literature, within a single formalism. In this paper, we investigate the consequences of these results for particles with extrinsic and intrinsic angular momentum and obtain generalisations of the canonical so ( 3 ) and su ( 2 ) algebras. We find that, although SO ( 3 ) symmetry is preserved on three-dimensional slices of an enlarged phase space, corresponding to a superposition of background geometries, individual subcomponents of the generalised generators obey nontrivial subalgebras. These give rise to GURs for orbital angular momentum while leaving the canonical commutation relations intact except for a simple rescaling, ħ ħ + β . The value of the new parameter, β ħ × 10 61 , is determined by the ratio of the dark energy density to the Planck density, and its existence is required by the presence of both minimum length and momentum uncertainties. Here, we assume the former to be of the order of the Planck length and the latter to be of the order of the de Sitter momentum ħ Λ , where Λ is the cosmological constant, which is consistent with the existence of a finite cosmological horizon. In the smeared-space model, ħ and β are interpreted as the quantisation scales for matter and geometry, respectively, and a quantum state vector is associated with the spatial background. We show that this also gives rise to a rescaled Lie algebra for generalised spin operators, together with associated subalgebras that are analogous to those for orbital angular momentum. Remarkably, consistency of the algebraic structure requires the quantum state associated with a flat background to be fermionic, with spin eigenvalues ± β / 2 . Finally, the modified spin algebra leads to GURs for spin measurements. The potential implications of these results for cosmology and high-energy physics, and for the description of spin and angular momentum in relativistic theories of quantum gravity, including dark energy, are briefly discussed. Full article
(This article belongs to the Special Issue Rotation Effects in Relativity)
Open AccessArticle
Gravitoelectromagnetism, Solar System Tests, and Weak-Field Solutions in f (T,B) Gravity with Observational Constraints
Universe 2020, 6(2), 34; https://doi.org/10.3390/universe6020034 - 18 Feb 2020
Cited by 11
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, [...] Read more.
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. Full article
(This article belongs to the Special Issue Rotation Effects in Relativity)
Open AccessFeature PaperArticle
Influence of Cosmic Repulsion and Magnetic Fields on Accretion Disks Rotating around Kerr Black Holes
Universe 2020, 6(2), 26; https://doi.org/10.3390/universe6020026 - 29 Jan 2020
Cited by 25
Abstract
We present a review of the influence of cosmic repulsion and external magnetic fields on accretion disks rotating around rotating black holes and on jets associated with these rotating configurations. We consider both geometrically thin and thick disks. We show that the vacuum [...] Read more.
We present a review of the influence of cosmic repulsion and external magnetic fields on accretion disks rotating around rotating black holes and on jets associated with these rotating configurations. We consider both geometrically thin and thick disks. We show that the vacuum energy represented by the relic cosmological constant strongly limits extension of the accretion disks that is for supermassive black holes comparable to extension of largest galaxies, and supports collimation of jets at large distances from the black hole. We further demonstrate that an external magnetic field crucially influences the fate of ionized Keplerian disks causing creation of winds and jets, enabling simultaneously acceleration of ultra-high energy particles with energy up to 10 21 eV around supermassive black holes with M 10 10 M surrounded by sufficiently strong magnetic field with B 10 4 G. We also show that the external magnetic fields enable existence of “levitating” off-equatorial clouds or tori, along with the standard equatorial toroidal structures, if these carry a non-vanishing, appropriately distributed electric charge. Full article
(This article belongs to the Special Issue Rotation Effects in Relativity)
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Open AccessArticle
Electrodynamics and Radiation from Rotating Neutron Star Magnetospheres
Universe 2020, 6(1), 15; https://doi.org/10.3390/universe6010015 - 15 Jan 2020
Cited by 3
Abstract
Neutron stars are compact objects rotating at high speed, up to a substantial fraction of the speed of light (up to 20% for millisecond pulsars) and possessing ultra-strong electromagnetic fields (close to and sometimes above the quantum critical field of 4.4 ×10 [...] Read more.
