Papapetrou field as the gravitoelectromagnetic field tensor in stationary spacetimes

Aliasghar, Parvizi,

doi:10.1007/s10714-016-2032-7

Cited by 6 publications

(11 citation statements)

References 29 publications

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“…To prove the above statement, we first note that the gravitoelectromagnetic 3-vector fields defined in the previous section could be elevated to the following covariant 4-vector fields [16] (16) in which, in analogy with the definition of the electromagnetic field tensor in curved spacetimes, the gravitoelectromagnetic field tensor F g (or Papapetrou field [16]) is defined as (also refer to Sec. 18.1 of Ref.…”

Section: Staticity Condition In Terms Of the Absence Of The Gravmentioning

confidence: 99%

Dark fluid or cosmological constant: Why there are different de Sitter-type spacetimes

Koohbor

Ramezani-Aval

2015

Phys. Rev. D

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Many different forms of the de Sitter metric in different coordinate systems are used in the general relativity literature. Two of them are the most common, the static form and the cosmological (exponentially expanding) form. The staticity and non-stationarity of these two different forms are traced back to the noncomoving and comoving nature of the corresponding coordinate systems. In this paper using the quasi-Maxwell form of the Einstein field equations and a definition of static spacetimes based upon them, we look at these two different forms of the same solution from a new perspective which classifies them as a special case in a general one-parameter family of solutions. fluid's velocity in defining a preferred (comoving) coordinate system in de Sitter-type spacetimes.

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Section: Staticity Condition In Terms Of the Absence Of The Gravmentioning

confidence: 99%

Dark fluid or cosmological constant: Why there are different de Sitter-type spacetimes

Koohbor

Ramezani-Aval

2015

Phys. Rev. D

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“…in which ln √ h and A g are the so-called gravitoelectric and gravitomagnetic potentials respectively [10]. We notice that gravitoelectric part of the GEM Lorentz force is the general relativistic version of the gravitational force in Newtonian gravity [11], while its gravitomagnetic part has no counterpart in Newtonian gravity.…”

Section: Gravitoelectromagnetism and The Quasi-maxwell Form Of The Ei...mentioning

confidence: 90%

Static and stationary dark fluid universes: A gravitoelectromagnetic perspective

Nouri-Zonoz¹

2020

Preprint

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We introduce a physical characterization of the static and stationary perfect fluid solutions of the Einstein field equations with a single or 2-component perfect fluid sources, according to their gravitoelectric and gravitomagnetic fields. The absence or presence of either or both of these fields could restrict the equations of state of the underlying perfect fluid sources. As an example and representative of each class we consider solutions that include the cosmological term as a fluid source with the equation of state p = −ρ = constant. All these solutions share the feature that go over smoothly into the Minkowski spacetime as Λ → 0.

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“…) is the 4-velocity of the Killing observers, the above equations reduce to those defined in the 1 + 3 decomposition formalism (also called projection formalism [10]), namely equations (1) and (2) [11]. This could also be seen from the fact that according to the above setting, the points A 0 and B 0 (being on the joining spacelike geodesic segments)…”

Section: A Note On Synge's Definition Of Spatial Distance and Rementioning

confidence: 98%

“…The 3-space Σ 3 defined in this way is called a quotient space/manifold and in general is not a submanifold of the original 4-d manifold [10,11].…”

Section: Malismmentioning

confidence: 99%

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A tale of two velocities: Threading versus slicing

Gharechahi

Tavanfar

2018

Int. J. Geom. Methods Mod. Phys.

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Two principal definitions of a 3-velocity assigned to a test particle following timelike trajectories in stationary spacetimes are introduced and analyzed systematically. These definitions are based on the 1+3 (threading) and 3+1 (slicing) spacetime decomposition formalisms and defined relative to two different sets of observers. After showing that Synge's definition of spatial distance and 3-velocity are equivalent to those defined in the 1 + 3 (threading) formalism, we exemplify differences between the two definitions, by calculating them for particles in circular orbits in axially symmetric stationary spacetimes. Illustrating its geometric nature, the relative linear velocity between the corresponding observers is obtained in terms of the spacetime metric components. Circular particle orbits in the Kerr spacetime, as the prototype and the most well known of stationary spacetimes, are examined with respect to these definitions to highlight their observer-dependent nature.We also examine the Kerr-NUT spacetime in which the NUT parameter contributing to the offdiagonal terms in the metric is mainly interpreted not as a rotation parameter but as a gravitomagnetic monopole charge. Finally, in a specific astrophysical setup which includes rotating black holes, it is shown how these local definitions are related to the velocity measurements made by distant observers using spectral line shifts. * Electronic address: r.gharechahi@ut.ac.ir †

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Papapetrou field as the gravitoelectromagnetic field tensor in stationary spacetimes

Cited by 6 publications

References 29 publications

Dark fluid or cosmological constant: Why there are different de Sitter-type spacetimes

Dark fluid or cosmological constant: Why there are different de Sitter-type spacetimes

Static and stationary dark fluid universes: A gravitoelectromagnetic perspective

A tale of two velocities: Threading versus slicing

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