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Frame-Dragging and Gravitomagnetism
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Frame-Dragging and Gravitomagnetism

A special issue of Universe (ISSN 2218-1997). This special issue belongs to the section "Gravitation".

Deadline for manuscript submissions: closed (10 March 2022) | Viewed by 29151

Special Issue Editors

Prof. Dr. Lorenzo Iorio

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Guest Editor
Ministero dell'Istruzione e del Merito, Viale Unità di Italia 68, 70125 Bari, BA, Italy
Interests: general relativity and gravitation; classical general relativity; post-newtonian approximation, perturbation theory, related approximations; gravitational waves; observational cosmology; mathematical and relativistic aspects of cosmology; modified theories of gravity; higher-dimensional gravity and other theories of gravity; experimental studies of gravity; experimental tests of gravitational theories; geodesy and gravity; harmonics of the gravity potential field; geopotential theory and determination; satellite orbits; orbit determination and improvement; astrometry and reference systems; ephemerides, almanacs, and calendars; lunar, planetary, and deep-space probes
Special Issues, Collections and Topics in MDPI journals
Dr. Ashkbiz Danehkar

E-Mail Website
Guest Editor
Department of Astronomy, University of Michigan, 1085 S. University, Ann Arbor, MI 48109, USA
Interests: Supermassive Black Holes (SMBH); Galaxy Evolution; Active Galactic Nuclei (AGN); Relativistic Jets; Ultra Fast Outflows in AGN; Accretion Disks around SMBHs; Black Hole Spin Measurements; Gravitational Physics; General Relativity and Gravitation; Experimental Tests of General Relativity; Linearized Gravity; Observational Cosmology; Extragalactic Observations; Nebular Astrophysics; X-ray Astronomy; Optical and UV Observations; Integral Field Spectroscopy; Emission Line Kinematic Analysis; Astrophysical Plasma Diagnostics; Chemical Abundance Analysis of Emission Lines; Computational Astrophysics; Photoionization Modeling of Astrophysical Plasmas; Hydrodynamic Simulations of Astrophysical Fluid Dynamics; Theoretical Plasma Physics

Special Issue Information

Dear Colleagues,

Gravitomagnetism and frame-dragging, in addition to gravitational waves, have been initially predicted by using the linear perturbation approach to the general theory of relativity. The wave solution in general relativity first appeared in the weak field approximation to Einstein’s field equations in 1916. In particular, the application of the weak-field limit to a rotating massive object by Lense and Thirring in 1918 pointed to a frame-dragging effect, so called the Lense-Thirring precession. Moreover, Thirring obtained Maxwell-like equations for gravity in the weak-field approach, suggesting the presence of magnetic-type fields in gravity, so later called gravitomagnetism by Thorne in 1980s.

Our understanding of gravitomagnetism has been further deepened by the 1960s development of the 1+3 covariant approach to general relativity, where the Newtonian tidal gravity is prescribed by the electric part of the Weyl curvature, so called the gravitoelectric field. We notice that the magnetic part of the Weyl tensor offers an additional field, the gravitomagnetic field, associated with the non-local nature of gravity that is generated by the angular momentum of a rotating massive body. The 1+3 decomposition of the Bianchi identities in terms of the electric and magnetic components of the Weyl tensor provided some dynamical constraints for the gravitoelectric and gravitomagnetic fields, which are analogous to Maxwell’s equations in electromagnetism. Both the gravitoelectric and gravitomagnetic fields were found to have a fundamental role in supporting long-range gravitational waves in empty space.

Moreover, it has been demonstrated by Cohen and other people in the framework of the parameterized post-Newtonian approximation that the gravitomagnetic field of a rotating massive body can influence the proper time of a clock in a test particle orbiting around, so called the gravitomagnetic clock effect. It follows that the clock of equatorial particles prograding are slower than the clock of equatorial particles retrograding the rotation direction of the spinning massive body. This effect implies that the local time of the artificial satellites around the Earth should be slightly different because of the gravitomagnetic perturbation generated by the rotation of the Earth. Similarly, we expect that a spinning black hole affects the local time of prograding and retrograding particles in equatorial orbits around its event horizon, so the gravitomagnetic clock effect should be observable on electromagnetic radiations passing nearby spinning black holes as surrounding twisted light spectra.

