scholarly journals Exact treatment of time-dependent axisymmetric gravitation

1993 ◽  
Vol 440 (1910) ◽  
pp. 711-715 ◽  
Keyword(s):  
Exact Solution ◽  
Time Dependent ◽  
New Method ◽  
Vacuum Field ◽  
Axially Symmetric ◽  
Field Equations ◽  
Canonical Solution ◽  
Gravitational Fields ◽  
Einstein Vacuum

This paper extends an earlier treatment of time-dependent gravitational fields that are axially symmetric and non-rotating. From a consideration of the canonical solution of the Einstein vacuum field equations previously obtained as an axial expansion, a new method has been found that now provides the exact solution, whenever a certain generative key function X ( t , z ) is known.

The general axially symmetric static solution of Einstein’s vacuum field equations

1982 ◽  
Vol 382 (1783) ◽  
pp. 467-470 ◽  
Keyword(s):  
General Solution ◽  
Potential Function ◽  
Line Element ◽  
Static Solution ◽  
Vacuum Field ◽  
Axially Symmetric ◽  
Field Equations ◽  
Axis Of Symmetry ◽  
Axisymmetric Solutions ◽  
Associated Function

The general solution in closed form, including all the static axisymmetric solutions of Weyl, is presented in the canonical coordinates ρ and z of his line element. This general solution is constructed from an arbitrary function f ( z ), which coincides with his potential function along the axis of symmetry. To illustrate how the solution may be used, a particular function f , one resulting from a Newtonian solution, is used to find both the potential function and its associated function in the line element.

scholarly journals A class of axially symmetric stationary exact solutions of Einstein's vacuum field equations

1978 ◽  
Vol 20 (3) ◽  
pp. 344-351
Author(s):  
M. D. Patel
Keyword(s):  
Gravitational Field ◽  
Exact Solutions ◽  
Coordinate System ◽  
Stationary Distribution ◽  
Vacuum Field ◽  
Axially Symmetric ◽  
Field Equations ◽  
System A ◽  
Oblate Spheroidal

AbstractEinstein's vacuum field equations of an axially symmetric stationary rotating source are studied. Using the oblate spheroidal coordinate system, a class of asymptotically fiat solutions representing the exterior gravitational field of a stationary rotating oblate spheroidal source is obtained. Also it is proved that an analytic axisymmetric and stationary distribution of dust cannot be the source for the gravitational field described by the axisymmetric stationary metric.

scholarly journals Approximate perfect fluid solutions with quadrupole moment

2021 ◽  
Author(s):  
Medeu Abishev ◽  
Nurzada Beissen ◽  
Farida Belissarova ◽  
Kuantay Boshkayev ◽  
Aizhan Mansurova ◽  
...  
Keyword(s):  
Perfect Fluid ◽  
Quadrupole Moment ◽  
Line Element ◽  
Approximate Solutions ◽  
Axially Symmetric ◽  
Field Equations ◽  
Matching Conditions ◽  
Fluid Source ◽  
Gravitational Fields ◽  
Spherically Symmetry

We investigate the interior Einstein’s equations in the case of a static, axially symmetric, perfect fluid source. We present a particular line element that is specially suitable for the investigation of this type of interior gravitational fields. Assuming that the deviation from spherically symmetry is small, we linearize the corresponding line element and field equations and find several classes of vacuum and perfect fluid solutions. We find some particular approximate solutions by imposing appropriate matching conditions.

TIME-DEPENDENT SOLUTIONS OF 5D VACUUM EINSTEIN EQUATIONS WITH COSMOLOGICAL CONSTANT

2011 ◽  
Vol 26 (22) ◽  
pp. 1673-1679 ◽  
Author(s):  
TAE HOON LEE
Keyword(s):  
Cosmological Constant ◽  
Time Dependence ◽  
Scale Factor ◽  
Einstein Equations ◽  
Time Dependent ◽  
Vacuum Field ◽  
Field Equations ◽  
Vacuum Einstein Equations ◽  
Dimensional Gravity

We solve vacuum field equations in five-dimensional gravity with cosmological constant to determine the time-dependence of the Robertson–Walker scale factor. We discuss its cosmological implications.

On the superposition of gravitational waves

1975 ◽  
Vol 77 (3) ◽  
pp. 559-565 ◽  
Author(s):  
J. B. Griffiths
Keyword(s):  
Exact Solution ◽  
General Theory ◽  
Gravitational Waves ◽  
Vacuum Field ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
Field Equations ◽  
Linear Interaction ◽  
Non Linear ◽  
Transverse And Longitudinal Components

AbstractThe nature of the non-linear interaction between two gravitational waves in the general theory of relativity is considered. A new exact solution of the vacuum field equations describing this case is given. It describes two gravitational waves with both transverse and longitudinal components, propagating in opposite directions along ‘shearing’ and ‘twisting’ geodesic congruences with zero contraction

Exact solutions of the Einstein vacuum field equations in Weyl co-ordinates

1969 ◽  
Vol 61 (2) ◽  
pp. 411-424 ◽  
Author(s):  
R. Gautreau ◽  
R. B. Hoffman
Keyword(s):  
Exact Solutions ◽  
Vacuum Field ◽  
Field Equations ◽  
Einstein Vacuum
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