Neutron stars are compact objects rotating at high speed, up to a substantial fraction of the speed of light (up to 20% for millisecond pulsars) and possessing ultra-strong electromagnetic fields (close to and sometimes above the quantum critical field of 4.4 × 10 9 T ). Moreover, due to copious e ± pair creation within the magnetosphere, the relativistic plasma surrounding the star is forced into corotation up to the light cylinder where the corotation speed reaches the speed of light. The neutron star electromagnetic activity is powered by its rotation which becomes relativistic in the neighborhood of this light cylinder. These objects naturally induce relativistic rotation on macroscopic scales about several thousands of kilometers, a crucial ingredient to trigger the central engine as observed on Earth. In this paper, we elucidate some of the salient features of this corotating plasma subject to efficient particle acceleration and radiation, emphasizing several problems and limitations concerning current theories of neutron star magnetospheres. Relativistic rotation in these systems is indirectly probed by the radiation produced within the magnetosphere. Depending on the underlying assumptions about particle motion and radiation mechanisms, different signatures on their light curves, spectra, pulse profiles and polarization angles are expected in their broadband electromagnetic emission. We show that these measurements put stringent constraints on the way to describe particle electrodynamics in a rotating neutron star magnetosphere. Full article
(This article belongs to the Special Issue Rotation Effects in Relativity)
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Open AccessArticle
Simultaneity and Precise Time in Rotation
Universe 2019, 5(12), 226; https://doi.org/10.3390/universe5120226 - 16 Dec 2019
Cited by 3
Abstract
I analyse the role of simultaneity in relativistic rotation by building incrementally on its role in simpler scenarios. Historically, rotation has been analysed in 1+1 dimensions; but my stance is that a 2+1-dimensional treatment is necessary. This treatment [...] Read more.
I analyse the role of simultaneity in relativistic rotation by building incrementally on its role in simpler scenarios. Historically, rotation has been analysed in 1 + 1 dimensions; but my stance is that a 2 + 1 -dimensional treatment is necessary. This treatment requires a discussion of what constitutes a frame, how coordinate choices differ from frame choices, and how poor coordinates can be misleading. I determine how precisely we are able to define a meaningful time coordinate on a gravity-free rotating Earth, and discuss complications due to gravity on our real Earth. I end with a critique of several statements made in relativistic precision-timing literature, that I maintain contradict the tenets of relativity. Those statements tend to be made in the context of satellite-based navigation; but they are independent of that technology, and hence are not validated by its success. I suggest that if relativistic precision-timing adheres to such analyses, our civilian timing is likely to suffer in the near future as clocks become ever more precise. Full article
(This article belongs to the Special Issue Rotation Effects in Relativity)
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Open AccessArticle
Monitoring Jovian Orbital Resonances of a Spacecraft: Classical and Relativistic Effects
Universe 2019, 5(12), 222; https://doi.org/10.3390/universe5120222 - 03 Dec 2019
Cited by 1
Abstract
Orbital resonances continue to be one of the most difficult problems in celestial mechanics. They have been studied in connection with the so-called Kirkwood gaps in the asteroid belt for many years. On the other hand, resonant trans-Neptunian objects are also an active [...] Read more.
