A variational principle and a stability criterion for the dipole modes of pulsation of stellar models in general relativity

1975 ◽  
Vol 201 ◽  
pp. 440 ◽  
Author(s):  
S. L. Detweiler
Keyword(s):  
General Relativity ◽  
Variational Principle ◽  
Stability Criterion ◽  
Stellar Models

Analytic stellar models in general relativity

1975 ◽  
Vol 198 ◽  
pp. 507 ◽  
Author(s):  
R. C. Adams ◽  
J. M. Cohen
Keyword(s):  
General Relativity ◽  
Stellar Models

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.

scholarly journals Creating Generalized and Hybrid Set and Library with Neutrosophy and Quad-Stage Method

2016 ◽  
pp. 308-320
Author(s):  
Yuhua Fu
Keyword(s):  
General Relativity ◽  
Variational Principle ◽  
Uncertainty Principle ◽  
Neutrosophic Set ◽  
Unified Theory ◽  
Law Of Gravity

Generalized and hybrid set can be created with neutrosophy and quad-stage method. Firstly the generalized and hybrid neutrosophic set is discussed. Secondly the combination or synthetical body of generalized and hybrid sets is named as “library” (various generalized and hybrid sets can be put into the related “library”); such as “mathematics library”, “physics library”, and the like. As for the constitution of “library”, the concept and methodology of a special “Four-library” are proposed. Neutrosophy and quad-stage method can also be used to solve many actual problems within the framework of “set” and “library”; for example, based on the analyses of one “Four-library”, jointly solving problem of advance of planet's perihelion with partial results of law of gravity and general relativity; and jointly expanding “uncertainty principle” to “certainty-uncertainty principle set”. Finally, we introduce the concepts of “variational principle of set” and “variational principle of library”, and establish a kind of “partial and temporary unified theory of mathematics so far”.

scholarly journals Bimetric variational principle for general relativity

2012 ◽  
Vol 86 (8) ◽  
Author(s):  
Jose Beltrán Jiménez ◽  
Alexey Golovnev ◽  
Mindaugas Karčiauskas ◽  
Tomi S. Koivisto
Keyword(s):  
General Relativity ◽  
Variational Principle

ON EQUATIONS OF MOTION IN GENERAL RELATIVITY

1955 ◽  
Vol 33 (12) ◽  
pp. 824-827
Author(s):  
G. E. Tauber
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Charged Particle ◽  
Variational Principle ◽  
Classical Theory ◽  
Equations Of Motion ◽  
Field Equations

It has been shown that both the equations of motion of a charged particle in a gravitational field and the field equations can be obtained from one variational principle by suitably generalizing Dirac's classical theory of electrons.

scholarly journals Addendum to ‘Coherent Lagrangian vortices: the black holes of turbulence’

2014 ◽  
Vol 755 ◽  
Author(s):  
G. Haller ◽  
F. J. Beron-Vera
Keyword(s):  
Black Holes ◽  
General Relativity ◽  
Variational Principle ◽  
Strain Tensor ◽  
Null Geodesics ◽  
Lorentzian Metric ◽  
Lagrange Strain ◽  
Mathematical Analogy

AbstractIn Haller & Beron-Vera (J. Fluid Mech., vol. 731, 2013, R4) we developed a variational principle for the detection of coherent Lagrangian vortex boundaries. The solutions of this variational principle turn out to be closed null geodesics of the Lorentzian metric induced by a generalized Green–Lagrange strain tensor family. This metric interpretation implies a mathematical analogy between coherent Lagrangian vortex boundaries and photon spheres in general relativity. Here, we give an improved discussion of this analogy.

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