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If we study the quantum effects in plasmas in terms of traditional hydrodynamics via the continuity and Euler equations we find the quantum Bohm potential and the force of spin-spin interaction. However, if we extend the set hydrodynamic…

We provide a covariant derivation of plasma physics coupled to gravitation by utilizing the 3+1 formulation of general relativity, including a discussion of the Lorentz force law. We then reduce the system to the spherically symmetric case…

Motion equations describing streams of relativistic particles and their properties are explored in detail in the framework of Cosmological Perturbation Theory. Those equations, derived in any metric both in the linear and nonlinear regimes,…

We propose a field-theoretic framework for ideal hydrodynamics of charged relativistic fluids formulated in terms of a complex scalar field defined on a spacelike hypersurface comoving with the fluid. In the normal phase, the dynamics of…

Charged fluids rotating around compact objects can form unique equilibrium structures when ambient large-scale electromagnetic fields combine with strong gravity. Equatorial as well as off-equatorial toroidal structures are among such…

Conservation laws have many applications in numerical relativity. However, it is not straightforward to define local conservation laws for general dynamic spacetimes due the lack of coordinate translation symmetries. In flat space, the rate…

Numerous experimental and theoretical results in liquids and plasmas suggest the presence of a critical momentum at which the shear diffusion mode collides with a non-hydrodynamic relaxation mode, giving rise to propagating shear waves.…

We investigate the convergence of relativistic hydrodynamics in charged fluids, within the framework of holography. On the one hand, we consider the analyticity properties of the dispersion relations of the hydrodynamic modes on the complex…

We present a new numerical code which solves the general relativistic magneto-hydrodynamics (GRMHD) equations coupled to the Einstein equations for the evolution of a dynamical spacetime within the conformally-flat approximation. This code…

Many systems of current interest in relativistic astrophysics require a knowledge of radiative transfer in a magnetized gas flowing in a strongly-curved, dynamical spacetime. Such systems include coalescing compact binaries containing…

We present a general approach for the formulation of equations of motion for compact objects in general relativistic theories. The particle is assumed to be moving in a geometric background which in turn is asymptotically flat. Our approach…

Despite the fact that the Schwarzschild and Kerr solutions for the Einstein equations, when written in standard Schwarzschild and Boyer-Lindquist coordinates, present coordinate singularities, all numerical studies of accretion flows onto…

A detailed analysis of the coupled relativistic kinetic equations for two domains separated by a hypersurface having both space- and time-like parts is presented. Integrating the derived set of transport equations, we obtain the correct…

Hydrodynamics provides a concise but powerful description of long-time and long-distance physics of correlated systems out of thermodynamic equilibrium. Here we construct hydrodynamic equations for nonrelativistic particles with a…

We present hydrodynamic equations with relativistic pressure and velocity in the presence of weak gravity, in a cosmological context. Previously we consistently derived special relativistic hydrodynamic equations with weak gravity in…

In astrophysical systems, radiation-matter interactions are important in transferring energy and momentum between the radiation field and the surrounding material. This coupling often makes it necessary to consider the role of radiation…

We construct a general relativistic conservation law for linear and angular momentum for matter and gravitational fields in a finite volume of space that does not rely on any spacetime symmetries. This work builds on our previous…

In this work, we briefly review the progress made in the formulation of hydrodynamics with spin with emphasis on the application to the relativistic heavy-ion collisions. In particular, we discuss the formulation of hydrodynamics with spin…

Quantum hydrodynamics is a formulation of quantum mechanics based on the probability density and flux (current) density of a quantum system. It can be used to define trajectories which allow for a particle-based interpretation of quantum…

General relativity uses curved space-time to describe accelerating frames. The movement of particles in different curved space-times can be regarded as equivalent physical processes based on the covariant transformation between different…