Orbital resonances continue to be one of the most difficult problems in celestial mechanics. They have been studied in connection with the so-called Kirkwood gaps in the asteroid belt for many years. On the other hand, resonant trans-Neptunian objects are also an active area of research in Solar System dynamics, as are the recently discovered resonances in extrasolar planetary systems. A careful monitoring of the trajectories of these objects is hindered by the small size of asteroids or the large distances of the trans-Neptunian bodies. In this paper, we propose a mission concept, called CHRONOS (after the greek god of time), in which a spacecraft could be sent to with the initial condition of resonance with Jupiter in order to study the future evolution of its trajectory. We show that radio monitoring of these trajectories could allow for a better understanding of the initial stages of the evolution of resonant trajectories and the associated relativistic effects. Full article
(This article belongs to the Special Issue Rotation Effects in Relativity)
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Open AccessArticle
Dynamics of Electromagnetic Fields and Structure of Regular Rotating Electrically Charged Black Holes and Solitons in Nonlinear Electrodynamics Minimally Coupled to Gravity
Universe 2019, 5(10), 205; https://doi.org/10.3390/universe5100205 - 27 Sep 2019
Cited by 6
Abstract
We study the dynamics of electromagnetic fields of regular rotating electrically charged black holes and solitons replacing naked singularities in nonlinear electrodynamics minimally coupled to gravity (NED-GR). They are related by electromagnetic and gravitational interactions and described by the axially symmetric NED-GR solutions [...] Read more.
We study the dynamics of electromagnetic fields of regular rotating electrically charged black holes and solitons replacing naked singularities in nonlinear electrodynamics minimally coupled to gravity (NED-GR). They are related by electromagnetic and gravitational interactions and described by the axially symmetric NED-GR solutions asymptotically Kerr-Newman for a distant observer. Geometry is described by the metrics of the Kerr-Schild class specified by T t t = T r r ( p r = ρ ) in the co-rotating frame. All regular axially symmetric solutions obtained from spherical solutions with the Newman-Janis algorithm belong to this class. The basic generic feature of all regular objects of this class, both electrically charged and electrically neutral, is the existence of two kinds of de Sitter vacuum interiors. We analyze the regular solutions to dynamical equations for electromagnetic fields and show which kind of a regular interior is favored by electromagnetic dynamics for NED-GR objects. Full article
(This article belongs to the Special Issue Rotation Effects in Relativity)
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Open AccessArticle
Nonlocal Gravitomagnetism
Universe 2019, 5(9), 195; https://doi.org/10.3390/universe5090195 - 05 Sep 2019
Cited by 7
Abstract
We briefly review the current status of nonlocal gravity (NLG), which is a classical nonlocal generalization of Einstein’s theory of gravitation based on a certain analogy with the nonlocal electrodynamics of media. Nonlocal gravity thus involves integro-differential field equations and a causal constitutive [...] Read more.
We briefly review the current status of nonlocal gravity (NLG), which is a classical nonlocal generalization of Einstein’s theory of gravitation based on a certain analogy with the nonlocal electrodynamics of media. Nonlocal gravity thus involves integro-differential field equations and a causal constitutive kernel that should ultimately be determined from observational data. We consider the stationary gravitational field of an isolated rotating astronomical source in the linear approximation of nonlocal gravity. In this weak-field and slow-motion approximation of NLG, we describe the gravitomagnetic field associated with the rotating source and compare our results with gravitoelectromagnetism (GEM) of the standard general relativity theory. Moreover, we briefly study the energy-momentum content of the GEM field in nonlocal gravity. Full article
(This article belongs to the Special Issue Rotation Effects in Relativity)
Open AccessArticle
Kerr Black Holes within a Modified Theory of Gravity
Universe 2019, 5(9), 191; https://doi.org/10.3390/universe5090191 - 28 Aug 2019
Cited by 4
Abstract
The Kerr black hole is studied within a modified theory of gravity, which adds the effects of vacuum fluctuations near a black hole. These vacuum fluctuations are treated as a dark energy. A parameter is introduced to account for these fluctuations. It is [...] Read more.
