Related papers: On a weak solution of Einstein equations for expan…
We give a model of the higher-dimensional spherically symmetric gravitational collapse of a dust cloud in Einstein-Gauss-Bonnet gravity. A simple formulation of the basic equations is given for the spacetime $M \approx M^2 \times K^{n-2}$…
The equation of motion announced in the title was already deduced for the cases the inner metric being flat and the shell being negligibly small (test matter), using surface layers and geodesic trajectories resp. Here we derive the general…
We consider a system representing self-gravitating balls of dust in an expanding Universe. It is demonstrated that one can prescribe data for such a system at infinity and evolve it backward in time without the development of shocks or…
Models of effective stellar collapse inspired by loop quantum gravity predict a bounce when the stellar energy density reaches the Planck scale, typically followed by the formation of shell-crossing singularities. This work aims to extend…
In this work we contrast the behaviour of two spherically symmetric matter models in a class of spherically symmetric spacetimes which feature a weak null singularity. This class in particular contains spherically symmetric perturbations of…
The weak-strong uniqueness of solutions to a broad class of cross-diffusion systems with volume filling is established. In general, the diffusion matrices are neither symmetric nor positive definite. This issue is overcome by supposing that…
A class of spherical collapsing exact solutions with electromagnetic charge is derived. This class of solutions -- in general anisotropic -- contains however as a particular case the charged dust model already known in literature. Under…
The Raychaudhuri equations for the expansion, shear and vorticity are generalized in a spacetime with torsion for timelike as well as null congruences. These equations are purely geometrical like the original Raychaudhuri equations and…
A piecewise Tolman-Bondi-Lemaitre (TBL) cell-model for the universe incorporating local collapsing and expanding inhomogeneities is presented here. The cell-model is made up of TBL underdense and overdense spherical regions surrounded by an…
Approximations are commonly employed to find approximate solutions to the Einstein equations. These solutions, however, are usually only valid in some specific spacetime region. A global solution can be constructed by gluing approximate…
In this paper we analyze the interaction of an incompressible Newtonian fluid with a linearly elastic Koiter shell whose motion is restricted to transverse displacements. The middle surface of the shell constitutes the mathematical boundary…
The existence and uniqueness of weak solutions is shown for a system related to the Willis model of elastodynamics. Both the whole space case and the case of a bounded smooth domain are studied. To this end the equations are reformulated as…
The universe is viewed as a dust gas filling a sphere and floating in infinite empty space. Einstein's gravitational equations are applied to this case together with appropriate boundary values. The equations are solved for initial…
The collapse of thin dust shells in 2+1 dimensional gravity with and without a cosmological constant in analyzed. A critical value of the shell's mass as a function of its radius and position is derived. For $\Lambda < 0$, a naked…
Physical (and weak) regularity conditions are used to determine and classify all the possible types of spherically symmetric dust spacetimes in general relativity. This work unifies and completes various earlier results. The junction…
Exact solutions to static and non-static Einstein-Maxwell equations in the presence of extremely charged dust embedded on thin shells are constructed. Singularities of multi-black hole Majumdar-Papapetrou and Kastor-Trashen solutions are…
A rotating metric solution in Einstein-Gauss-Bonnet gravity with a negative cosmological constant was recently found in the Chern-Simons point. We construct a rotating thin shell gluing two spacetimes in Einstein-Gauss-Bonnet gravity, using…
Five tensor equations are obtained for a thin shell in Gauss-Bonnet gravity. There is the well known junction condition for the singular part of the stress tensor intrinsic to the shell, which we also prove to be well defined. There are…
A simple model for a scalar field and gravity admits homogeneous isotropic cosmological solutions which cross the Big Bang singularity. In the scaling frame with field dependent effective Planck mass these solutions are regular. They become…
We classify all spherically symmetric dust solutions of Einstein's equations which are self-similar in the sense that all dimensionless variables depend only upon $z\equiv r/t$. We show that the equations can be reduced to a special case of…