On the sources of static plane symmetric vacuum space-times

Silva, M. F. A. da; Wang, Anzhong; Santos, N. O.

doi:10.1016/s0375-9601(98)00355-7

Cited by 20 publications

(22 citation statements)

References 14 publications

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“…Then neither m nor n is entitled to be an angular coordinate, and the three coordinates r, m and n are better visualized as Cartesian coordinates x, y and z. Hence metric (2.7) can be written as 16) which is the static plane symmetric vacuum spacetime obtained by Rindler [125,169,268].…”

Section: Bmentioning

confidence: 99%

“…The coordinates are numbered x 0 = t, x 1 = r, x 2 = z and x 3 = φ. The general vacuum solution R αβ = 0 for the metric (6.1), in the notation given by [121] and [125], is…”

Section: A Stationary Cylindrical Vacuum Spacetimementioning

confidence: 99%

“…The metric coefficients (6.2) with (6.3) become [125,219] f = r(a 2 1 − b 2 1 ) cos(m ln r) + 2ra 1 b 1 sin(m ln r), k = −r(a 1 a 2 − b 1 b 2 ) cos(m ln r) −r(a 1 b 2 + a 2 b 1 ) sin(m ln r), l = −r(a 2 2 − b 2 2 ) cos(m ln r) − 2ra 2 b 2 sin(m ln r), e µ = r −(m 2 +1)/2 . (6.5)…”

Section: A Stationary Cylindrical Vacuum Spacetimementioning

confidence: 99%

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Cylindrical systems in general relativity

Бронников

Santos

Wang

2020

Class. Quantum Grav.

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With the arrival of the era of gravitational wave astronomy, the strong gravitational field regime will be explored soon in various aspects. In this article, we provide a general review over cylindrical systems in Einstein's theory of general relativity. In particular, we first review the general properties, both local and global, of several important solutions of Einstein's field equations, including the Levi-Civita and Lewis solutions and their extensions to include the cosmological constant and matter fields, and pay particular attention to properties that represent the generic features of the theory, such as the formation of the observed extragalactic jets and gravitational Faraday rotation. We also review studies of cylindrical wormholes, gravitational collapse and Hoop conjecture, and polarizations of gravitational waves. In addition, by rigorously defining cylindrically symmetric spacetimes, we clarify various (incorrect) claims existing in the literature, regarding to the generality of such spacetimes.

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Section: Bmentioning

confidence: 99%

“…The coordinates are numbered x 0 = t, x 1 = r, x 2 = z and x 3 = φ. The general vacuum solution R αβ = 0 for the metric (6.1), in the notation given by [121] and [125], is…”

Section: A Stationary Cylindrical Vacuum Spacetimementioning

confidence: 99%

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Cylindrical systems in general relativity

Бронников

Santos

Wang

2020

Class. Quantum Grav.

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“…For σ = 1/2, neither p nor q is entitled to be an angular coordinate, and the three coordinates (r, p, q) are better visualized as Cartesian coordinates x, y and z. 5,16 The σ < 0 case is isotropic to the σ > 0 case.…”

Section: Properties Of Cylindrically Symmetric Static Spacetimementioning

confidence: 99%

Trapping Photons by a Line Singularity

Arık

Delice

2003

Int. J. Mod. Phys. D

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“…This metric is the Rindler's metric [5] which describes static plane symmetric vacuum spacetime [6]. It corresponds to a uniform gravitational field and test particles are uniformly accelerated in this field whereas the Riemann tensor is identically zero.…”

mentioning

confidence: 99%

Letter: Multiple Photonic Shells Around a Line Singularity

Arık

Delice

2003

General Relativity and Gravitation

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Line singularities including cosmic strings may be screened by photonic shells until they appear as a planar wall.KEY WORDS: Levi-Civita spacetime, photonic shells.Infinitely thin static photonic shells composed of equal amounts of oppositely moving photons following circular, helical or axial trajectories around a cosmic string [1] and, around a general line singularity [2] have recently been found. In this paper, we will find solutions giving multiple photonic shells around a line singularity. Multiple photonic shells around cosmic strings will be obtained as a limiting case. We will show that the exterior region of the (multiple) shells may become an infinite plane wall.The vacuum spacetime exterior to a static, cylindrically symmetric source is described by the Levi-Civita metric [3] which can be written as:where t , ρ, z and φ are the time, the radial, the axial and the angular variables of the cylindrical coordinates with ranges −∞ < t, z < ∞, 0 ≤ ρ < ∞ and 0 ≤ φ ≤ 2π. σ, P and Q are real constants. Transforming the radius ρ into a proper radius r by defining dr = ρ 2σ(2σ−1) dρ puts (1) in the Kasner form:

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On the sources of static plane symmetric vacuum space-times

Cited by 20 publications

References 14 publications

Cylindrical systems in general relativity

Cylindrical systems in general relativity

Trapping Photons by a Line Singularity

Letter: Multiple Photonic Shells Around a Line Singularity

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