Two-parameter static and five-parameter stationary solutions of the Einstein-Maxwell equations

1975 ◽  
Vol 27 (2) ◽  
pp. 213-228 ◽  
Author(s):  
G. Önengüt ◽  
M. Serdaroĝlu
Keyword(s):  
Maxwell Equations ◽  
Stationary Solutions ◽  
Two Parameter

A class of exact interior solutions of the Einstein-Maxwell equations

1977 ◽  
Vol 353 (1675) ◽  
pp. 523-531 ◽  
Keyword(s):  
Angular Velocity ◽  
Laplace Equation ◽  
Maxwell Equations ◽  
Flat Space ◽  
Stationary Solutions ◽  
Constant Angular Velocity ◽  
Arbitrary Solution ◽  
Charged Matter ◽  
Axis Of Symmetry ◽  
Interior Solutions

A class of exact interior stationary solutions of the Einstein-Maxwell equations is found in terms of an arbitrary solution of the flat-space Laplace equation. These solutions represent pressure-free charged matter rotating with constant angular velocity about an axis of symmetry. Some properties of the solution are discussed.

A one-to-one correspondence between the static Einstein-Maxwell and stationary Einstein-vacuum space-times

1989 ◽  
Vol 423 (1865) ◽  
pp. 379-386 ◽  
Keyword(s):  
Coordinate System ◽  
Maxwell Equations ◽  
Stationary Solutions ◽  
Einstein Vacuum Equations ◽  
Static Solutions ◽  
Maxwell Space ◽  
Einstein Vacuum ◽  
One To One ◽  
The One ◽  
Vacuum Space

A one-to-one correspondence is established between the static solutions of the Einstein-Maxwell equations and the stationary solutions of the Einstein-vacuum equations, that enables one to directly write down a solution for the one from a known solution of the other, and conversely, by a simple transcription. The directness of the correspondence is achieved by writing the metric for static Einstein-Maxwell space-times in a coordinate system and a gauge adapted to the two-centre problem and the metric for stationary Einstein-vacuum space-times in a coordinate system and a gauge adapted to black holes with event horizons.

The classical hydraulic jump in a model of shear shallow-water flows

2013 ◽  
Vol 725 ◽  
pp. 492-521 ◽  
Author(s):  
G. L. Richard ◽  
S. L. Gavrilyuk
Keyword(s):  
Shallow Water ◽  
Froude Number ◽  
Hydraulic Jump ◽  
Surface Profile ◽  
Stationary Solutions ◽  
Water Flows ◽  
Shallow Water Flows ◽  
Free Surface Profile ◽  
Sequent Depth ◽  
Two Parameter

AbstractA conservative hyperbolic two-parameter model of shear shallow-water flows is used to study the classical turbulent hydraulic jump. The parameters of the model, which are the wall enstrophy and the roller dissipation coefficient, are determined from measurements of the roller length and the deviation from the Bélanger equation of the sequent depth ratio (experimental data by Hager & Bremen, J. Hydraul. Res., vol. 27, 1989, pp. 565–585; and Hager, Bremen & Kawagoshi, J. Hydraul. Res., vol. 28, 1990, pp. 591–608). Stationary solutions to the model describe with a good accuracy the free-surface profile of the hydraulic jump. The model is also capable of predicting the oscillations of the jump toe. We show that if the upstream Froude number is larger than ${\sim }1. 5$, the jump toe oscillates with a particular frequency, while for the Froude number smaller than 1.5 the solution becomes stationary. In particular, we show that for a given flow discharge, the oscillation frequency is a decreasing function of the Froude number.

scholarly journals SINGULARITY FREE COSMOLOGICAL SOLUTIONS OF EINSTEIN–MAXWELL EQUATIONS

2003 ◽  
Vol 18 (36) ◽  
pp. 2555-2562 ◽  
Author(s):  
STOYTCHO S. YAZADJIEV ◽  
VENTSESLAV A. RIZOV
Keyword(s):  
Maxwell Equations ◽  
Globally Hyperbolic ◽  
Curvature Invariants ◽  
Cosmological Solutions ◽  
Geodesically Complete ◽  
Two Parameter

We report on a new two-parameter class of cosmological solutions of the Einstein–Maxwell equations. The solutions have everywhere regular curvature invariants. We prove that the solutions are geodesically complete and globally hyperbolic.

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