Several space-based experiments aiming at detecting frame-dragging effects around the Earth, including Gravity Probe B and LAGEOS, and other scenarios in our Solar system (Sun and Mercury, probes around Mars, Juno at Jupiter) have been proposed and conducted so far. Although the gravitomagnetic field around the Earth is extremely weak and very difficult to be detected, the gravitomagnetic field of a spinning massive compact object such as a black hole is predicted to be very large near its event horizon. The gravitomagnetic field and frame-dragging effects are expected to be observable in quasars and active galactic nuclei, where spinning supermassive black holes are resident. Contemporaneity high energy X-ray observations revealed the presence of compact relativistic outflows launched near supermassive black holes, which could be related to less understood physics of gravitomagnetism. In 1971, Penrose theorized the extraction of rotational energy from a rotating black hole in the Kerr spacetime that yields the first theoretical explanation for relativistic jets nearby black holes based on the general-relativistic non-Newtonian field generated by rotating black holes. While the presence of gravitational waves have been confirmed through the recent LIGO and Virgo detection in 2016, experimental and observational tests of gravitomagnetism and frame-dragging will definitely validate the general theory of relativity, and it will help us understand better the quantum nature of gravity.

The main aim of this Special issue is to review the recent developments in theatrical studies of frame-dragging and gravitomagnetism in the general theory of relativity, as well as observational evidence for the gravitomagnetic field in astrophysics and cosmology.

Some relevant references:

1. Iorio et al., Astrophysics and Space Science, Volume 331, Issue 2, pp.351-395, 2011
2. Renzetti, Central European Journal of Physics, Volume 11, Issue 5, pp.531-544, 2013
3. Will, Living Reviews in Relativity, Volume 17, No. 4, 2014
4. Tamburini et al. Nature Physics, Volume 7, Issue 3, pp. 195-197, 2011
5. Ciufolini & Wheeler, Gravitation and Inertia, Princeton University Press, 1995
6. Thorne ‎et al., Black Holes: The Membrane Paradigm, Yale University Press, 1986
7. Lämmerzahl et al. Gyros, Clocks, Interferometers...: Testing Relativistic Gravity in Space, Springer Science, 2001

Prof. Dr. Lorenzo Iorio
Dr. Ashkbiz Danehkar
Guest Editors

Manuscript Submission Information

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Keywords

  • Gravitational physics
  • Gravitomagnetism
  • General relativity
  • Gravitomagnetic clock effect
  • Frame-dragging effects
  • Lense-Thirring precession
  • Penrose process
  • Physics of rotating black holes
  • Experimental tests of general relativity
  • Gravitational waves

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Published Papers (10 papers)

