相关论文: Fluids in Weyl Geometries

It is shown that (except for two well defined cases), the necessary and sufficient condition for any spherically symmetric distribution of fluid to leave the state of equilibrium (or quasi-equilibrium), is that the Weyl tensor changes with…

We examine relations between geometry and the associated curvature decompositions in Weyl geometry.

This article is dedicated to the analysis of Weyl symmetry in the context of relativistic hydrodynamics. Here is discussed how this symmetry is properly implemented using the prescription of minimal coupling: $\partial\to \partial +\omega…

Short review of the Weyl geometry is given. To describe the phenomenological particle creation we suggest the modified perfect fluid model taking into account the back reaction on the geometry of both the already created particles and the…

We are concerned with underlying connections between fluids, elasticity, isometric embedding of Riemannian manifolds, and the existence of wrinkled solutions of the associated nonlinear partial differential equations. In this paper, we…

We derive the evolution equations for the electric and magnetic parts of the Weyl tensor for cold dust from both general relativity and Newtonian gravity. In a locally inertial frame at rest in the fluid frame, the Newtonian equations agree…

We discuss the possibility of extending different versions of the Campbell-Magaard theorem, which have already been established in the context of semi-Riemannian geometry, to the context of Weyl's geometry. We show that some of the known…

This brief paper investigates the consequences for the metric tensor of space-time when the Weyl tensor (in its conformally invariant form) and the energy-momentum tensor is specified. It is shown that, unless rather special conditions…

We study Weyl conformal geometry as a general gauge theory of the Weyl group (of Poincar\'e and dilatations symmetries) in a manifestly Weyl gauge covariant formalism in which this geometry is automatically metric and physically relevant.…

According to folklore in general relativity, the Weyl tensor can be decomposed into parts corresponding to Newton-like, incoming and outgoing wavelike field components. It is shown here that this one-to-one correspondence does not hold for…

We consider compressible fluid flow on an evolving surface with a piecewise Lipschitz-continuous boundary from an energetic point of view. We employ both an energetic variational approach and the first law of thermodynamics to make a…

The Reynolds transport theorem occupies a central place in fluid dynamics, providing a generalized integral conservation equation for the transport of any conserved quantity within a fluid, and connected to its corresponding differential…

We consider several tensorial wave equations, specifically the equations of Maxwell, Yang-Mills, and Weyl fields, posed on a curved spacetime, and we establish new energy inequalities under certain one-sided geometric conditions. Our…

The appearance of a geometric flow in the conservation law of particle number in classical particle diffusion and in the conservation law of probability in quantum mechanics is discussed in the geometrical environment of a two-dimensional…

Electromagnetic waves and fluids have locally conserved mechanical properties associated with them and we may expect these to exist for matter waves. We present a semiclassical description of the continuity equations relating to these…

The non--linear dynamics of cosmological perturbations of an irrotational collisionless fluid is analyzed within General Relativity. Relativistic and Newtonian solutions are compared, stressing the different role of boundary conditions in…

The equations of General Relativity are recast in the form of a wave equation for the Weyl tensor. This allows to reformulate gravitational wave theory in terms of curvature waves, rather than metric waves. The existence of two transverse…

The study rederives the fundamental equations of fluid flow and examines the inherent relationship between momentum conservation and mechanical energy conservation. It is shown that the material derivative of velocity is to depict the…

Symmetries of geometrical and physical quantities in general relativity provide important information about the curvature structure of the spacetimes. Symmetries of the curvature and the Weyl tensors, known as curvature and Weyl…

The gradient-flow equations with respect to the potential functions in information geometry are reconsidered from the perspective of the Weyl integrable geometry. The pre-geodesic equations associated with the gradient-flow equations are…