Related papers: On the Magnetohydrodynamics/Gravity Correspondence
For vacuum Maxwell theory in four dimensions, a supplementary condition exists (due to Eastwood and Singer) which is invariant under conformal rescalings of the metric, in agreement with the conformal symmetry of the Maxwell equations.…
We derive the relativistic non-resistive, viscous second-order magnetohydrodynamic equations for the dissipative quantities using the relaxation time approximation. The Boltzmann equation is solved for a system of particles and…
The coupled system of the spherically symmetric Einstein--Maxwell differential equations is solved under two different source conditions: non-zero electric charge and pressure anisotropy. Expressions for the metric functions, and pressures…
The squashed and stretched 7-dimensional internal metric preserving U(1) x U(1) x U(1)_R symmetry possesses an Einstein-Kahler 2-fold which is a base manifold of 5-dimensional Sasaki-Einstein L^{p, q, r} space. The r(transverse to the…
In the light of intriguing results of C.C.Barros, we investigate in this thesis the possibilities of geometrical interpretation of all the fundamental interactions in order to unify them. More exactly we try to supply a unified geometrical…
We formulate a general framework to study the flow of the electron liquid in two dimensions past a random array of impenetrable obstacles in the presence of a magnetic field. We derive a linear-response formula for the resistivity tensor…
In this paper we review recent progress on relativistic hydrodynamics in (2 + 1)-dimensions with an external magnetic field. We discuss the formalism allowing for momentum loss due to the explicit and spontaneous breaking of translation…
We assemble the equations of general relativistic magnetohydrodynamics (MHD) in 3+1 form. These consist of the complete coupled set of Maxwell equations for the electromagnetic field, Einstein's equations for the gravitational field, and…
In this talk we show a stiff fluid solution of the Einstein equations for a cylindrically symmetric spacetime. The main features of this metric are that it is non-separable in comoving coordinates for the congruence of the worldlineS of the…
We derive a manifestly duality-symmetric formulation of the action principle for conformal gravity linearized around Minkowski space-time. The analysis is performed in the Hamiltonian formulation, the fourth-order character of the equations…
We study the problem of coupling Einstein's equations to a relativistic and physically well-motivated version of the Navier-Stokes equations. Under a natural evolution condition for the vorticity, we prove existence and uniqueness in a…
We show that relativistic fluids behave as non-Newtonian fluids. First, we discuss the problem of acausal propagation in the diffusion equation and introduce the modified Maxwell-Cattaneo-Vernotte (MCV) equation. By using the modified MCV…
We consider the Einstein-Maxwell equations in space-dimension $n$. We point out that the Lindblad-Rodnianski stability proof applies to those equations whatever the space-dimension $n\ge 3$. In even space-time dimension $n+1\ge 6$ we use…
We prove that the Einstein equations can be solved in a very general form for arbitrary spacetime dimensions and various types of vacuum and non-vacuum cases following a geometric method of anholonomic frame deformations for constructing…
We propose a novel action principle for two dimensional incompressible fluid dynamics that naturally incorporates both vorticity and viscous dissipation via gauge field couplings. The action features a Chern Simons like term,…
We present a new code for solving the coupled Einstein-hydrodynamics equations to evolve relativistic, self-gravitating fluids. The Einstein field equations are solved on one grid using pseudospectral methods, while the fluids are evolved…
We consider the motion of several rigid bodies immersed in a two-dimensional incompress-ible perfect fluid, the whole system being bounded by an external impermeable fixed boundary. The fluid motion is described by the incompressible Euler…
A port-Hamiltonian model for compressible Newtonian fluid dynamics is presented in entirely coordinate-independent geometric fashion. This is achieved by use of tensor-valued differential forms that allow to describe describe the…
We formulate the equations of fluid dynamics as an intersection-theoretic problem on an infinite-dimensional symplectic manifold naturally associated with spacetime. This perspective separates the structures determined by the equation of…
The evolution of an electrically conducting imcompressible fluid with nonconstant density can be described by a set of equations combining the continuity, momentum and Maxwell's equations; altogether known as the inhomogeneous…