Related papers: Shear free barotropic perfect fluids cannot rotate…
In this article we write the equations of barotropic compressible fluid mechanics as a geodesic equation on an infinite-dimensional manifold. The equations are given by \begin{align} u_t + \nabla_uu = -\frac{1}{\rho} \grad p \\ \rho_t +…
Slowly rotating perfect fluid balls with regular center and asymptotically flat exterior are considered to second order in the rotation parameter. The necessary condition for being Petrov type D is given for general perfect fluid matter. As…
We prove that in Robertson-Walker space-times (and in generalized Robertson-Walker spacetimes of dimension greater than 3 with divergence-free Weyl tensor) all higher-order gravitational corrections of the Hilbert-Einstein Lagrangian…
Gravitational collapse of a spherically symmetric homogeneous perfect barotropic fluid with linear as well as polytropic type Equation of State (EoS) has been investigated in the framework of a linear model of $f(R,T)$ gravity. This…
The fluid dynamics video shows rigid, spatially asymmetric bodies interacting with oscillating background flows. A free rigid object, here a hollow "pyramid," can hover quite stably against gravity in the oscillating airflow with a zero…
In a recent series of papers new exact analytical interior spacetimes sourced by stationary rigidly rotating cylinders of fluids have been displayed. A fluid with an axially directed pressure has been first considered, then a perfect fluid,…
The full set of equations governing the evolution of self--gravitating spherically symmetric dissipative fluids with anisotropic stresses is deployed and used to carry out a general study on the behaviour of such systems, in the context of…
It has been argued that an extended, quasi-rigid body evolving freely in curved spacetime can deviate from its natural trajectory by simply performing cyclic deformations. More interestingly, in the limit of rapid cycles, the amount of…
An inhomogeneous fluid in accelerated motion is investigated. When the velocity field $v(x)$ is not constant, the geometry viewed by a static observer is curved, as if the observer were immersed in a gravitational field. A…
Skew-symmetric massless fields, their potentials being $r$-forms, are close analogues of Maxwell's field (though the non-linear cases also should be considered). We observe that only two of them ($r=$2 and 3) automatically yield…
We consider various forms of action allowing us to describe a perfect fluid in the framework of General Relativity. First we consider a potential motion without pressure. Starting from an action in terms of the current density vector built…
We consider the interaction of a compressible fluid with a flexible plate in two space dimensions. The fluid is described by the Navier--Stokes equations in a domain that is changing in accordance with the motion of the structure. The…
The equations governing the flow of a viscous incompressible fluid around a rigid body that performs a prescribed time-periodic motion with constant axes of translation and rotation are investigated. Under the assumption that the period and…
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…
In this paper we study the motion of an internal water wave and an internal wave in a porous medium. For these problems we establish that, if the free boundary and, in the case of the Euler equations, also the tangential velocity at the…
Ho\v{r}ava--Lifshitz gravity has covariance only under the foliation-preserving diffeomorphism. This implies that the quantities on the constant-time hypersurfaces should be regular. In the original theory, the projectability condition,…
The motion of a deformable active particle in linear shear flow is explored theoretically. Based on symmetry considerations, in two spatial dimensions, we propose coupled nonlinear dynamical equations for the particle position, velocity,…
We consider the subject of self--binding in static, spherically symmetric objects consisting of a charged fluid. We have shown previously that in the case of a perfect fluid, only the localized part of the mass contributes to gravitational…
The implications of shearfree condition on instability range of anisotropic fluid in $f(R,T)$ are studied in this manuscript. A viable $f(R, T)$ model is chosen to arrive at stability criterion, where $R$ is Ricci scalar and $T$ is the…
It is shown that time-harmonic motions of spherical and toroidal surfaces can be deformed non-locally without loosing the existence of infinitely many constants of the motion.