### Citations

2942 |
Classical electrodynamics
- Jackson, Fox
- 1999
(Show Context)
Citation Context ...(Eu)µ(Bu)ν , (162) or, in vector notation, 8piρEM = ~E(u) 2 + ~B(u)2; ~pEM = ~E(u) × ~B(u)/4pi. Now note that the significance of these expressions as energy and momentum densities can be traced back =-=[76, 52]-=-, at the most fundamental level, to the Lorentz force (together with the Maxwell equations), the work done by it, and its spatial momentum transfer. It is thus clear that it cannot have a direct physi... |

904 |
The large scale structure of space-time Cambridge
- Hawking, Ellis
(Show Context)
Citation Context ...−1 2 αβγδωαβu δ. (47) According to definition above, ωα yields half the curl of uα; this is in agreement with the convention in e.g. [20, 27], but differs by a minus sign from the definition in e.g. =-=[35, 87]-=-. Note however that for the vorticity tensor ωαβ we are using the more general definition given in [35, 87], differing from a minus sign from the one in [27] (consequently, ωα given by Eq. (47) is min... |

504 |
in Gravitation: An introduction to current research
- Amowit, Deser, et al.
- 1962
(Show Context)
Citation Context ...e frame is adapted to an hypersurface orthogonal (i.e., vorticity free) congruence, corresponding to the “hypersurface point of view” [19, 20], leading to the well known ADM “3+1 formalism” (see e.g. =-=[125, 124]-=-) which is obtained by setting ~H = 0 in the equations above. Let us start by case i), also known as the “1+3 formalism” (e.g. [94]) or threading picture [19, 20] for stationary spacetimes, which is w... |

331 |
Relativity: The general theory
- Synge
- 1960
(Show Context)
Citation Context ...ame 4-velocity. For clarity we will treat the gravitational and electromagnetic interactions separately. We will start with the gravitational problem. Consider a system of Fermi coordinates (see e.g. =-=[99, 100]-=-) with origin along a worldline passing trough the location P1, and denote by eα its basis vectors. Assuming the Mathisson-Pirani spin condition SαβUβ = 0, the spin vector of a gyroscope undergoes Fer... |

225 |
Classical electrodynamics, 3-rd edition
- Jackson
- 1999
(Show Context)
Citation Context ...(Eu)µ(Bu)ν , (163) or, in vector notation, 8piρEM = ~E(u) 2 + ~B(u)2; ~pEM = ~E(u) × ~B(u)/4pi. Now note that the significance of these expressions as energy and momentum densities can be traced back =-=[73, 26]-=-, at the most fundamental level, to the Lorentz force (together with the Maxwell equations), the work done by it, and its spatial momentum transfer. It is thus clear that it cannot have a direct physi... |

108 |
Relativity: The General Theory (North-Holland,
- Synge
- 1956
(Show Context)
Citation Context ... = ijk ?Rk0γτ . We thus have Γi0j(P2) = ijk ?Rk0l0 (P1)δxl = ijkHklδxl . Γi0j(P2) is an antisymmetric matrix, which we can write as Γi0j(P2) = ijkδΩkG, where δΩiG ≡ Hilδxl . (29) 7Following Synge =-=[95]-=-, by Fermi coordinates we mean the locally rectangular coordinate system associated to a tetrad Fermi-Walker transported along a worldline (the curve being the origin of the frame, and its tangent the... |

63 | Exact Solutions to Einstein’s Field Equations, 2nd ed., - Stephani, Dietrich, et al. - 2003 |

61 |
General relativity and cosmology.
- Ellis
- 1971
(Show Context)
Citation Context ...e spatial tensors; 2) these tensors obey differential equations — Maxwell’s equations and the so called “higher order” gravitational field equations — which are formally analogous to a certain extent =-=[30, 31, 85, 32, 49]-=-; and 3) they form invariants in a similar fashion [30, 31, 50, 51]. In this section we will briefly review these analogies and clarify their physical content in the light of the previous approaches. ... |

