Related papers: Nonuniqueness and Structural Stability of Self-Con…
In this paper we review a recently developed approximate method for investigation of dynamics of compressible ellipsoidal figures. Collapse and subsequent behaviour are described by a system of ordinary differential equations for time…
We investigate the emergence of singular solutions in a non-local model for a magnetic system. We study a modified Gilbert-type equation for the magnetization vector and find that the evolution depends strongly on the length scales of the…
In this work we investigate the dynamics of cosmological models with spherical topology containing up to 600 Schwarzschild black holes arranged in an irregular manner. We solve the field equations by tessellating the 3-sphere into eight…
We develop here a new procedure within Einstein's theory of gravity to generate equilibrium configurations that result as the final state of gravitational collapse from regular initial conditions. As a simplification, we assume that the…
We investigate the relevance of the conformal method by investigating stability issues for the Einstein-Lichnerowicz conformal constraint system in a nonlinear scalar-field setting. We prove the stability of the system with respect to…
We consider a self-gravitating collisionless gas as described by the Vlasov-Poisson or Einstein-Vlasov system or a self-gravitating fluid ball as described by the Euler-Poisson or Einstein-Euler system. We give a simple proof for the finite…
This article describes the Schwarzschild orbit superposition method. It is the state-of-the-art dynamical modelling tool for early-type galaxies. Tests with analytic models show that masses and orbital anisotropies of not too face-on…
We present a flexible and efficient method to construct triaxial dynamical models of galaxies with a central black hole, using Schwarzschild's orbital superposition approach. Our method is general and can deal with realistic luminosity…
A class of solutions of Einstein field equations satisfying Karmarkar embedding condition is presented which could describe static, spherical fluid configurations, and could serve as models for compact stars. The fluid under consideration…
This paper discusses the possibility of constructing time-independent solutions to the collisionless Boltzmann equation which depend on quantities other than global isolating integrals such as energy and angular momentum. The key point is…
(Abridged) We describe a new iterative approach for the realization of equilibrium N-body systems for given density distributions. Our method uses elements of Schwarzschild's technique and of the made-to-measure method, but is based on a…
The stability of equilibrium configurations of galaxies or stars are time honored problems in astrophysics. We present mathematical results on these problems which have in recent years been obtained by Yan Guo and the author in the context…
We consider the self-dual Chern-Simons-Schr\"odinger equation (CSS) under equivariance symmetry. Among others, (CSS) has a static solution $Q$ and pseudoconformal symmetry. We study the conditional stability of pseudoconformal blow-up…
The extreme Schwarzschild-de Sitter space-time is a spherically symmetric solution of Einstein's equations with a cosmological constant Lambda and mass parameter m>0 which is characterized by the condition that 9 Lambda m^2=1. The global…
We discuss the stability of (charged) static black holes in higher-dimensional spacetimes with and without cosmological constant by using gauge-invariant master equations of the Schroedinger equation type for black hole perturbations…
The non-linear stability of the sub-extremal Schwarzschild-de Sitter spacetime in the stationary region near the conformal boundary is analysed using a technique based on the extended conformal Einstein field equations and a conformal…
In this work we study a system of Schr\"odinger equations involving nonlinearities with quadratic growth. We establish sharp criterion concerned with the dichotomy global existence versus blow-up in finite time. Such a criterion is given in…
Structural optimization of non-conservative systems with respect to stability criteria is a research area with important applications in fluid-structure interactions, friction-induced instabilities, and civil engineering. In contrast to…
We study a spherical, self-gravitating fluid model, which finds applications in cosmic structure formation. We argue that since the system features nonlinearity and gravity-induced dispersion, the emergence of solitons becomes possible. We…
We study the existence and radial stability of static, spherically symmetric thin shells separating two Schwarzschild--de Sitter spacetimes with parameters $(m_\pm,\Lambda_\pm)$. Using the Israel junction formalism and a linear barotropic…