Related papers: Energetic Stability of the Solutions of the Einste…
Approximate solutions representing the gravitational-electrostatic balance of two arbitrary point sources in general relativity have led to contradictory arguments in the literature with respect to the condition of balance. Up to the…
We prove the non-linear asymptotic stability of the Schwarzschild family as solutions to the Einstein vacuum equations in the exterior of the black hole region: general vacuum initial data, with no symmetry assumed, sufficiently close to…
We present an analysis of the stability, energy and torque properties of a model Bursian diode in a one dimensional Eulerian framework using the cold Euler-Poisson fluid equations. In regions of parameter space where there are two sets of…
Via a straightforward integration of the Einstein equations with cosmological constant, all static circularly symmetric perfect fluid 2+1 solutions are derived. The structural functions of the metric depend on the energy density, which…
We present a class of thermodynamic systems with constant thermodynamic curvature which, within the context of geometric approaches of thermodynamics, can be interpreted as constant thermodynamic interaction among their components. In…
We investigate all static spherically symmetric solutions in the context of general relativity surrounded by a minimally-coupled quintessence field, using dynamical system analysis. Applying the 1+1+2 formalism and introducing suitable…
It is well known that the Schwarzschild solution describes the gravitational field outside compact spherically symmetric mass distribution in General Relativity. In particular, it describes the gravitational field outside a point particle.…
We analyze the stability of generic spherically symmetric thin shells to linearized perturbations around static solutions. We include the momentum flux term in the conservation identity, deduced from the ''ADM'' constraint and the Lanczos…
Static spherically symmetric solutions to the Einstein-Euler equations with prescribed central densities are known to exist, be unique and smooth for reasonable equations of state. Some criteria are also available to decide whether…
We investigate the properties of relativistic star spheres made of an electrically charged incompressible fluid, generalizing, thus, the Schwarzschild interior solution. The investigation is carried by integrating numerically the…
We discuss how the assumption of variable equation of state (EoS) allows the elimination of the instability at equilibrium throat radius $a_0=3M$ featured by previous Schwarzschild thin-shell wormhole models. Unobstructed stability regions…
A new class of static plane symmetric solution of Einstein field equation generated by a perfect fluid source is put forward. A special family of this new solution is investigated in detail. The constraints on the parameters by different…
This study explores singularity-free solutions to the static, spherical symmetric Einstein equations with the standard Schwarzschild solution as a boundary condition. Imposing the absence of curvature singularities and requiring…
The general solution of hydrostatic equilibrium equations for a two-component fluid of ions and electrons without a local electroneutrality constraint is found in the framework of Newtonian gravity theory. In agreement with the Poincar\'e…
We look for "static" spherically symmetric solutions of Einstein's Equations for perfect fluid source with equation of state $p=w\rho$. In order to include the possibilities of recently popularized dark energy and phantom energy possibly…
The entropic lattice Boltzmann framework proposed the construction of the discrete equilibrium by taking into consideration minimization of a discrete entropy functional. The effect of this form of the discrete equilibrium on properties of…
We consider conditions for existence and stability of a static cosmological solution in quadratic gravity. It appears that such a solution for a Universe filled by only one type of perfect fluid is possible in a wide range of the equation…
We present an algorithm to generalize a plethora of well-known solutions to Einstein field equations describing spherically symmetric relativistic fluid spheres by relaxing the pressure isotropy condition on the system. By suitably fixing…
The problem of a test body in the Schwarzschild geometry is investigated in a Keplerian limit. Beginning with the Schwarzschild metric, a solution to the limited case of approximately elliptical (Keplerian) motion is derived in terms of…
This diploma thesis analyses static, spherically symmetric perfect fluid solutions to Einstein's field equations with cosmological constant. Constant density solutions are derived for different values of the cosmological constant. Eleven…