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Research

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15 pages, 390 KiB  
Article
Gravitating Electron Based on Overrotating Kerr-Newman Solution
by Alexander Burinskii
Universe 2022, 8(11), 553; https://doi.org/10.3390/universe8110553 - 25 Oct 2022
Cited by 3 | Viewed by 1478
Abstract
We consider a consistent with gravity electron based on the overrotating Kerr-Newman (KH) solution and show that the earlier KH electron models proposed by Carter, Israel and López in 1970–1990 should be modified by the Landau-Ginzburg theory, leading to a superconducting electron model [...] Read more.
We consider a consistent with gravity electron based on the overrotating Kerr-Newman (KH) solution and show that the earlier KH electron models proposed by Carter, Israel and López in 1970–1990 should be modified by the Landau-Ginzburg theory, leading to a superconducting electron model consistent with gravity and quantum theory. Truncated by Israel and López, the second sheet of the KN solution is rearranged and represented in a mirror form as a sheet of the positron, so that the modified KN system forms a quantum electron-positron vacuum interacting with gravity. Regularization of the KN black hole solution creates two new important effects leading to a strong gravitational interaction that acts on the Compton scale contrary to the usual Planck scale of Schwarzschild gravity: (A)—gravitational frame-dragging creates two Wilson loops acting at two boundaries of the modified KN solution, and (B)—formation of the flat superconducting core of the regularized KN solution creates a superconducting electron-positron vacuum state. The Landau-Ginzburg model shows that Wilson loops determine phases of two Higgs fields forming superconducting vacuum state of the modified KN solution, quantum vacuum of the electron-positron pairs. The phases of these Higgs fields correspond to two light-like modes of a classical relativistic ring string. We come to the conclusion that the electron models considered by Israel and López are not complete and must be supplemented by a mirror structure that forms a quantum system consistent with QED. Full article
(This article belongs to the Special Issue Frame-Dragging and Gravitomagnetism)
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7 pages, 448 KiB  
Article
Frame-Dragging in Extrasolar Circumbinary Planetary Systems
by Lorenzo Iorio
Universe 2022, 8(10), 546; https://doi.org/10.3390/universe8100546 - 21 Oct 2022
Cited by 5 | Viewed by 1556
Abstract
Extrasolar circumbinary planets are so called because they orbit two stars instead of just one; to date, an increasing number of such planets have been discovered with a variety of techniques. If the orbital frequency of the hosting stellar pair is much higher [...] Read more.
Extrasolar circumbinary planets are so called because they orbit two stars instead of just one; to date, an increasing number of such planets have been discovered with a variety of techniques. If the orbital frequency of the hosting stellar pair is much higher than the planetary one, the tight stellar binary can be considered as a matter ring current generating its own post-Newtonian stationary gravitomagnetic field through its orbital angular momentum. It affects the orbital motion of a relatively distant planet with Lense-Thirring-type precessional effects which, under certain circumstances, may amount to a significant fraction of the static, gravitoelectric ones, analogous to the well known Einstein perihelion precession of Mercury, depending only on the masses of the system’s bodies. Instead, when the gravitomagnetic field is due solely to the spin of each of the central star(s), the Lense-Thirring shifts are several orders of magnitude smaller than the gravitoelectric ones. In view of the growing interest in the scientific community about the detection of general relativistic effects in exoplanets, the perspectives of finding new scenarios for testing such a further manifestation of general relativity might be deemed worth of further investigations. Full article
(This article belongs to the Special Issue Frame-Dragging and Gravitomagnetism)
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11 pages, 288 KiB  
Communication
A Note on the Gravitoelectromagnetic Analogy
by Matteo Luca Ruggiero
Universe 2021, 7(11), 451; https://doi.org/10.3390/universe7110451 - 19 Nov 2021
Cited by 20 | Viewed by 2325
Abstract
We discuss the linear gravitoelectromagnetic approach used to solve Einstein’s equations in the weak-field and slow-motion approximation, which is a powerful tool to explain, by analogy with electromagnetism, several gravitational effects in the solar system, where the approximation holds true. In particular, we [...] Read more.
We discuss the linear gravitoelectromagnetic approach used to solve Einstein’s equations in the weak-field and slow-motion approximation, which is a powerful tool to explain, by analogy with electromagnetism, several gravitational effects in the solar system, where the approximation holds true. In particular, we discuss the analogy, according to which Einstein’s equations can be written as Maxwell-like equations, and focus on the definition of the gravitoelectromagnetic fields in non-stationary conditions. Furthermore, we examine to what extent, starting from a given solution of Einstein’s equations, gravitoelectromagnetic fields can be used to describe the motion of test particles using a Lorentz-like force equation. Full article
(This article belongs to the Special Issue Frame-Dragging and Gravitomagnetism)
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35 pages, 2688 KiB  