12 | The theory of relativity. Oxford, at the Clarendon - Møller - 1952 |

10 |
The Many Faces of Gravitoelectromagnetism
- Jantzen, Bini
- 1992
(Show Context)
Citation Context ...mes introduced by Landau-Lifshitz [74], and further worked out by other authors [15, 14, 16, 93, 94, 92]. Also not well known is the existence of an exact formulation applying to arbitrary spacetimes =-=[19, 20]-=-, which considers an arbitrary timelike congruence of observers and does a general 1+3 splitting in terms of a time direction, parallel to the observer’s worldlines, and the local rest spaces orthogon... |

10 |
M.L., in Relativity in Rotating
- Rizzi, Ruggiero
- 2004
(Show Context)
Citation Context ...Lorentz force; many other effects related to frame dragging can be treated exactly with the GEM fields: gyroscope “precession” (relative to the “distant stars”) [4, 19, 20, 40, 14], the Sagnac effect =-=[111]-=-, the Faraday rotation [94], the force on a gyroscope (Sec. 3.7 and [14]; note however that it is not as general as the the tidal tensor formulation of the same force); and other applications, such as... |

5 |
Spacetime And Geometry.
- Carrol
- 2004
(Show Context)
Citation Context ...gravitoelectromagnetism The oldest and best known gravito-electromagnetic analogies are the ones based on linearized gravity, which have been worked out by many authors throughout the years, see e.g. =-=[23, 97, 98, 22, 61, 24, 67, 105, 34, 7, 123]-=-. As is usually presented, one considers a metric given by small perturbations |hαβ| 1 around Minkowski spacetime, gαβ = ηαβ + hαβ, and from the components hαβ one defines the 3-vectors ~G and ~H, i... |

4 |
Electric and magnetic Weyl tensors: classification and analysis
- McIntosh, Arianrhod, et al.
- 1994
(Show Context)
Citation Context ...tromagnetic scalar invariants (145). However, by contrast with the latter, these are not the only independent scalar invariants one can construct from Cαβµν ; there are also two cubic invariants, see =-=[60, 31, 52, 33]-=-. As stated above, these tensors obey also differential equations which have some formal similarities with Maxwell’s; such equations, dubbed the “higher order field equations” are obtained from Bianch... |

3 |
Purely gravito-magnetic vacuum space-times
- Bergh
(Show Context)
Citation Context ...put forth in the literature, possibly for two reasons: one is that in the literature dealing with the higher order field equations the physical interpretation of Hαβ appears as an unanswered question =-=[84, 87, 53, 82, 83, 32]-=-; the other is that in the literature dealing with the interaction of gravitational waves with spinning particles [69, 68, 70, 71], neither the waves are written in tidal tensor form (but instead in t... |

2 |
12Relativity in Rotating Frames, edited by
- Rizzi, L
- 2003
(Show Context)
Citation Context ...s is cast in a form similar to Lorentz force; many other 56 effects related to frame dragging can be treated exactly with the GEM fields: gyroscope “precession” [6, 27, 28, 58, 20], the Sagnac effect =-=[107]-=-, the Faraday rotation [24], the force on a gyroscope (Sec. 3.6 and [20]; note however that it is not as general as the the tidal tensor formulation of the same force); and other applications, such as... |

1 | Thorne in “Near Zero: New Frontiers of Physics”, Eds - Kip - 1988 |

1 | Reference Frames and Gravitomagnetism”, edited by - Pascual-Sanchez, Floria, et al. - 2001 |

1 |
Cahiers de Physique, 16
- Bel
- 1962
(Show Context)
Citation Context ...e spatial tensors; 2) these tensors obey differential equations — Maxwell’s equations and the so called “higher order” gravitational field equations — which are formally analogous to a certain extent =-=[30, 31, 85, 32, 49]-=-; and 3) they form invariants in a similar fashion [30, 31, 50, 51]. In this section we will briefly review these analogies and clarify their physical content in the light of the previous approaches. ... |

1 |
Meccanica 10
- Massa, Zordan
- 1975
(Show Context)
Citation Context ...ral choice, of great usefulness in this framework, is to lock the rotation of the tetrads to the vorticity of the congruence, ~Ω = ~ω. We will dub such frame “congruence adapted frame”7; as argued in =-=[38, 36]-=-, where it was introduced, this is the most natural generalization of the non-relativistic concept of reference frame; and the corresponding transport law ~Ω = ~ω has been dubbed “co-rotating Fermi-Wa... |