The Kerr black hole is studied within a modified theory of gravity, which adds the effects of vacuum fluctuations near a black hole. These vacuum fluctuations are treated as a dark energy. A parameter is introduced to account for these fluctuations. It is zero for the standard theory and acquires a maximal value, just before there would be no event horizon. The existence of an event horizon not only depends on the value of this parameter, but also on the spin of the black hole. In addition, we study the existence of a light-ring. We also elaborate on the relation of the appearance and vanishing of the event horizon and light-ring to phase transitions. Full article
(This article belongs to the Special Issue Rotation Effects in Relativity)
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Open AccessArticle
Rotation Sensing Lasers in General Relativity: Some Technical Notes and Current Advances
Universe 2019, 5(9), 190; https://doi.org/10.3390/universe5090190 - 21 Aug 2019
Cited by 1
Abstract
We review the current status of large ring laser gyroscopes having the potential to contribute to terrestrial measurements of general relativistic precessions. At this point in time, although these devices possess the raw sensitivity for such a measurement, they remain limited by long-term [...] Read more.
We review the current status of large ring laser gyroscopes having the potential to contribute to terrestrial measurements of general relativistic precessions. At this point in time, although these devices possess the raw sensitivity for such a measurement, they remain limited by long-term geometric instability, detection noise and imperfections in the physical models required to isolate geophysical effects. Furthermore, minute non-reciprocal biases provide a null-shift error and therefore no currently constructed laser system meets the requirement of absolute rotation rate sensing. Nevertheless, we are of the view that these are surmountable problems and the ability of ring laser gyroscopes to measure low frequency to DC signals has vastly increased in the last decade. Full article
(This article belongs to the Special Issue Rotation Effects in Relativity)
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Open AccessArticle
A Theory of Inertia Based on Mach’s Principle
Universe 2019, 5(8), 188; https://doi.org/10.3390/universe5080188 - 16 Aug 2019
Cited by 1
Abstract
A non-relativistic theory of inertia based on Mach’s principle is presented as has been envisaged, but not achieved, by Ernst Mach in 1872. The central feature is a space-dependent, anisotropic, symmetric inert mass tensor. The contribution of a mass element dm to [...] Read more.
A non-relativistic theory of inertia based on Mach’s principle is presented as has been envisaged, but not achieved, by Ernst Mach in 1872. The central feature is a space-dependent, anisotropic, symmetric inert mass tensor. The contribution of a mass element d m to the inertia of a particle m 0 experiencing an acceleration from rest is proportional to cos 2 α , where α is the angle between the line connecting m 0 and d m and the direction of the acceleration. Apsidal precession for planets circling around a central star is not a consequence of this theory, thereby avoiding the prediction of an apsidal precession with the wrong sign as is done by Mach-like theories with isotropic inert mass. Full article
(This article belongs to the Special Issue Rotation Effects in Relativity)
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Open AccessEditor’s ChoiceArticle
A HERO for General Relativity
Universe 2019, 5(7), 165; https://doi.org/10.3390/universe5070165 - 05 Jul 2019
Cited by 2
Abstract
HERO (Highly Eccentric Relativity Orbiter) is a space-based mission concept aimed to perform several tests of post-Newtonian gravity around the Earth with a preferably drag-free spacecraft moving along a highly elliptical path fixed in its plane undergoing a relatively fast secular precession. We [...] Read more.