Article
Penrose Process: Its Variants and Astrophysical Applications
by Zdeněk Stuchlík, Martin Kološ and Arman Tursunov
Universe 2021, 7(11), 416; https://doi.org/10.3390/universe7110416 - 31 Oct 2021
Cited by 41 | Viewed by 4266
Abstract
We present a review of the Penrose process and its modifications in relation to the Kerr black holes and naked singularities (superspinars). We introduce the standard variant of this process, its magnetic version connected with magnetized Kerr black holes or naked singularities, the [...] Read more.
We present a review of the Penrose process and its modifications in relation to the Kerr black holes and naked singularities (superspinars). We introduce the standard variant of this process, its magnetic version connected with magnetized Kerr black holes or naked singularities, the electric variant related to electrically charged Schwarzschild black holes, and the radiative Penrose process connected with charged particles radiating in the ergosphere of magnetized Kerr black holes or naked singularities. We discuss the astrophysical implications of the variants of the Penrose process, concentrating attention to the extreme regime of the magnetic Penrose process leading to extremely large acceleration of charged particles up to ultra-high energy E∼1022 eV around magnetized supermassive black holes with mass M∼1010M⊙ and magnetic intensity B∼104 G. Similarly high energies can be obtained by the electric Penrose process. The extraordinary case is represented by the radiative Penrose process that can occur only around magnetized Kerr spacetimes but just inside their ergosphere, in contrast to the magnetic Penrose process that can occur in a more extended effective ergosphere determined by the intensity of the electromagnetic interaction. The explanation is simple, as the radiative Penrose process is closely related to radiated photons with negative energy whose existence is limited just to the ergosphere. Full article
(This article belongs to the Special Issue Frame-Dragging and Gravitomagnetism)
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27 pages, 2361 KiB  
Article
Frame-Dragging: Meaning, Myths, and Misconceptions
by L. Filipe. O. Costa and José Natário
Universe 2021, 7(10), 388; https://doi.org/10.3390/universe7100388 - 18 Oct 2021
Cited by 16 | Viewed by 4085
Abstract
Originally introduced in connection with general relativistic Coriolis forces, the term frame-dragging is associated today with a plethora of effects related to the off-diagonal element of the metric tensor. It is also frequently the subject of misconceptions leading to incorrect predictions, even of [...] Read more.
Originally introduced in connection with general relativistic Coriolis forces, the term frame-dragging is associated today with a plethora of effects related to the off-diagonal element of the metric tensor. It is also frequently the subject of misconceptions leading to incorrect predictions, even of nonexistent effects. We show that there are three different levels of frame-dragging corresponding to three distinct gravitomagnetic objects: gravitomagnetic potential 1-form, field, and tidal tensor, whose effects are independent, and sometimes opposing. It is seen that, from the two analogies commonly employed, the analogy with magnetism holds strong where it applies, whereas the fluid-dragging analogy (albeit of some use, qualitatively, in the first level) is, in general, misleading. Common misconceptions (such as viscous-type “body-dragging”) are debunked. Applications considered include rotating cylinders (Lewis–Weyl metrics), Kerr, Kerr–Newman and Kerr–dS spacetimes, black holes surrounded by disks/rings, and binary systems. Full article
(This article belongs to the Special Issue Frame-Dragging and Gravitomagnetism)
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33 pages, 1083 KiB  
Article
The CMB, Preferred Reference System, and Dragging of Light in the Earth Frame
by Maurizio Consoli and Alessandro Pluchino
Universe 2021, 7(8), 311; https://doi.org/10.3390/universe7080311 - 23 Aug 2021
Cited by 7 | Viewed by 2477
Abstract
The dominant CMB dipole anisotropy is a Doppler effect due to a particular motion of the solar system with a velocity of 370 km/s. Since this derives from peculiar motions and local inhomogeneities, one could meaningfully consider a fundamental frame of rest Σ [...] Read more.
The dominant CMB dipole anisotropy is a Doppler effect due to a particular motion of the solar system with a velocity of 370 km/s. Since this derives from peculiar motions and local inhomogeneities, one could meaningfully consider a fundamental frame of rest Σ associated with the Universe as a whole. From the group properties of Lorentz transformations, two observers, individually moving within Σ, would still be connected by the relativistic composition rules. However, the ultimate implications could be substantial. Physical interpretation is thus traditionally demanded in order to correlate some of the dragging of light observed in the laboratory with the direct CMB observations. Today, the small residuals—from those of Michelson–Morley to present experiments with optical resonators—are just considered instrumental artifacts. However, if the velocity of light in the interferometers is not the same parameter “c” of Lorentz transformations, nothing would prevent a non-zero dragging. Furthermore, the observable effects would be much smaller than what is classically expected and would most likely be of an irregular nature. We review an alternative reading of experiments that leads to remarkable correlations with the CMB observations. Notably, we explain the irregular 10−15 fractional frequency shift presently measured with optical resonators operating in vacuum and solid dielectrics. For integration times of about 1 s and a typical Central European latitude, we also predict daily variations of the Allan variance in the range (5÷12)·10−16. Full article
