A variational principle for the even-parity perturbations of spherically symmetric star clusters in general relativity

1979 ◽  
Vol 229 ◽  
pp. 1098 ◽  
Author(s):  
J. R. Ipser ◽  
R. Semenzato
Keyword(s):  
General Relativity ◽  
Variational Principle ◽  
Star Clusters ◽  
Spherically Symmetric ◽  
Symmetric Star

Odd-parity perturbations of spherically symmetric star clusters in general relativity

1981 ◽  
Vol 247 ◽  
pp. 671 ◽  
Author(s):  
R. Semenzato ◽  
J. R. Ipser
Keyword(s):  
General Relativity ◽  
Star Clusters ◽  
Spherically Symmetric ◽  
Symmetric Star

Relativistic, Spherically Symmetric Star Clusters. III. Stability of Compact Isotropic Models

1969 ◽  
Vol 158 ◽  
pp. 17 ◽  
Author(s):  
James R. Ipser
Keyword(s):  
Star Clusters ◽  
Spherically Symmetric ◽  
Symmetric Star

scholarly journals EXPANSIONFREE FLUID EVOLUTION AND SKRIPKIN MODEL IN f(R) THEORY

2011 ◽  
Vol 20 (11) ◽  
pp. 2239-2252 ◽  
Author(s):  
M. SHARIF ◽  
H. RIZWANA KAUSAR
Keyword(s):  
General Relativity ◽  
The Self ◽  
Spherically Symmetric ◽  
Junction Conditions ◽  
Dynamical Equations ◽  
Constant Energy ◽  
Isotropic Pressure ◽  
Symmetric Star ◽  
Constant Energy Density ◽  
General Influence

We consider the modified f(R) theory of gravity whose higher-order curvature terms are interpreted as a gravitational fluid or dark source. The gravitational collapse of a spherically symmetric star, made up of locally anisotropic viscous fluid, is studied under the general influence of the curvature fluid. Dynamical equations and junction conditions are modified in the context of f(R) dark energy and by taking into account the expansionfree evolution of the self-gravitating fluid. As a particular example, the Skripkin model is investigated which corresponds to isotropic pressure with constant energy density. The results are compared with corresponding results in General Relativity.

scholarly journals Compact Nuclei of Galaxies and Sources of Their Energy

1999 ◽  
Vol 194 ◽  
pp. 323-323
Author(s):  
L.Sh. Grigoryan ◽  
G.S. Sahakian
Keyword(s):  
Equation Of State ◽  
Star Clusters ◽  
Galactic Nuclei ◽  
Star Cluster ◽  
Statistical Equilibrium ◽  
Spherically Symmetric ◽  
Symmetric Star ◽  
Age Of The Universe ◽  
The Universe

A model of compact nuclei of galaxies as spherically-symmetric star clusters is proposed. A concept of the equation of state for star clusters in statistical equilibrium is introduced (galactic nuclei are systems in statistical equilibrium if their age is of the order of the age of the Universe). It is shown that a statistically equilibrium star cluster is described by the equation of state of a polytrope P = aρ3, and with its help the main parameters of compact nuclei of galaxies are calculated. The formula M = 2.524GR5/a for mass M and radius R of the cluster is derived.

Relativistic Stellar Dynamics in Rotating Axially Symmetric Systems

1968 ◽  
Vol 1 (3) ◽  
pp. 86-87 ◽  
Author(s):  
E.D. Fackerell
Keyword(s):  
General Relativity ◽  
Star Clusters ◽  
Stellar Dynamics ◽  
Spherically Symmetric ◽  
Axially Symmetric ◽  
Relativistic Star ◽  
General Relativistic ◽  
Stellar Sources ◽  
Symmetric Systems

Recently the possibility has been raised of using general relativistic star clusters as models for quasi-stellar sources. The theory of static, spherically symmetric, collisionless star clusters has been developed within the framework of general relativity. In particular, analogues have been found of the Newtonian polytropic models and of Woolley’s truncated Maxwellian systems. However, in view of the importance of rotation on stability in relativistic astrophysical problems, it is of considerable interest to include the effect of rotation in relativistic stellar dynamics.

scholarly journals The Concentric Shell Method for Relativistic Star Clusters

1975 ◽  
Vol 69 ◽  
pp. 433-439 ◽  
Author(s):  
E. D. Fackerell
Keyword(s):  
Star Clusters ◽  
Spherically Symmetric ◽  
Spherical Shells ◽  
Relativistic Star ◽  
Symmetric Star ◽  
Concentric Shell

The analytic aspects of the Campbell-Hénon method of concentric spherical shells are generalized for application to relativistic spherically symmetric star clusters.

Relativistic, Spherically Symmetric Star Clusters. I. Stability Theory for Radial Perturbations

1968 ◽  
Vol 154 ◽  
pp. 251 ◽  
Author(s):  
James R. Ipser ◽  
Kip S. Thorne
Keyword(s):  
Stability Theory ◽  
Star Clusters ◽  
Spherically Symmetric ◽  
Symmetric Star

scholarly journals Off-Shell Noether Currents and Potentials for First-Order General Relativity

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 348
Author(s):  
Merced Montesinos ◽  
Diego Gonzalez ◽  
Rodrigo Romero ◽  
Mariano Celada
Keyword(s):  
General Relativity ◽  
Vector Fields ◽  
Killing Vector ◽  
Spherically Symmetric ◽  
Killing Vector Fields ◽  
Arbitrary Vector ◽  
Four Dimensions ◽  
First Order ◽  
Direct Form ◽  
Definition Of

We report off-shell Noether currents obtained from off-shell Noether potentials for first-order general relativity described by n-dimensional Palatini and Holst Lagrangians including the cosmological constant. These off-shell currents and potentials are achieved by using the corresponding Lagrangian and the off-shell Noether identities satisfied by diffeomorphisms generated by arbitrary vector fields, local SO(n) or SO(n−1,1) transformations, ‘improved diffeomorphisms’, and the ‘generalization of local translations’ of the orthonormal frame and the connection. A remarkable aspect of our approach is that we do not use Noether’s theorem in its direct form. By construction, the currents are off-shell conserved and lead naturally to the definition of off-shell Noether charges. We also study what we call the ‘half off-shell’ case for both Palatini and Holst Lagrangians. In particular, we find that the resulting diffeomorphism and local SO(3,1) or SO(4) off-shell Noether currents and potentials for the Holst Lagrangian generically depend on the Immirzi parameter, which holds even in the ‘half off-shell’ and on-shell cases. We also study Killing vector fields in the ‘half off-shell’ and on-shell cases. The current theoretical framework is illustrated for the ‘half off-shell’ case in static spherically symmetric and Friedmann–Lemaitre–Robertson–Walker spacetimes in four dimensions.

Sign in / Sign up

Export Citation Format

Share Document