HERO (Highly Eccentric Relativity Orbiter) is a space-based mission concept aimed to perform several tests of post-Newtonian gravity around the Earth with a preferably drag-free spacecraft moving along a highly elliptical path fixed in its plane undergoing a relatively fast secular precession. We considered two possible scenarios—a fast, 4-h orbit with high perigee height of 1047 km and a slow, 21-h path with a low perigee height of 642 km . HERO may detect, for the first time, the post-Newtonian orbital effects induced by the mass quadrupole moment J 2 of the Earth which, among other things, affects the semimajor axis a via a secular trend of ≃4–12 cm yr 1 , depending on the orbital configuration. Recently, the secular decay of the semimajor axis of the passive satellite LARES was measured with an error as little as 0 . 7 cm yr 1 . Also the post-Newtonian spin dipole (Lense-Thirring) and mass monopole (Schwarzschild) effects could be tested to a high accuracy depending on the level of compensation of the non-gravitational perturbations, not treated here. Moreover, the large eccentricity of the orbit would allow one to constrain several long-range modified models of gravity and accurately measure the gravitational red-shift as well. Each of the six Keplerian orbital elements could be individually monitored to extract the G J 2 / c 2 signature, or they could be suitably combined in order to disentangle the post-Newtonian effect(s) of interest from the competing mismodeled Newtonian secular precessions induced by the zonal harmonic multipoles J of the geopotential. In the latter case, the systematic uncertainty due to the current formal errors σ J of a recent global Earth’s gravity field model are better than 1 % for all the post-Newtonian effects considered, with a peak of 10 7 for the Schwarzschild-like shifts. Instead, the gravitomagnetic spin octupole precessions are too small to be detectable. Full article
(This article belongs to the Special Issue Rotation Effects in Relativity)
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Open AccessArticle
Gravitational Radiation, Vorticity And Super–Energy: A Conspicuous Threesome
Universe 2019, 5(7), 164; https://doi.org/10.3390/universe5070164 - 04 Jul 2019
Cited by 1
Abstract
We elaborate on the link relating gravitational radiation, vorticity and a flux of super–energy on the plane orthogonal to the vorticity vector. We examine the vorticity appearing in the congruence of observers at the outside of the source, as well as the vorticity [...] Read more.
We elaborate on the link relating gravitational radiation, vorticity and a flux of super–energy on the plane orthogonal to the vorticity vector. We examine the vorticity appearing in the congruence of observers at the outside of the source, as well as the vorticity of the fluid distribution, the source of the gravitational radiation is made of. The information provided by the study of the physical aspects of the source poses new questions which could, in principle, be solved by the observational evidence. Besides the study of the theoretical issues associated to such relationship, we also stress the new observational possibilities to detect gravitational radiation, appearing as consequence of the above mentioned link. The high degree of development achieved in the gyroscope technology, as well as recent proposals to detect rotations by means of ring lasers, atom interferometers, atom lasers and anomalous spin–precession experiments, lead us to believe that an alternative to the laser interferometers used so far to detect gravitational waves, may be implemented based on the detection of the vorticity associated with gravitational radiation. Additionally, this kind of detectors might be able to elucidate the open question about the physical properties of the tail of the waves appearing as the consequence of the violation of the Huygens’s principle in general relativity. Full article
(This article belongs to the Special Issue Rotation Effects in Relativity)
Open AccessArticle
Gravitational Qubits
Universe 2019, 5(5), 123; https://doi.org/10.3390/universe5050123 - 21 May 2019
Cited by 2
Abstract
We report on the behavior of two-level quantum systems, or qubits, in the background of rotating and non-rotating metrics and provide a method to derive the related spin currents and motions. The calculations are performed in the external field approximation. Full article
(This article belongs to the Special Issue Rotation Effects in Relativity)

Review

Jump to: Editorial, Research

Open AccessFeature PaperEditor’s ChoiceReview
Measuring Electromagnetic Fields in Rotating Frames of Reference
Universe 2020, 6(2), 31; https://doi.org/10.3390/universe6020031 - 11 Feb 2020
Cited by 2
Abstract
We review the problem of transforming electromagnetic fields between inertial and rotating reference frames. We compare the method of straightforward tensor coordinate transformations adopted by Schiff in his well-known paper of 1939 with the method of Orthogonal Tetrads (OT) that was applied to [...] Read more.
