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We consider plane-symmetric spacetimes satisfying Einstein's field equations with positive cosmological constant, when the matter is a fluid whose pressure is equal to its mass-energy density (i.e. a so-called stiff fluid). We study the…
A string-inspired duality symmetry of the spatially flat Friedmann equations of general-relativistic cosmology is discussed and generalized, providing a map between exact solutions corresponding to different values of the barotropic index.
The derivation of the general solutions for stationary and static cylindrically symmetric Einstein spaces of Lewis form is revisited and the physical and geometrical meaning of the parameters appearing in the resulting solutions are…
We prove an asymptotic stability result for the water wave equations linearized around small solitary waves. The equations we consider govern irrotational flow of a fluid with constant density bounded below by a rigid horizontal bottom and…
In this paper, we have searched the existence of the similarity solution for plane symmetric inhomogeneous cosmological models in general relativity. The matter source consists of perfect fluid with proportionality relation between…
This talk gives an overview of the recently-formulated Fluid/Gravity correspondence, which was developed in the context of gauge/gravity duality. Mathematically, it posits that Einstein's equations (with negative cosmological constant) in…
The Einstein-Maxwell (or Einstein) system of field equations plays a substantial role in the modeling of compact stars. Although due to its non-linearity getting an exact solution for the system of field equations is a difficult task, the…
For general relativistic spacetimes filled with an irrotational perfect fluid a generalized form of Friedmann's equations governing the expansion factor of spatially averaged portions of inhomogeneous cosmologies is derived. The averaging…
A method of calculating a new class of symmetries is presented for partial differential equations. The method give a new dynamical solution for an isothermal and cylindrically symmetric hydrodynamics equations under self-gravity. The…
The following note shows that the symmetry of various resistance formulae, often based on Lorentz reciprocity for linearly viscous fluids, applies to a wide class of non-linear viscoplastic fluids. This follows from Edelen's non-linear…
In a recent series of papers new exact analytical solutions of the field equations of General Relativity representing interior spacetimes sourced by stationary rigidly rotating cylinders of fluids with various equations of state have been…
Static spherically symmetric anisotropic source has been studied for the Einstein-Maxwell field equations assuming the erstwhile cosmological constant $ \Lambda $ to be a space-variable scalar, viz., $ \Lambda = \Lambda(r) $. Two cases have…
Fluid-dynamical equations of motion can be derived from the Boltzmann equation in terms of an expansion around a single-particle distribution function which is in local thermodynamical equilibrium, i.e., isotropic in momentum space in the…
The linear stability of the homogeneous equilibrium of non-relativistic fluids with mass flux and special relativistic fluids with the absolute value of the energy vector as internal energy is investigated. It is proved that the equilibrium…
Einstein's field equations for spatially self-similar locally rotationally symmetric perfect fluid models are investigated. The field equations are rewritten as a first order system of autonomous ordinary differential equations.…
Spherically symmetric expansionfree distributions are systematically studied. The whole set of field equations and junction conditions are presented for a general distribution of dissipative anisotropic fluid (principal stresses unequal),…
The fluid models mentioned in the title are classified. All characteristics of the fluid are expressed through a master potential, satisfying an ordinary second order differential equation. Different constraints are imposed on this core of…
Systems of interacting networks of strings such as cosmic strings or quantum vortices can be approximated in a certain regime as an anisotropic fluid with an equation of state depending on a conserved flux. The equations for ideal…
We generalize recent work to construct a map from the conformal Navier Stokes equations with holographically determined transport coefficients, in d spacetime dimensions, to the set of asymptotically locally AdS_{d+1} long wavelength…
A solution of the linearized Einstein's equations for a spherically symmetric perturbation of the ultrarelativistic fluid in the homogeneous and isotropic universe is obtained. Conditions on the boundary of the perturbation are discussed.…