Quasi-local variables, i.e. quantities whose values can be derived from physics accessible within an arbitrarily small neighborhood of a spacetime point, are used to construct the equation of state ...(EoS) for the anisotropic fluid in the spherical symmetry. One parameter families of equilibrium solutions are obtained making it possible to assess stability properties by means of the standard M(R) method. Normal modes of radial pulsation are computed as well and are found to confirm the onset of instability as predicted by the M(R) method. As an example, a stable configuration with outwardly increasing energy density in the core is obtained with a simple quasi-local extension of the polytropic EoS. It is also found that the loss of stability occurs at higher surface compactness when the anisotropy of pressures is present.
Can. J. Phys. 85 (2007) 957-965 Solutions for the static spherically symmetric extremally charged dust in the
Majumdar--Papapetrou system have been found. For a certain amount of the
allocated ...mass/charge, the solutions have singularities of a type which could
render them physically unacceptable, since the corresponding physically
relevant quantities are singular as well. These solutions, with a number of
zero-nodes in the metric tensor, are regularized through the $\delta$-shell
formalism, thus redefining the mass/charge distributions. The bifurcating
behaviour of regular solutions found before is no longer present in these
singular solutions, but quantized-like behaviour in the total mass is observed.
Spectrum of regularized solutions restores the equality of the
Tolman--Whittaker and ADM mass, as well the equality of the net charge and ADM
mass, which is the distinctive feature of Majumdar--Papapetrou systems.
We present a swarm model of Brownian particles with harmonic interactions, where the individuals undergo canonical active Brownian motion, i.e. each Brownian particle can convert internal energy to ...mechanical energy of motion. We assume the existence of a single global internal energy of the system. Numerical simulations show amorphous swarming behavior as well as static configurations. Analytic understanding of the system is provided by studying stability properties of equilibria.
Active Brownian motion is the complex motion of active Brownian particles. They are active in the sense that they can transform their internal energy into energy of motion and thus create complex ...motion patterns. Theories of active Brownian motion so far imposed couplings between the internal energy and the kinetic energy of the system. We investigate how this idea can be naturally taken further to include also couplings to the potential energy, which finally leads to a general theory of canonical dissipative systems. Explicit analytical and numerical studies are done for the motion of one particle in harmonic external potentials. Apart from stationary solutions, we study non-equilibrium dynamics and show the existence of various bifurcation phenomena.
The notion of a compact object immune to the horizon problem and comprising an anisotropic inhomogeneous fluid with a specific radial pressure behavior, i.e. the gravastar, is extended by introducing ...an electrically charged component. Einstein-Maxwell field equations are solved in the asymptotically de Sitter interior where a source of the electric field is coupled to the fluid energy density. Two different solutions which satisfy the dominant energy condition are given: one is the delta-shell model for which the analysis is carried out within Israel's thin shell formalism, the other approach - the continuous profile model - is solved numerically and the interior solutions have been (smoothly) joined with the Reissner-Nordstrom exterior. The effect of electric charge is considered, and the equation of state, the speed of sound and the surface redshift are calculated for both models.
Solutions for the static spherically symmetric extremally charged dust in the Majumdar--Papapetrou system have been found. For a certain amount of the allocated mass/charge, the solutions have ...singularities of a type which could render them physically unacceptable, since the corresponding physically relevant quantities are singular as well. These solutions, with a number of zero-nodes in the metric tensor, are regularized through the \(\delta\)-shell formalism, thus redefining the mass/charge distributions. The bifurcating behaviour of regular solutions found before is no longer present in these singular solutions, but quantized-like behaviour in the total mass is observed. Spectrum of regularized solutions restores the equality of the Tolman--Whittaker and ADM mass, as well the equality of the net charge and ADM mass, which is the distinctive feature of Majumdar--Papapetrou systems.
The Active Universe Gluck, Alexander; Huffel, Helmuth; Ilijic, Sasa ...
arXiv.org,
10/2009
Paper, Journal Article
Odprti dostop
Active motion is a concept in complex systems theory and was successfully applied to various problems in nonlinear dynamics. Explicit studies for gravitational potentials were missing so far. We ...interpret the Friedmann equations with cosmological constant as a dynamical system, which can be made active in a straightforward way. These active Friedmann equations lead to a cyclic universe, which is shown numerically.
Class. Quantum Grav. 22 (2005) 3817-3831 Static spherically symmetric distributions of electrically counterpoised dust
(ECD) are used to construct solutions to Einstein-Maxwell equations in
...Majumdar--Papapetrou formalism. Unexpected bifurcating behaviour of solutions
with regard to source strength is found for localized, as well as for the
delta-function ECD distributions. Unified treatment of general ECD
distributions is accomplished and it is shown that for certain source strengths
one class of regular solutions approaches Minkowski spacetime, while the other
comes arbitrarily close to black hole solutions.
Static spherically symmetric distributions of electrically counterpoised dust (ECD) are used to construct solutions to Einstein-Maxwell equations in Majumdar--Papapetrou formalism. Unexpected ...bifurcating behaviour of solutions with regard to source strength is found for localized, as well as for the delta-function ECD distributions. Unified treatment of general ECD distributions is accomplished and it is shown that for certain source strengths one class of regular solutions approaches Minkowski spacetime, while the other comes arbitrarily close to black hole solutions.
