Related papers: Expanding Spherically Symmetric Models without She…
We present new results concerning the existence of static, electrically charged, perfect fluid spheres that have a regular interior and are arbitrarily close to a maximally charged black-hole state. These configurations are described by…
The properties of some locally rotationally symmetric (LRS) perfect fluid space-times are examined in order to demonstrate the usage of the description of geometries in terms of the Riemann tensor and a finite number of its covariant…
In the present paper we analyze and discuss some mathematical aspects of the fluid-static configurations of a self-gravitating perfect gas enclosed in a spherical solid shell. The mathematical model we consider is based on the well-known…
We analyse shear-free spherically symmetric relativistic models of gravitating fluids with heat flow and electric charge defined on higher dimensional manifolds. The solution to the Einstein-Maxwell system is governed by the pressure…
Perfect fluid spacetimes admitting a kinematic self-similarity of infinite type are investigated. In the case of plane, spherically or hyperbolically symmetric space-times the field equations reduce to a system of autonomous ordinary…
It is shown that different approaches towards the solution of the Einstein equations for a static spherically symmetric perfect fluid with a gamma-law equation of state lead to an Abel differential equation of the second kind. Its only…
In this article, a special static spherically symmetric perfect fluid solution of Einstein's equations is provided. Though pressure and density both diverge at the origin, their ratio remains constant. The solution presented here fails to…
General theoretical results via a Hamiltonian formulation are developed for zonal shear flows with the inclusion of the vortex stretching effect of the deformed free surface. These results include a generalization of the…
In order to describe the dynamics of monochromatic surface waves in deep water, we derive a nonlinear and dispersive system of equations for the free surface elevation and the free surface velocity from the Euler equations in infinite…
We consider a well known model for lipid-bilayer membrane vesicles exhibiting phase separation, incorporating a phase field with finite curvature elasticity. We prove the existence of a plethora of equilibria, corresponding to…
In this paper we show that steady states $u$ of the pressureless Euler equation which belong to $L^3_{loc}(\mathbb{R}^2,\mathbb{R}^2)$ are shear flows. This is achieved by combining results of degenerate Monge-Amp\`ere-type equations with…
We determine the exact solution of the Einstein field equations for the case of a spherically symmetric shell of liquid matter, characterized by an energy density which is constant with the Schwarzschild radial coordinate $r$ between two…
In this paper, the massless Schwinger model or two dimensional quantum electrodynamics is exactly solved on a Riemann surface. The partition function and the generating functional of the correlation functions involving the fermionic…
We develop a new covariant formalism to treat spherically symmetric spacetimes in metric} f(R) theories of gravity. Using this formalism we derive the general equations for a static and spherically symmetric metric in a general…
We construct models of static spherical distributions of perfect fluid in trace--free Einstein gravity theory. The equations governing the gravitational field are equivalent to the standard Einstein's equations however, their presentation…
We consider the Einstein equations coupled to an ultrastiff perfect fluid and prove the existence of a family of solutions with an initial singularity whose structure is that of explicit isotropic models. This family of solutions is…
The algebraic properties of drift-flux two-phase fluids models without gravitational and wall friction forces are studied. More precisely, for the two fluids we consider equation of states of polytropic gases. We perform a classification…
Static spherically symmetric perfect fluid solutions are studied in metric $f(R)$ theories of gravity. We show that pressure and density do not uniquely determine $f(R)$ ie. given a matter distribution and an equation state, one cannot…
In this second of the set of two papers on Lie symmetry analysis of a class of Li\'enard type equation of the form $\ddot {x} + f(x)\dot {x} + g(x)= 0$, where over dot denotes differentiation with respect to time and $f(x)$ and $g(x)$ are…
In this thesis we consider the free surface flow due to a submerged source in a channel of finite depth. This problem has been considered previously in the literature, with some disagreement about whether or not a train of waves exist on…