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Non-Maxwellian metaequilibria can exist in low-collisionality plasmas as evidenced by satellite and laboratory measurements. By including the full pressure tensor dynamics in a fluid plasma model, we show that a sheared velocity field can…
Extensions of Einstein's General Relativity (GR) can formally be given a GR structure in which additional geometric degrees of freedom are mapped on an effective energy-momentum tensor. The corresponding effective cosmic medium can then be…
The semi-review paper studies the null geodesics which appear for black hole solutions in the gravitational $4d$ model with anisotropic fluid. The equations of state for the fluid and solutions itselves depend upon integer parameter $q = 1,…
In this paper, we derive multiple anisotropic analogs from the established isotropic model by means of the gravitational decoupling approach in a fluid-geometry interaction based theory. To accomplish this, we initially consider a static…
A formalism for anisotropic fluid dynamics is proposed. It is designed to describe boost-invariant systems with anisotropic pressure. Such systems are expected to be produced at the early stages of relativistic heavy-ion collisions, when…
In the present paper we have discussed the mechanics of incompressible test bodies moving in Riemannian spaces with non-trivial curvature tensors. For Hamilton's equations of motion the solutions have been obtained in the parametrical form…
In this talk a sufficient condition for a diagonal orthogonally transitive cylindrical $G_2$ metric to be geodesically complete is given. The condition is weak enough to comprise all known diagonal perfect fluid cosmological models that are…
We derive the equations of motion for a system undergoing boost-invariant longitudinal and azimuthally-symmetric transverse "Gubser flow" using leading-order anisotropic hydrodynamics. This is accomplished by assuming that the one-particle…
In this paper, we prove Ruelle's inequality for the geodesic flow in non-compact manifolds with Anosov geodesic flow and some assumptions on the curvature. In the same way, we obtain Pesin's formula for Anosov geodesic flow in non-compact…
A new important relation between fluid mechanics and differential geometry is established. We study smooth steady solutions to the Euler equations with the additional property: the velocity vector is orthogonal to the gradient of the…
We propose an effective anisotropic fluid description for a generic infrared-modified theory of gravity. In our framework, the additional component of the acceleration, commonly attributed to dark matter, is explained as a radial pressure…
The primary goal of this paper is to develop robust methods to handle two ubiquitous features appearing in the modeling of geophysical flows: (i) the anisotropy of the viscous stress tensor, (ii) stratification effects. We focus on the…
We construct a category of examples of partially hyperbolic geodesic flows which are not Anosov, deforming the metric of a compact locally symmetric space of nonconstant negative curvature. Candidates for such example as the product metric…
The affine motion of two-dimensional (2d) incompressible fluids surrounded by vacuum can be reduced to a completely integrable and globally solvable Hamiltonian system of ordinary differential equations for the deformation gradient in ${\rm…
The framework of anisotropic hydrodynamics is generalized to include finite particle masses. Two schemes are introduced and their predictions compared with exact solutions of the kinetic equation in the relaxation time approximation. The…
Any closed, oriented, hyperbolic three-manifold with nontrivial second homology has many quasigeodesic flows, where quasigeodesic means that flow lines are uniformly efficient in measuring distance in relative homotopy classes. The flows…
We investigate the geodesic motions of a massive particle and light ray in the hyperplane orthogonal to the symmetry axis in the 5-dimensional hypercylindrical spacetime. The class of the solutions depends on one constant a which is the…
A spacetime endowed with an anisotropic fluid is proposed for the interior of a Schwarzschild black hole. The geometry has an instantaneous Minkowski form and is a solution of Einstein's equations with a stress tensor on the r.h.s. obeying…
It is shown that small elements of perfect fluid in adiabatic processes move along geodesic lines of a Riemannian space-time.
The elusive physical nature of Horndeski gravity is elucidated in a new approach depicting this class of theories as a dissipative effective fluid. Requiring the constitutive equations of the latter to be those of a Newtonian fluid…