(This article belongs to the Special Issue Frame-Dragging and Gravitomagnetism)
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13 pages, 332 KiB  
Article
Gravitoelectromagnetic Knot Fields
by Adina Crişan, Cresus Godinho and Ion Vancea
Universe 2021, 7(3), 46; https://doi.org/10.3390/universe7030046 - 24 Feb 2021
Cited by 1 | Viewed by 1886
Abstract
We construct a class of knot solutions of the time-dependent gravitoelectromagnetic (GEM) equations in vacuum in the linearized gravity approximation by analogy with the Rañada–Hopf fields. For these solutions, the dual metric tensors of the bi-metric geometry of the gravitational vacuum with knot [...] Read more.
We construct a class of knot solutions of the time-dependent gravitoelectromagnetic (GEM) equations in vacuum in the linearized gravity approximation by analogy with the Rañada–Hopf fields. For these solutions, the dual metric tensors of the bi-metric geometry of the gravitational vacuum with knot perturbations are given and the geodesic equation as a function of two complex parameters of the time-dependent GEM knots are calculated. By taking stationary potentials, which formally amount to particularizing to time-independent GEM equations, we obtain a set of stationary fields subjected to constraints from the time-dependent GEM knots. Finally, the Landau–Lifshitz pseudo-tensor and a scalar invariant of the static fields are computed. Full article
(This article belongs to the Special Issue Frame-Dragging and Gravitomagnetism)
18 pages, 312 KiB  
Article
Deconstructing Frame-Dragging
by Luis Herrera
Universe 2021, 7(2), 27; https://doi.org/10.3390/universe7020027 - 27 Jan 2021
Cited by 2 | Viewed by 2419
Abstract
The vorticity of world-lines of observers associated with the rotation of a massive body was reported by Lense and Thirring more than a century ago. In their example, the frame-dragging effect induced by the vorticity is directly (explicitly) related to the rotation of [...] Read more.
The vorticity of world-lines of observers associated with the rotation of a massive body was reported by Lense and Thirring more than a century ago. In their example, the frame-dragging effect induced by the vorticity is directly (explicitly) related to the rotation of the source. However, in many other cases, it is not so, and the origin of vorticity remains obscure and difficult to identify. Accordingly, in order to unravel this issue, and looking for the ultimate origin of vorticity associated to frame-dragging, we analyze in this manuscript very different scenarios where the frame-dragging effect is present. Specifically, we consider general vacuum stationary spacetimes, general electro-vacuum spacetimes, radiating electro-vacuum spacetimes, and Bondi–Sachs radiating spacetimes. We identify the physical quantities present in all these cases, which determine the vorticity and may legitimately be considered as responsible for the frame-dragging. Doing so, we provide a comprehensive, physical picture of frame-dragging. Some observational consequences of our results are discussed. Full article
(This article belongs to the Special Issue Frame-Dragging and Gravitomagnetism)
22 pages, 736 KiB  
Article
A 1% Measurement of the Gravitomagnetic Field of the Earth with Laser-Tracked Satellites
by David Lucchesi, Massimo Visco, Roberto Peron, Massimo Bassan, Giuseppe Pucacco, Carmen Pardini, Luciano Anselmo and Carmelo Magnafico
Universe 2020, 6(9), 139; https://doi.org/10.3390/universe6090139 - 31 Aug 2020
Cited by 18 | Viewed by 3310
Abstract
A new measurement of the gravitomagnetic field of the Earth is presented. The measurement has been obtained through the careful evaluation of the Lense-Thirring (LT) precession on the combined orbits of three passive geodetic satellites, LAGEOS, LAGEOS II, and LARES, tracked by the [...] Read more.
A new measurement of the gravitomagnetic field of the Earth is presented. The measurement has been obtained through the careful evaluation of the Lense-Thirring (LT) precession on the combined orbits of three passive geodetic satellites, LAGEOS, LAGEOS II, and LARES, tracked by the Satellite Laser Ranging (SLR) technique. This general relativity precession, also known as frame-dragging, is a manifestation of spacetime curvature generated by mass-currents, a peculiarity of Einstein’s theory of gravitation. The measurement stands out, compared to previous measurements in the same context, for its precision (≃7.4×10−3, at a 95% confidence level) and accuracy (≃16×10−3), i.e., for a reliable and robust evaluation of the systematic sources of error due to both gravitational and non-gravitational perturbations. To achieve this measurement, we have largely exploited the results of the GRACE (Gravity Recovery And Climate Experiment) mission in order to significantly improve the description of the Earth’s gravitational field, also modeling its dependence on time. In this way, we strongly reduced the systematic errors due to the uncertainty in the knowledge of the Earth even zonal harmonics and, at the same time, avoided a possible bias of the final result and, consequently, of the precision of the measurement, linked to a non-reliable handling of the unmodeled and mismodeled periodic effects. Full article
(This article belongs to the Special Issue Frame-Dragging and Gravitomagnetism)
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Review

