General Relativistic Variational Principle for Perfect Fluids

1954 ◽  
Vol 94 (6) ◽  
pp. 1468-1470 ◽  
Author(s):  
A. H. Taub
Keyword(s):  
Variational Principle ◽  
Perfect Fluids ◽  
General Relativistic

scholarly journals The Hamiltonian structure of general relativistic perfect fluids

1985 ◽  
Vol 99 (3) ◽  
pp. 319-345 ◽  
Author(s):  
David Bao ◽  
Jerrold Marsden ◽  
Ronald Walton
Keyword(s):  
Hamiltonian Structure ◽  
Perfect Fluids ◽  
General Relativistic

A NONSINGULAR PERFECT FLUID CLASSICAL LEPTON MODEL OF ARBITRARILY SMALL RADIUS

2013 ◽  
Vol 22 (14) ◽  
pp. 1350088 ◽  
Author(s):  
THOMAS E. KIESS
Keyword(s):  
Electric Field ◽  
Perfect Fluid ◽  
Small Radius ◽  
Spherically Symmetric ◽  
Model Based ◽  
Perfect Fluids ◽  
General Relativistic ◽  
Relativistic Models ◽  
Lepton Model

We exhibit a classical lepton model based on a perfect fluid that reproduces leptonic charges and masses in arbitrarily small volumes without metric singularities or pressure discontinuities. This solution is the first of this kind to our knowledge, because to date the only classical general relativistic models that have reproduced leptonic charges and masses in arbitrarily small volumes are based on imperfect (anisotopic) fluids or perfect fluids with electric field discontinuities. We use a Maxwell–Einstein exact metric for a spherically symmetric static perfect fluid in a region in which the pressure vanishes at a boundary, beyond which the metric is of the Reissner–Nordström form. This construction models lepton mass and charge in the limit as the boundary → 0.

scholarly journals SELFGRAVITATION IN A GENERAL-RELATIVISTIC ACCRETION OF STEADY FLUIDS

2007 ◽  
Vol 04 (01) ◽  
pp. 197-208 ◽  
Author(s):  
BOGUSZ KINASIEWICZ ◽  
PATRYK MACH ◽  
EDWARD MALEC
Keyword(s):  
Total Mass ◽  
Accretion Rate ◽  
The Other ◽  
Newtonian Gravity ◽  
Spherically Symmetric ◽  
Steady Flows ◽  
Fluid Content ◽  
Mass Accretion Rate ◽  
Perfect Fluids ◽  
General Relativistic

The selfgravity of an infalling gas can alter significantly the accretion of gases. In the case of spherically symmetric steady flows of polytropic perfect fluids the mass accretion rate achieves maximal value when the mass of the fluid is 1/3 of the total mass. There are two weakly accreting regimes, one over-abundant and the other poor in fluid content. The analysis within the newtonian gravity suggests that selfgravitating fluids can be unstable, in contrast to the accretion of test fluids.

scholarly journals Points of general relativistic shock wave interaction are ‘regularity singularities’ where space–time is not locally flat

2012 ◽  
Vol 468 (2146) ◽  
pp. 2962-2980 ◽  
Author(s):  
Moritz Reintjes ◽  
Blake Temple
Keyword(s):  
Shock Wave ◽  
Wave Interaction ◽  
Delta Function ◽  
Space Time ◽  
Coordinate Transformations ◽  
Metric Tensor ◽  
Shock Wave Interaction ◽  
Perfect Fluids ◽  
Time Singularities ◽  
General Relativistic

We show that the regularity of the gravitational metric tensor in spherically symmetric space–times cannot be lifted from C 0,1 to C 1,1 within the class of C 1,1 coordinate transformations in a neighbourhood of a point of shock wave interaction in General Relativity, without forcing the determinant of the metric tensor to vanish at the point of interaction. This is in contrast to Israel's theorem, which states that such coordinate transformations always exist in a neighbourhood of a point on a smooth single shock surface. The results thus imply that points of shock wave interaction represent a new kind of regularity singularity for perfect fluids evolving in space–time, singularities that make perfectly good sense physically, that can form from the evolution of smooth initial data, but at which the space–time is not locally Minkowskian under any coordinate transformation. In particular, at regularity singularities, delta function sources in the second derivatives of the metric exist in all coordinate systems of the C 1,1 -atlas, but due to cancellation, the full Riemann curvature tensor remains supnorm bounded .

Shear-free fluids in general relativity

1986 ◽  
Vol 64 (2) ◽  
pp. 191-199 ◽  
Author(s):  
C. B. Collins
Keyword(s):  
General Relativity ◽  
Equation Of State ◽  
Global Scale ◽  
Rigid Rotation ◽  
Perfect Fluids ◽  
Global Properties ◽  
Barotropic Equation ◽  
General Relativistic ◽  
Frw Models ◽  
Friedmann Robertson Walker

For a large class of shear-free general-relativistic perfect fluids that obey a barotropic equation of state, either the expansion or the rotation is zero; well-known examples include the Friedmann–Robertson–Walker (FRW) models, the Gödel solution, and stationary axisymmetric systems in rigid rotation. It has been conjectured that this is necessarily the case. Several results prove that restricted versions of this conjecture are valid, although no proof is known for the general case. A survey of these special results is given, together with physical and mathematical reasons for the study of shear-free fluids.If the conjecture is true, then there are three mutually exclusive subclasses, according to whether or not the expansion and the rotation are zero separately or simultaneously. Of these, the physically most interesting subclass is that in which the expansion is not zero, since this subclass might be thought to contain space-times that are suitable for the description of collapsing stars or expanding cosmologies. All space-times of this particular subclass are given, and their global properties are investigated. It turns out that the FRW models are the only ones in which the matter is physically reasonable on a global scale. This consequently provides a global uniqueness theorem for the FRW models.

A note on Hamilton's principle for perfect fluids

1970 ◽  
Vol 44 (1) ◽  
pp. 19-31 ◽  
Author(s):  
Francis P. Bretherton
Keyword(s):  
Variational Principle ◽  
Equations Of Motion ◽  
Velocity Fields ◽  
Lagrangian Formulation ◽  
Hamilton’S Principle ◽  
Hamilton's Principle ◽  
Barotropic Fluid ◽  
Perfect Fluids ◽  
Vortex Lines ◽  
Equal Density

A derivation is given of the Eulerian equations of motion directly from the Lagrangian formulation of Hamilton's principle. The circulation round a circuit of material particles of uniform entropy appears as a constant of the motion associated with the indistinguishability of fluid elements with equal density, entropy and velocity. A discussion is given of the Lin constraint, and it is pointed out that, for a barotropic fluid, the variational principle recently suggested by Seliger & Whitham does not permit velocity fields in which the vortex lines are knotted.

Shear-free perfect fluids with divergence free magnetic Weyl curvature

2008 ◽  
Vol 30 ◽  
pp. 241-244
Author(s):  
N. Van den Bergh ◽  
H. Reza Karimian
Keyword(s):  
Weyl Curvature ◽  
Perfect Fluids ◽  
Divergence Free
Sign in / Sign up

Export Citation Format

Share Document