We review the problem of transforming electromagnetic fields between inertial and rotating reference frames. We compare the method of straightforward tensor coordinate transformations adopted by Schiff in his well-known paper of 1939 with the method of Orthogonal Tetrads (OT) that was applied to this problem in 1964 by Irvine. Although both methods are mathematically rigorous, the transformed fields have different forms depending on the method adopted. We emphasize that the OT method is expected to predict the fields that would actually be measured by an observer in a rotating frame of reference. We briefly discuss existing experimental evidence that supports the OT approach, but point out that there appears to be little awareness in the physics community of this problem or its resolution. We use both methods to transform the electrostatic and magnetic fields generated by rotating charged spherical shells from an inertial into a co-rotating system. We also briefly describe how such an arrangement of shells could be used to measure rotation relative to the fixed stars. Full article
(This article belongs to the Special Issue Rotation Effects in Relativity)
Open AccessFeature PaperReview
Rotating Disc around a Schwarzschild Black Hole
Universe 2020, 6(2), 27; https://doi.org/10.3390/universe6020027 - 03 Feb 2020
Cited by 1
Abstract
A stationary and axisymmetric (in fact circular) metric is reviewed which describes the first-order perturbation of a Schwarzschild black-hole space-time due to a rotating finite thin disc encircling the hole symmetrically. The key Green functions of the problem (corresponding to an infinitesimally thin [...] Read more.
A stationary and axisymmetric (in fact circular) metric is reviewed which describes the first-order perturbation of a Schwarzschild black-hole space-time due to a rotating finite thin disc encircling the hole symmetrically. The key Green functions of the problem (corresponding to an infinitesimally thin ring)—the one for the gravitational potential and the one for the dragging angular velocity—were already derived, in terms of infinite series, by Will in 1974, but we have now put them into closed forms using elliptic integrals. Such forms are more practical for numerical evaluation and for integration in problems involving extended sources. This last point mostly remains difficult, but we illustrate that it may be workable by using the simple case of a finite thin disc with constant Newtonian surface density. Full article
(This article belongs to the Special Issue Rotation Effects in Relativity)
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Open AccessReview
Rotation and Spin and Position Operators in Relativistic Gravity and Quantum Electrodynamics
Universe 2020, 6(2), 24; https://doi.org/10.3390/universe6020024 - 26 Jan 2020
Cited by 1
Abstract
First, we examine how spin is treated in special relativity and the necessity of introducing spin supplementary conditions (SSC) and how they are related to the choice of a center-of-mass of a spinning particle. Next, we discuss quantum electrodynamics and the Foldy–Wouthuysen transformation [...] Read more.
First, we examine how spin is treated in special relativity and the necessity of introducing spin supplementary conditions (SSC) and how they are related to the choice of a center-of-mass of a spinning particle. Next, we discuss quantum electrodynamics and the Foldy–Wouthuysen transformation which we note is a position operator identical to the Pryce–Newton–Wigner position operator. The classical version of the operators are shown to be essential for the treatment of classical relativistic particles in general relativity, of special interest being the case of binary systems (black holes/neutron stars) which emit gravitational radiation. Full article
(This article belongs to the Special Issue Rotation Effects in Relativity)
Open AccessFeature PaperReview
In the Quest for Cosmic Rotation
Universe 2020, 6(1), 14; https://doi.org/10.3390/universe6010014 - 15 Jan 2020
Cited by 2
Abstract
This paper analyzes the problem of global rotation in general relativity (GR) theory. Simple cosmological models with rotation and expansion are presented, which give a natural explanation of the modern values of the acceleration parameter at different red shifts without involving the concepts [...] Read more.
This paper analyzes the problem of global rotation in general relativity (GR) theory. Simple cosmological models with rotation and expansion are presented, which give a natural explanation of the modern values of the acceleration parameter at different red shifts without involving the concepts of “dark energy” and “dark matter”. It is shown that due to the smallness of the cosmological rotation, for its detection one should use observations that do not depend on the magnitude of the angular velocity of the Universe. Such tests include the effects of the cosmic mirror and the cosmic lens. For the first time on the basis of modern electronic catalogs the search on the celestial sphere of images of our Galaxy and other galaxies is made. Viable candidates for both effects have been found. Full article
(This article belongs to the Special Issue Rotation Effects in Relativity)
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