Related papers: Collapsing Spheres Satisfying An "Euclidean Condit…

The consideration of the so-called rotation minimizing frames allows for a simple and elegant characterization of plane and spherical curves in Euclidean space via a linear equation relating the coefficients that dictate the frame motion.…

In this paper we consider spherically symmetric general fluids with heat flux, motivated by causal thermodynamics, and give the appropriate set of conditions that define separating shells defining the divide between expansion and collapse.…

Static spherically symmetric solutions of the Einstein's field equations in isotropic coordinates representing perfect fluid matter distributions from Newtonian potential-density pairs are investigated. The approach is illustrated with…

The purpose of this paper is to further investigate the solution space of self-similar spherically symmetric perfect-fluid models and gain deeper understanding of the physical aspects of these solutions. We achieve this by combining the…

We study the evolution of radiating and viscous fluid spheres assuming an additional homothetic symmetry on the spherically simmetric space--time. We match a very simple solution to the symmetry equations with the exterior one (Vaidya). We…

We exhibit a simple and explicit formula for the metric of an arbitrary static spherically symmetric perfect fluid spacetime. This class of metrics depends on one freely specifiable monotone non-increasing generating function. We also…

We express Einstein's field equations for a spherically symmetric ball of general fluid such that they are conducive to an initial value problem. We show how the equations reduce to the Vaidya spacetime in a non-null coordinate frame,…

We study the evolution of a perfect--fluid sphere coupled to a scalar radiation field. By ensuring a Ricci invariant regularity as a conformally flat spacetime at the central world line we find that the fluid coupled to the scalar field…

The dynamics of a circular thin vortex ring and a sphere moving along the symmetry axis of the ring in an inviscid incompressible fluid is studied on the basis of Euler's equations of motion. The equations of motion for position and radius…

This paper presents a class of exact spherical symmetric solutions of the Einstein equations admitting heat-conducting anisotropic fluid as a collapsing matter. The exterior spacetime is assumed to be the Vaidya metric. This class of…

In this paper we consider the novel scenario where a spherically symmetric perfect fluid star is undergoing continual gravitational collapse while continuously radiating energy in an exterior radiating spacetime. There are no trapped…

Hodograph equations for the Euler equation in curved spaces with constant pressure are discussed. It is shown that the use of known results concerning geodesics and associated integrals allows to construct several types of hodograph…

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…

The structure of the Einstein field equations describing the gravitational collapse of spherically symmetric isotropic fluids is analyzed here for general equations of state. A suitable system of coordinates is constructed which allows us,…

We study the evolution of an anisotropic shear-free fluid with heat flux and kinematic self-similarity of the second kind. We found a class of solution to the Einstein field equations by assuming that the part of the tangential pressure…

We study the spherically symmetric collapse of a perfect fluid using area-radial coordinates. We show that analytic mass functions describe a static regular centre in these coordinates. In this case, a central singularity can not be…

We study some properties of static spherically symmetric elastic bodies in general relativity using both analytical and numerical tools. The materials considered belong to the class of John elastic materials and reduce to perfect fluids…

A class of solutions to Einstein field equations is studied, which represents gravitational collapse of thick spherical shells made of self-similar and shear-free fluid with heat flow. It is shown that such shells satisfy all the energy…

We study the gravitational collapse of a non-interacting mix of perfect fluid and a spatially homogeneous scalar field within a Chiellini-integrable framework. We choose an extended Higgs-type self-interaction potential and reduce the…

Exact self-consistent particle-like solutions with spherical and/or cylindrical symmetry to the equations governing the interacting system of scalar, electromagnetic and gravitational fields have been obtained. As a particular case it is…