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Solutions to flat space Friedmann-Robertson-Walker cosmologies in Brans-Dicke theory with a cosmological constant are investigated. The matter is modelled as a $\gamma$-law perfect fluid. The field equations are reduced from fourth order to…
In astrophysics, the gravitational stability of a self-gravitating polytropic fluid sphere is an intriguing subject, especially when trying to comprehend the genesis and development of celestial bodies like planets and stars. This stability…
The stability of a Nambu-Goto membrane at the equatorial plane of the Reissner-Nordstr{\o}m-de Sitter spacetime is studied. The covariant perturbation formalism is applied to study the behavior of the perturbation of the membrane. The…
The stability of a rapid dynamic crack in a two dimensional infinite strip is studied in the framework of Linear Elasticity Fracture Mechanics supplemented with a modified principle of local symmetry. It is predicted that a single crack…
This paper is dedicated to revisit the modifications caused by branes in the collapse of a stellar structure under the Snyder-Oppenheimer scheme. Due to the homogeneity and isotropy of the model, we choose study the case of a closed…
We show the instability of two self-tuning brane world models with gauge invariant linear perturbation theory. This general method confirms a known instability of the original model with vanishing bulk potential. We also show the dynamical…
The stability of convection rolls in a fluid heated from below is limited by secondary instabilities, including the skew-varicose and crossroll instabilities. We observe a stability boundary defined by the same instabilities in stripe…
Following fresh attempts to resolve the problem of the energy density of the vacuum, we reconsider the case where the cosmological constant is derived from a higher-dimensional version of general relativity, and interpret the…
The property of adiabatic invariance is studied for the generalized potential satisfying the condition of identity of sphere's and point mass's gravity. That function contains a second term corresponding to the cosmological constant as…
In this manuscript, we have identified the dynamical instability constraints of a self-gravitating cylindrical object within the framework of $f(R,T)$ theory of gravity. We have explored the modified field equations and corresponding…
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 perform 3D numerical simulations in full general relativity to study the stability of rapidly rotating, supramassive neutron stars at the mass-shedding limit to dynamical collapse. We adopt an adiabatic equation of state with $\Gamma =…
The stability of Lattice Boltzmann Equations modelling Shallow Water Equations in the special case of reduced gravity is investigated theoretically. A stability notion is defined as applied in incompressible Navier-Stokes equations in…
In this lecture, I explain the gauge-invariant formulation for perturbations of background spacetimes with untwisted homologous Einstein fibres, which include lots of practically important spacetimes such as static black holes, static black…
We investigate the role played by density inhomogeneities and dissipation on the final outcome of collapse of a self-gravitating sphere. By imposing a perturbative scheme on the thermodynamical variables and gravitational potentials we…
We study the dynamics of small fluctuations about the uniform state of a crystal moving through a dissipative medium, e.g. a sedimenting colloidal crystal or a moving flux lattice, using a set of continuum equations for the displacement…
We investigate gravitational collapse of thick shell of fluid in the isotropic homogeneous universe without radiation described by the Einstein gravity with cosmological constant. We construct analytic solutions of this kind interpolating…
The gravitational field of a stationary circular cosmic string loop ,externally supported against collapse, is investigated in the context of Brans-Dicke theory in the weak field approximation of the field equations. The solution is…
We analyze previous results on the stability of uniformly and differentially rotating, self-gravitating, gaseous and stellar, axisymmetric systems to derive a new stability criterion for the appearance of toroidal, m=2 Intermediate (I) and…
Cosmological singularity and asymptotic behaviour of scale factor of generalized cosmological models are analyzed in respect of their structural stability. It is shown, that cosmological singularity is structurally unstable for the majority…