Related papers: Structural stability and general relativity
Possibilities emerging out of the dynamical evolutions of collapsing systems are addressed in this thesis through analytical investigations of the highly non-linear Einstein Field Equations. Studies of exact solutions and their properties,…
In this paper, we prove the linear stability of weakly charged and slowly rotating Kerr-Newman black holes under coupled gravitational and electromagnetic perturbations. We show that the solutions to the linearized Einstein-Maxwell…
We consider steady state solutions of the massive, asymptotically flat, spherically symmetric Einstein-Vlasov system, i.e., relativistic models of galaxies or globular clusters, and steady state solutions of the Einstein-Euler system, i.e.,…
This paper summarises a number of new, potentially significant, results, obtained recently by the author and his collaborators, which impact on various issues related to the gravitational N-body problem, both Newtonianly and in the context…
The full set of equations governing the structure and the evolution of self--gravitating cylindrically symmetric dissipative fluids with anisotropic stresses, is written down in terms of scalar quantities obtained from the orthogonal…
We show future global non-linear stability of surface symmetric solutions of the Einstein-Vlasov system with a positive cosmological constant. Estimates of higher derivatives of the metric and the matter terms are obtained using an…
The perturbation theory plays an important role in studying structure formation in cosmology and post-Newtonian physics, but not all phenomena can be described by the linear perturbation theory. Thus, It is necessary to study exact…
After a brief summary of the foundations of general relativity, we will concentrate on the stationary exact solutions of the Einstein and Einstein-Maxwell equations. A number of these solutions can be interpreted as black holes,…
We analyze the classical stability of Schwarzschild black hole in massive conformal gravity which was recently proposed for another massive gravity model. This model in the Jordan frame is conformally equivalent to the Einstein-Weyl gravity…
We study the stability of fracton gravity, a variant of linearized gravity where the gauge symmetry is restricted to longitudinal diffeomorphisms. These transformations can be connected to a spacetime generalization of dipole symmetry,…
In $3+1$ dimensions, we study the stability of Kasner solutions for the Einstein-Maxwell-scalar field-Vlasov system. This system incorporates gravity, electromagnetic, weak and strong interactions for the initial stage of our universe. Due…
A solution to a given equation is structurally stable if it suffers only an infinitesimal change when the equation (not the solution) is perturbed infinitesimally. We have found that structural stability can be used as a velocity selection…
We investigate stability issues for steady states of the spherically symmetric Einstein-Vlasov system numerically in Schwarzschild, maximal areal, and Eddington-Finkelstein coordinates. Across all coordinate systems we confirm the…
Shape dynamics is a classical theory of gravity which agrees with general relativity in many important cases, but possesses different gauge symmetries and constraints. Rather than spacetime diffeomorphism invariance, shape dynamics takes…
Recently, zero-point length cosmology has shown some positive insights into some non-singular aspects of the early Universe. In addition, topological defects are known to play a significant role by its presence as a part of the total energy…
In order to investigate the evolutionary process of many deterministic Dynamical systems with unfixed parameter, a set of dynamical models with parameter changing continuously and the accumulation of this change might be large is introduced…
We investigate perturbations of a class of spherically symmetric solutions in massive gravity and bi-gravity. The background equations of motion for the particular class of solutions we are interested in reduce to a set of the Einstein…
We study the stability of static, spherically symmetric, traversable wormholes existing due to conformal continuations in a class of scalar-tensor theories with zero scalar field potential (so that Fisher's well-known scalar-vacuum solution…
We discuss the Sundman-Weierstrass theorem of total collapse in its historical context. This remarkable and relatively simple result, a type of stability criterion, is at the crossroads of some interesting developments in the gravitation…
Recently, static and spherically symmetric configurations of globally regular self-gravitating scalar solitons were found. These configurations are unstable with respect to radial linear perturbations. In this paper we study the dynamical…