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We apply the 1+1+2 covariant approach to describe a general static and spherically symmetric relativistic stellar object which contains two interacting fluids. We then use the 1+1+2 equations to derive the corresponding…
We show that the Heun confluent equation admits infinitely many solutions in terms of the confluent generalized hypergeometric functions. For each of these solutions a characteristic exponent of a regular singularity of the Heun confluent…
An important question in mathematical relativity theory is that of the nature of spacetime singularities. The equations of general relativity, the Einstein equations, are essentially hyperbolic in nature and the study of spacetime…
We study the geometry of streamlines and stability properties for steady state solutions of the Euler equations for ideal fluid.
We apply the 1+1+2 covariant semi-tetrad approach to describe a general static and spherically symmetric relativistic stellar object which contains two fluids with anisotropic pressure. The corresponding Tolman-Oppenheimer-Volkoff equations…
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…
Interior perfect fluid solutions for the Reissner-Nordstrom metric are studied on the basis of a new classification scheme. General formulas are found in many cases. Explicit new global solutions are given as illustrations. Known solutions…
An interesting and satisfactory fluid model has been proposed in literature for the the description of relativistic electron beams. It was obtained with 14 independent variables by imposing the entropy principle and the relativity…
The various schemes for studying rigidly rotating perfect fluids in general relativity are reviewed. General conclusions one may draw from these are: (i) There is a need to restrict the scope of the possible ansatze, and (ii) the angular…
Assuming conformally flat metric we obtain inhomogeneous solutions of Einstein equations with the energy-momentum of a viscous fluid. We suggest that the viscous solution can be applied as a model of an expanding inhomogeneous dark energy.
The existence of static self-gravitating Newtonian elastic balls is proved under general assumptions on the constitutive equations of the elastic material. The proof uses methods from the theory of finite-dimensional dynamical systems and…
Flexibility and rigidity properties of steady (time-independent) solutions of the Euler, Boussinesq and Magnetohydrostatic equations are investigated. Specifically, certain Liouville-type theorems are established which show that suitable…
We investigate a one-dimensional model describing the motion of liquid drops sliding down an inclined plane (the so-called quasi-static approximation model). We prove existence and uniqueness of a solution and investigate its long time…
We propose a simple algebraic method for constructing exact solutions of equations of two-dimensional hydrodynamics of an incompressible fluid. The problem reduces to consecutively solving three linear partial differential equations for a…
We investigate the field equations in the Einstein-aether theory for static spherically symmetric spacetimes and a perfect fluid source and subsequently with the addition of a scalar field (with an exponential self-interacting potential).…
The properties of LRS class II perfect fluid space-times are analyzed using the description of geometries in terms of the Riemann tensor and a finite number of its covariant derivatives. In this manner it is straightforward to obtain the…
We investigate solutions of Einstein field equations for the non-static spherically symmetric perfect fluid case using different equations of state. The properties of an exact spherically symmetric perfect fluid solutions are obtained which…
We find a new class of exact solutions to the Einstein-Maxwell equations which can be used to model the interior of charged relativistic objects. These solutions can be written in terms of special functions in general; for particular…
We present solution generating methods which allow to construct exact static solutions to the equations of four-dimensional Einstein-Maxwell-Dilaton gravity starting with arbitrary static solutions to the pure vacuum Einstein equations,…
Some classical and recent results on the Euler equations governing perfect (incompressible and inviscid) fluid motion are collected and reviewed, with some small novelties scattered throughout. The perspective and emphasis will be given…