GRAVITATIONAL COLLAPSE OF NEWTONIAN STARS

2000 ◽  
Vol 09 (01) ◽  
pp. 35-42 ◽  
Author(s):  
JUNG-HWAN JUN ◽  
YOUNG KWAK HO
Keyword(s):  
Equation Of State ◽  
Gravitational Collapse ◽  
Analytic Solutions ◽  
Ideal Gas ◽  
Oscillatory Behavior ◽  
Small Oscillation ◽  
Spherically Symmetric ◽  
Thermodynamic Equation ◽  
Spherically Symmetric Solutions ◽  
Collapse Behavior

We investigate spherically symmetric solutions for nonrelativistic cosmological fluid equations and thermodynamic equation of state for Newtonian stars of ideal gas. Using simple ansätze it is shown that the assumption of a polytrope, [Formula: see text], at the center of the star only suffices to obtain analytic solutions. We find collapse behavior for γ≤4/3 and oscillatory behavior for γ>4/3 along with the discussion on their mechanisms. For the oscillatory behavior we obtained the frequency of small oscillation ω which is [Formula: see text] times that obtained by Zel'dovich and Novikov.

scholarly journals Turning Point Principle for Relativistic Stars

2021 ◽  
Vol 387 (2) ◽  
pp. 729-759
Author(s):  
Mahir Hadžić ◽  
Zhiwu Lin
Keyword(s):  
Equation Of State ◽  
Gravitational Collapse ◽  
Turning Point ◽  
Euler System ◽  
Gravitation Theory ◽  
Spherically Symmetric ◽  
University Of Chicago ◽  
Relativistic Stars ◽  
The University ◽  
University Of Chicago Press

AbstractUpon specifying an equation of state, spherically symmetric steady states of the Einstein-Euler system are embedded in 1-parameter families of solutions, characterized by the value of their central redshift. In the 1960’s Zel’dovich (Voprosy Kosmogonii 9:157–170, 1963) and Harrison et al. (Gravitation Theory and Gravitational Collapse. The University of Chicago press, Chicago, 1965) formulated a turning point principle which states that the spectral stability can be exchanged to instability and vice versa only at the extrema of mass along the mass-radius curve. Moreover the bending orientation at the extrema determines whether a growing mode is gained or lost. We prove the turning point principle and provide a detailed description of the linearized dynamics. One of the corollaries of our result is that the number of growing modes grows to infinity as the central redshift increases to infinity.

scholarly journals Simple analytic solution of fireball hydrodynamics

Open Physics ◽  
2004 ◽  
Vol 2 (4) ◽  
Author(s):  
Tamás Csörgő
Keyword(s):  
Equation Of State ◽  
Temperature Profile ◽  
Analytic Solution ◽  
Analytic Solutions ◽  
Ideal Gas ◽  
New Family ◽  
Special Cases ◽  
Rotationally Symmetric

AbstractA new family of simple analytic solutions of hydrodynamics is found for slowly expanding, rotationally symmetric fireballs assuming an ideal gas equation of state. The temperature profile is position-independent only in the collisionless gas limit. The Zimányi-Bondorf-Garpman solution and the Buda-Lund parameterization of expanding hydrodynamic particle sources are recovered as special cases. The results are applied to predict new features of proton correlations and spectra for 1.93 AGeV Ni+Ni collisions.

Classical Kinetic Theory

2018 ◽  
Author(s):  
Klaus Morawetz
Keyword(s):  
Kinetic Equation ◽  
Equation Of State ◽  
Mean Field ◽  
Ideal Gas ◽  
Hydrodynamic Equations ◽  
Free Particles ◽  
Internal Mechanism ◽  
The Mean ◽  
Energy Gains ◽  
Non Locality

The classical non-ideal gas shows that the two original concepts of the pressure based of the motion and the forces have eventually developed into drift and dissipation contributions. Collisions of realistic particles are nonlocal and non-instant. A collision delay characterizes the effective duration of collisions, and three displacements, describe its effective non-locality. Consequently, the scattering integral of kinetic equation is nonlocal and non-instant. The non-instant and nonlocal corrections to the scattering integral directly result in the virial corrections to the equation of state. The interaction of particles via long-range potential tails is approximated by a mean field which acts as an external field. The effect of the mean field on free particles is covered by the momentum drift. The effect of the mean field on the colliding pairs causes the momentum and the energy gains which enter the scattering integral and lead to an internal mechanism of energy conversion. The entropy production is shown and the nonequilibrium hydrodynamic equations are derived. Two concepts of quasiparticle, the spectral and the variational one, are explored with the help of the virial of forces.

scholarly journals FERMIONS IN THE BACKGROUND OF DILATONIC SPHALERONS

1994 ◽  
Vol 09 (40) ◽  
pp. 3731-3739 ◽  
Author(s):  
GEORGE LAVRELASHVILI
Keyword(s):  
Gauge Field ◽  
Field Potential ◽  
Spherically Symmetric ◽  
Yang Mills ◽  
Zero Modes ◽  
Discrete Sequence ◽  
Number Of Zeros ◽  
Spherically Symmetric Solutions ◽  
Static Spherically Symmetric Solutions

We discuss the properties and interpretation of a discrete sequence of a static spherically symmetric solutions of the Yang-Mills dilaton theory. This sequence is parametrized by the number of zeros, n, of a component of the gauge field potential. It is demonstrated that solutions with odd n possess all the properties of the sphaleron. It is shown that there are normalizable fermion zero modes in the background of these solutions. The question of instability is critically analyzed.

Sign in / Sign up

Export Citation Format

Share Document