1 |
Nature 431 (2004) 958
- Ciufolini, Pavlis
- 2006
(Show Context)
Citation Context ...he companion paper [4], and in [60]. It also allows one to realize, for instance, that there is a distinction between the gravitomagnetic effect detected in the analysis of the LAGEOS Satellites data =-=[41]-=- (presently under scrutiny in the ongoing LARES mission [43]), and the one measured by the Gravity Probe B experiment. An important result of this approach is an exact expression for the geodesic equa... |

1 |
http://einstein.stanford.edu/ Review of Gravity Probe B (National Academy
- Everitt
- 1995
(Show Context)
Citation Context ...l scrutiny by the ongoing LARES mission [43]), measuring ~H from test particle’s deflection, is of a different mathematical origin from the one which was under scrutiny by the Gravity Probe B mission =-=[42]-=-, measuring ~Ω from gyroscope precession, the two being made to match by measuring both effects relative to the “frame of the distant stars” (see below). Another obvious difference is the presence of ... |

1 |
Ciufolini et al, Space Sci
- I
- 2009
(Show Context)
Citation Context ...ealize, for instance, that there is a distinction between the gravitomagnetic effect detected in the analysis of the LAGEOS Satellites data [41] (presently under scrutiny in the ongoing LARES mission =-=[43]-=-), and the one measured by the Gravity Probe B experiment. An important result of this approach is an exact expression for the geodesic equation, written in the language of GEM fields, that is fully g... |

1 |
Annales de l
- Bel
- 1961
(Show Context)
Citation Context ...y (the very question of whether it has any physical reality is an open one), due to the “strange” dimensions of W , namely L−4, which (taking L = M) can be interpreted an energy density per unit area =-=[48, 75, 76]-=-, or of an energy density times a frequency squared [72], or an energy density squared [75]. A detailed discussion of these issues, and of the possible relation between super-energy and energy is beyo... |

1 | Tidal effects cannot be absent in a vacuum - Bergh - 2003 |

1 |
Gravitational Waves in Eintein’s Theory”, Eng. Trans. by R
- Zakharov
- 1973
(Show Context)
Citation Context ...at the two invariants (145) vanish; likewise, the gravitational invariants (148) also vanish for a solution corresponding to pure gravitational radiation according to Bel’s second criterion (cf. e.g. =-=[57]-=- p. 53) — a definition based on “super-energy”, discussed below. An interesting aspect of this formulation of gravitational radiation, contrasting with the more usual approaches in the literature, e.g... |

1 |
work in progress (for a brief summary of the main results, see
- Costa, Natário, et al.
(Show Context)
Citation Context ...ence and the rotation ~Ω of the local tetrads (associated to each local observer) relative to local Fermi-Walker transport. This degree of generality is of use both in the companion paper [4], and in =-=[60]-=-. It also allows one to realize, for instance, that there is a distinction between the gravitomagnetic effect detected in the analysis of the LAGEOS Satellites data [41] (presently under scrutiny in t... |

1 |
The classical theory of fields”, 4th Ed., BH-Elsevier
- Landau, Lifshitz
- 1975
(Show Context)
Citation Context ...y, e.g. [23, 97, 22, 61, 24]; less well known is the exact “quasi-Maxwell” analogy, based on the inertial fields that arise in the 1+3 splitting of stationary spacetimes introduced by Landau-Lifshitz =-=[74]-=-, and further worked out by other authors [15, 14, 16, 93, 94, 92]. Also not well known is the existence of an exact formulation applying to arbitrary spacetimes [19, 20], which considers an arbitrary... |

1 |
The large scale structure of spacetime”, Cam
- Hawking, Ellis
(Show Context)
Citation Context ...−1 2 αβγδωαβu δ. (40) According to definition above, ωα yields half the curl of uα; this is in agreement with the convention in e.g. [14, 19], but differs by a minus sign from the definition in e.g. =-=[32, 86]-=-. Note however that for the vorticity tensor ωαβ we are using the more general definition given in [32, 86], differing from a minus sign from the one in [19] (consequently, ωα given by Eq. (40) is min... |

