Some magnetohydrostatic models of cylindrical symmetry in general relativity

1984 ◽  
Vol 25 (5) ◽  
pp. 1456-1459 ◽  
Author(s):  
S. R. Roy ◽  
Raj Bali
Keyword(s):  
General Relativity ◽  
Cylindrical Symmetry

scholarly journals CYLINDRICALLY SYMMETRIC SPINNING BRANS–DICKE SPACE–TIMES WITH CLOSED TIMELIKE CURVES

1999 ◽  
Vol 14 (17) ◽  
pp. 1105-1111 ◽  
Author(s):  
LUIS A. ANCHORDOQUI ◽  
SANTIAGO E. PEREZ BERGLIAFFA ◽  
MARTA L. TROBO ◽  
GRACIELA S. BIRMAN
Keyword(s):  
General Relativity ◽  
Exact Solutions ◽  
Cylindrical Symmetry ◽  
Space Time ◽  
Rigid Rotation ◽  
Closed Timelike Curves ◽  
New Exact Solutions ◽  
Cylindrically Symmetric

We present here three new exact solutions of Brans–Dicke theory for a stationary geometry with cylindrical symmetry in the presence of matter in rigid rotation with [Formula: see text]. All the solutions have eternal closed timelike curves in some region of space–time which has a size that depends on ω. Moreover, two of them do not go over a solution of general relativity in the limit ω→∞.

scholarly journals EXACT SOLUTION FOR THE MASSLESS CYLINDRICALLY SYMMETRIC SCALAR FIELD IN GENERAL RELATIVITY, WITH COSMOLOGICAL CONSTANT

2009 ◽  
Vol 24 (31) ◽  
pp. 5991-6000 ◽  
Author(s):  
D. MOMENI ◽  
H. MIRAGHAEI
Keyword(s):  
Exact Solution ◽  
General Relativity ◽  
Scalar Field ◽  
Cosmological Constant ◽  
Cylindrical Symmetry ◽  
Cosmological Models ◽  
Cyclic Universe ◽  
Cylindrically Symmetric

In this paper, we present a new exact solution for scalar field with cosmological constant in cylindrical symmetry. Associated cosmological models, including a model that describes a cyclic universe, are discussed.

scholarly journals Static cylindrical symmetric solutions in the Einstein-Aether theory

2021 ◽  
Author(s):  
R. Chan ◽  
M. F. A. da Silva
Keyword(s):  
General Relativity ◽  
Cylindrical Symmetry ◽  
Maximum Radius ◽  
Cylindrically Symmetric ◽  
Test Particles ◽  
Symmetric Spacetime

In this work, we present all the possible solutions for a static cylindrical symmetric spacetime in the Einstein-Aether (EA) theory. As far as we know, this is the first work in the literature that considers cylindrically symmetric solutions in the theory of EA. One of these solutions is the generalization in EA theory of the Levi-Civita (LC) spacetime in General Relativity (GR) theory. We have shown that this generalized LC solution has unusual geodesic properties, depending on the parameter [Formula: see text] of the aether field. The circular geodesics are the same of the GR theory, no matter the values of [Formula: see text]. However, the radial and [Formula: see text]-direction geodesics are allowed only for certain values of [Formula: see text] and [Formula: see text]. The [Formula: see text]-direction geodesics are restricted to an interval of [Formula: see text] different from those predicted by the GR and the radial geodesics show that the motion is confined between the origin and a maximum radius. The latter is not affected by the aether field but the velocity and acceleration of the test particles are besides, for [Formula: see text], when the cylindrical symmetry is preserved, this spacetime is singular at the axis [Formula: see text], although for [Formula: see text] exists interval of [Formula: see text] where the spacetime is not singular, which is completely different from that one obtained with the GR theory, where the axis [Formula: see text] is always singular.

