Virial Relations for Uniformly Rotating Fluid Masses in General Relativity

1967 ◽  
Vol 147 ◽  
pp. 383 ◽  
Author(s):  
S. Chandrasekhar
Keyword(s):  
General Relativity ◽  
Rotating Fluid

Rotating fluid masses in general relativity. II

1966 ◽  
Vol 62 (3) ◽  
pp. 495-501 ◽  
Author(s):  
R. H. Boyer
Keyword(s):  
General Relativity ◽  
Variational Principle ◽  
First Integrals ◽  
Constant Angular Velocity ◽  
Hydrodynamic Equations ◽  
Rotating Fluid ◽  
Axially Symmetric ◽  
Field Equations ◽  
Full Field ◽  
Specific Entropy

AbstractWe describe some properties of a stationary, isolated, axially symmetric, rotating body of perfect fluid, according to general relativity. We first specialize to the case of constant specific entropy and constant angular velocity. The latter condition is equivalent to rigidity in the Born sense; both conditions are consequences of a simple variational principle. The hydrodynamic equations can then be integrated completely. Analogous first integrals are given also for the case of differential rotation. No use is made of the full field equations.

The gravitational field of a rotating fluid mass in general relativity

1962 ◽  
Vol 270 (1343) ◽  
pp. 467-492 ◽  
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Residual Energy ◽  
The Body ◽  
Energy Tensor ◽  
Constant Density ◽  
Rotating Fluid ◽  
Fluid Mass

A method recently given by Das, Florides & Synge is now slightly modified and applied to find the gravitational field of a steadily rotating fluid mass, not necessarily of constant density. The result is approximate in the sense that, outside the body, there is a residual energy tensor T ij such that is small of the order (m/a) 3 , where m is the mass of the body and a a typical radius.

Rapidly rotating fluid bodies in general relativity

1975 ◽  
Vol 200 ◽  
pp. L103 ◽  
Author(s):  
E. M. Butterworth ◽  
J. R. Ipser
Keyword(s):  
General Relativity ◽  
Rotating Fluid

Slowly rotating fluid spheres in general relativity

1983 ◽  
Vol 27 (12) ◽  
pp. 3030-3031 ◽  
Author(s):  
Selçuk Ş. Bayin
Keyword(s):  
General Relativity ◽  
Rotating Fluid ◽  
Fluid Spheres

Singularities in general relativity

1970 ◽  
Vol 48 (8) ◽  
pp. 970-980 ◽  
Author(s):  
J. Pachner
Keyword(s):  
High Pressure ◽  
General Relativity ◽  
Angular Velocity ◽  
Mass Density ◽  
Rest Mass ◽  
First Integrals ◽  
Einstein Equations ◽  
Rotating Fluid ◽  
Relativistic Limit ◽  
Local Observer

The problem of singularities is examined from the standpoint of a local observer. A singularity is defined as a state with an infinite proper rest mass density. It is proved that any inhomogeneity and anisotropy in the distribution and motion of a nonrotating ideal fluid accelerates collapse. Collapse is also inevitable in a rotating fluid in the case of extremely high pressure when the relativistic limit of the equation of state must be applied. In order to investigate the influence of rotation on the existence of singularities in incoherent matter the Einstein equations together with their first integrals are written out for the points on a vortex filament. They show that rotation decelerates the contraction of space not only in the direction perpendicular to the vector of the angular velocity, but indirectly also along this vector and can prevent the occurrence of a singularity. This conclusion is confirmed by the numerical integration of the Einstein equations. The paper concludes with a discussion of some cosmological implications.

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