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48 pages, 622 KiB  
Review
Covariant Evolution of Gravitoelectromagnetism
by Ashkbiz Danehkar
Universe 2022, 8(6), 318; https://doi.org/10.3390/universe8060318 - 7 Jun 2022
Cited by 2 | Viewed by 2076
Abstract
The long-range gravitational terms associated with tidal forces, frame-dragging effects, and gravitational waves are described by the Weyl conformal tensor, the traceless part of the Riemann curvature that is not locally affected by the matter field. The Ricci and Bianchi identities provide a [...] Read more.
The long-range gravitational terms associated with tidal forces, frame-dragging effects, and gravitational waves are described by the Weyl conformal tensor, the traceless part of the Riemann curvature that is not locally affected by the matter field. The Ricci and Bianchi identities provide a set of dynamical and kinematic equations governing the matter coupling and evolution of the electric and magnetic parts of the Weyl tensor, so-called gravitoelectric and gravitomagnetic fields. A detailed analysis of the Weyl gravitoelectromagnetic fields can be conducted using a number of algebraic and differential identities prescribed by the 1+3 covariant formalism. In this review, we consider the dynamical constraints and propagation equations of the gravitoelectric/-magnetic fields and covariantly debate their analytic properties. We discuss the special conditions under which gravitational waves can propagate, the inconsistency of a Newtonian-like model without gravitomagnetism, the nonlinear generalization to multi-fluid models with different matter species, as well as observational effects caused by the Weyl fields via the kinematic quantities. The 1+3 tetrad and 1+1+2 semi-covariant methods, which can equally be used for gravitoelectromagnetism, are briefly explained, along with their correspondence with the covariant formulations. Full article
(This article belongs to the Special Issue Frame-Dragging and Gravitomagnetism)
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