Cylindrical waves in general relativity

1986 ◽  
Vol 408 (1835) ◽  
pp. 209-232 ◽  
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Energy Density ◽  
Perfect Fluid ◽  
Maxwell Equations ◽  
Cylindrical Symmetry ◽  
Hamiltonian Density ◽  
Cylindrical Waves ◽  
Cylindrically Symmetric ◽  
Set Up

A convenient framework is set up for constructing cylindrically symmetric solutions of the Einstein and the Einstein—Maxwell equations, and it is shown how a Hamiltonian density can be defined for space-times with cylindrical symmetry. Solutions are obtained that represent stationary monochromatic waves and satisfy all the requisite conditions of regularity. The case when the gravitational field is coupled with a perfect fluid in which the energy density is equal to the pressure is also briefly considered.

Fixing redundant degrees of teleparallel equivalent of general relativity

2017 ◽  
Vol 14 (11) ◽  
pp. 1750154
Author(s):  
Gamal G. L. Nashed ◽  
B. Elkhatib
Keyword(s):  
General Relativity ◽  
Lorentz Transformation ◽  
Arbitrary Function ◽  
Degrees Of Freedom ◽  
Symmetric Tensor ◽  
Cylindrical Symmetry ◽  
Radial Coordinate ◽  
Field Equations ◽  
Local Lorentz Transformation ◽  
Teleparallel Theory

It is well known that the field equation of teleparallel theory which is equivalent to general relativity completely agrees with the field equations of general relativity. However, teleparallel equivalent of general relativity has six redundant degrees of freedom which spoil the true physics. These extra degrees are related to the local Lorentz transformation. In this study, we give three different tetrad fields having cylindrical symmetry and depend only on the radial coordinate. One of these tetrads contains an arbitrary function, which is responsible to reproduce the other solutions, which come from local Lorentz transformation. We show by explicate calculations that this arbitrary function spoils the calculations of the conserved charges. We formulate a skew-symmetric tensor whose vanishing value puts a constraint on this arbitrary function. This constraint fixed the redundant degrees of freedom which characterize the teleparallel equivalent of general relativity.

On Invariant Qualitative Chaos in Multi-Black-Hole Spacetimes

1997 ◽  
Vol 06 (06) ◽  
pp. 741-770 ◽  
Author(s):  
Marek Szydłowski
Keyword(s):  
General Relativity ◽  
Black Hole ◽  
Optical Model ◽  
Chaotic Behavior ◽  
Initial Conditions ◽  
Cylindrical Symmetry ◽  
Geodesic Motion ◽  
Local Instability ◽  
Black Hole Spacetimes ◽  
Sensitive Dependence

It is analytically shown when chaos exists in the behavior of null and timelike geodesics in the general case of geodesic motion in static and diagonal fields of general relativity. We demonstrate the effectiveness of our method of investigating chaos in the behavior of geodesic motion in the multi-black-hole spacetimes. An optical model of chaotic behavior of geodesics in spacetimes with cylindrical symmetry is presented. The Lyapunov characteristic time is defined and estimated for geodesic motion of a test particle in the external fields of general relativity. We find that its value is positive in some compact regions of the configuration space. This means that the trajectories have the property of local instability which implies the sensitive dependence on initial conditions.

Probe size and 5th-order aberration

1987 ◽  
Vol 45 ◽  
pp. 134-135 ◽  
Author(s):  
Zhifeng Shao
Keyword(s):  
Electron Probe ◽  
Spherical Aberration ◽  
Wave Length ◽  
Cylindrical Symmetry ◽  
Electron Wave ◽  
Third Order ◽  
The Third ◽  
Probe Radius ◽  
Small Probe ◽  
Probe Size

A small electron probe has many applications in many fields and in the case of the STEM, the probe size essentially determines the ultimate resolution. However, there are many difficulties in obtaining a very small probe.Spherical aberration is one of them and all existing probe forming systems have non-zero spherical aberration. The ultimate probe radius is given byδ = 0.43Csl/4ƛ3/4where ƛ is the electron wave length and it is apparent that δ decreases only slowly with decreasing Cs. Scherzer pointed out that the third order aberration coefficient always has the same sign regardless of the field distribution, provided only that the fields have cylindrical symmetry, are independent of time and no space charge is present. To overcome this problem, he proposed a corrector consisting of octupoles and quadrupoles.

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