1 |
Geometric mechanics”, Springer (2002); Lect
- Oliva
- 2004
(Show Context)
Citation Context ...is the exact “quasi-Maxwell” analogy, based on the inertial fields that arise in the 1+3 splitting of stationary spacetimes introduced by Landau-Lifshitz [74], and further worked out by other authors =-=[15, 14, 16, 93, 94, 92]-=-. Also not well known is the existence of an exact formulation applying to arbitrary spacetimes [19, 20], which considers an arbitrary timelike congruence of observers and does a general 1+3 splitting... |

1 |
Nature 449
- Ciufolini
- 2007
(Show Context)
Citation Context ...gravitoelectromagnetism The oldest and best known gravito-electromagnetic analogies are the ones based on linearized gravity, which have been worked out by many authors throughout the years, see e.g. =-=[23, 97, 98, 22, 61, 24, 67, 105, 34, 7, 123]-=-. As is usually presented, one considers a metric given by small perturbations |hαβ| 1 around Minkowski spacetime, gαβ = ηαβ + hαβ, and from the components hαβ one defines the 3-vectors ~G and ~H, i... |

1 |
Colloques Internationaux du Centre national de la reserche scientifique
- Bel
- 1962
(Show Context)
Citation Context ...The motivation for the definition of this tensor is the analogy with electromagnetism; and the existing criteria for radiative states [109], states of intrinsic radiation [31, 108] or pure radiation (=-=[112]-=-, see also [57] p. 53), are also solely driven by it. The analogy is also useful for the understanding of the quadratic invariants of the curvature tensor; indeed, it will be shown elsewhere [60] that... |

1 |
Pascual Sánchez, Il Nuovo Cimento
- -F
- 2000
(Show Context)
Citation Context ...rms of (physically meaningful) GEM fields that does not rely on choosing the harmonic gauge condition and its inherent subtleties (which have been posing some difficulties in the literature, see e.g. =-=[22, 118, 61, 2]-=-). The usual expression for the force on a gyroscope in the literature (e.g. [7, 24, 23]) is also seen to be a (very) limiting case of the exact equation given in the tidal tensor formalism of Sec. 2.... |

1 |
APJ 162
- Bardeen
- 1970
(Show Context)
Citation Context ..., encompasses the many different gravitomagnetic fields that have been defined. That includes the case of the reference frames sometimes employed in the context of black hole physics and astrophysics =-=[17, 121, 122]-=-: the tetrads carried by hypersurface orthogonal observers, whose spatial axis are taken to be fixed to the background symmetries; for instance, in the Kerr spacetime, the congruence are the zero angu... |

1 | Data Analysis, Proceedings of the International Astronomical Union vol 5 S261, edited by - Frames - 2010 |

1 |
Nature 431, 958 (2004
- Ciufolini, Pavlis
- 2006
(Show Context)
Citation Context ... relative to a local Fermi-Walker transported tetrad, but also from the vorticity ~ω of the congruence. In this sense, one can say that the Lense-Thirring effect detected in the LAGEOS satellite data =-=[59]-=- (and presently under experimental scrutiny by the ongoing LARES mission [61]), measuring ~H from test particle’s deflection, is of a different mathematical origin from the one which was under scrutin... |

1 | in Reference Frames and Gravitomagnetism - Bini, Jantzen |

1 |
Tensor Calculus (McGraw-Hill
- Kay
- 1988
(Show Context)
Citation Context ...ration of the curve. Note that expression (53) is identical to the usual definition of 3-D acceleration for curved spaces (or non-rectangular coordinate systems in Euclidean space), e.g. Eq. (6.9) of =-=[127]-=-. It is easy to see in this sub-case (Ωα = ωα, K(αβ) = 0) that ~FGEM = D̃~U/dτ corresponds to the usual notion of inertial force from classical mechanics. Take a familiar example, a rigidly rotating f... |