Correction: Mashhoon, B. Critical Tidal Currents in General Relativity. Universe 2020, 6, 104

Mashhoon, Bahram

doi:10.3390/universe7020039

Cited by 4 publications

(5 citation statements)

References 2 publications

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“…(see, e.g., Landau &Lifshitz 1971 andPoisson &Will 2014, for a detailed description of higher-order post-Newtonian expansions; see also Rindler 1997;Lynden-Bell & Nouri-Zonoz 1998;Mashhoon et al 1999;Clark & Tucker 2000;Ruggiero & Tartaglia 2002;Mashhoon 2008;Costa &Natário 2021, andRuggiero 2021). We indicate with ∧ the vector (cross) product, ∇ is the usual nabla operator, and j = ρv is the gravitational current density, ρ and v being the mass density and velocity field of the sources.…”

Section: The Gravitomagnetic Equationsmentioning

confidence: 99%

On the Rotation Curve of Disk Galaxies in General Relativity

Ciotti

2022

ApJ

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Recently, it has been suggested that the phenomenology of flat rotation curves observed at large radii in the equatorial plane of disk galaxies can be explained as a manifestation of general relativity (GR) instead of the effect of dark matter (DM) halos. In this paper, by using the well-known weak-field, low-velocity gravitomagnetic formulation of GR, the expected rotation curves in GR are rigorously obtained for purely baryonic disk models with realistic density profiles and compared with the predictions of Newtonian gravity for the same disks in absence of DM. As expected, the resulting rotation curves are indistinguishable, with GR corrections at all radii of the order v 2/c 2 ≈ 10−6. Next, the gravitomagnetic Jeans equations for two-integral stellar systems are derived, and then solved for the Miyamoto–Nagai disk model, showing that finite-thickness effects do not change the previous conclusions. Therefore, the observed phenomenology of galactic rotation curves at large radii requires DM in GR exactly as in Newtonian gravity, unless the cases here explored are reconsidered in the full GR framework with substantially different results (with the surprising consequence that the weak-field approximation of GR cannot be applied to the study of rotating systems in the weak-field regime). In this article, the mathematical framework is described in detail, so that the present study can be extended to other disk models, or to elliptical galaxies (where DM is also required in Newtonian gravity, but their rotational support can be much less than in disk galaxies).

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Section: The Gravitomagnetic Equationsmentioning

confidence: 99%

On the Rotation Curve of Disk Galaxies in General Relativity

Ciotti

2022

ApJ

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“…If the nonlocal theory corresponds to reality, its predictions should be closer to quantum mechanical results in the correspondence regime than those of the standard local theory of accelerated systems. This turns out to be the case for the simple cases that have been worked out in detail [20]. Let us now return to the standard physical consequences of Dirac's equation in noninertial systems of reference.…”

Section: Nonlocal Electrodynamicsmentioning

confidence: 88%

“…This is contrary to the basic postulate of the nonlocal theory; therefore, the only modification in equation ( 27) occurs for the E ′ = 0 case. This circumstance is discussed in detail in [20].…”

Section: Spin-rotation Couplingmentioning

confidence: 97%

Quantum Theory in Accelerated Frames of Reference

Mashhoon

Special Relativity

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The observational basis of quantum theory in accelerated systems is studied. The extension of Lorentz invariance to accelerated systems via the hypothesis of locality is discussed and the limitations of this hypothesis are pointed out. The nonlocal theory of accelerated observers is briefly described. Moreover, the main observational aspects of Dirac's equation in noninertial frames of reference are presented.The Galilean invariance of nonrelativistic quantum mechanics and the mass superselection rule are examined in the light of the invariance of physical laws under inhomogeneous Lorentz transformations.

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“…Although not a formulation of general relativity by itself and not developed for numerical spacetime evolution, gravitoelectromagnetism (GEM) also provides a way of casting general relativity in a form that resembles Maxwell equations (see [70] for a review). GEM is extremely useful to study effects such as the spin-gravity coupling, in which almost direct analogies exist between gravity and electromagnetism.…”

Section: Relation To Other Formulationsmentioning

confidence: 99%

New first-order formulation of the Einstein equations exploiting analogies with electrodynamics

et al. 2022

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The Einstein and Maxwell equations are both systems of hyperbolic equations which need to satisfy a set of elliptic constraints throughout evolution. However, while electrodynamics and magnetohydrodynamics have benefited from a large number of evolution schemes that are able to enforce these constraints and are easily applicable to curvilinear coordinates, unstructured meshes, or N-body simulations, many of these techniques cannot be straightforwardly applied to existing formulations of the Einstein equations. We develop a 3 þ 1 a formulation of the Einstein equations that shows a striking resemblance to the equations of relativistic magnetohydrodynamics and to electrodynamics in material media. The fundamental variables of this formulation are the frame fields, their exterior derivatives, and the Nester-Witten and Sparling forms. These mirror the roles of the electromagnetic four potential, the electromagnetic field strengths, the field excitations and the electric current. The role of the lapse function and shift vector, corresponds exactly to that of the scalar electric potential. The formulation is manifestly first order and fluxconservative, which makes it suitable for high-resolution shock capturing schemes and finite-element methods. Being derived as a system of equations in exterior derivatives, it is directly applicable to any coordinate system and to unstructured meshes, and leads to a natural discretization potentially suitable for the use of machine-precision constraint propagation techniques such as the Yee algorithm and constrained transport. Due to these properties, we expect this new formulation to be beneficial in simulations of many astrophysical systems, such as binary compact objects and core-collapse supernovae as well as cosmological simulations of the early Universe.

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Correction: Mashhoon, B. Critical Tidal Currents in General Relativity. Universe 2020, 6, 104

Abstract: In writing out the tidal equation for X in my recent paper [...]

Cited by 4 publications

References 2 publications

On the Rotation Curve of Disk Galaxies in General Relativity

On the Rotation Curve of Disk Galaxies in General Relativity

Quantum Theory in Accelerated Frames of Reference

New first-order formulation of the Einstein equations exploiting analogies with electrodynamics

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