Related papers: Quasilocal Conservation Laws: Why We Need Them
Starting from the Maxwell-Lorentz equations, Poynting's theorem is reconsidered. The energy flux vector is introduced as S_e=(E x B)/mu_0 instead of E x H, because only by this choice the energy dissipation can be related to the balance of…
The general form of the global conservation laws for $N$-body systems in the first post-Newtonian approximation of general relativity is considered. Our approach applies to the motion of an isolated system of $N$ arbitrarily composed and…
In some models involving nonlinear conservation laws, physical mechanisms exist which prevent the formation of shocks. This gives rise to conservation laws with a constraint on the gradient of the solution. We approach this problem by…
We start by surveying the history of the idea of a fundamental conservation law and briefly examine the role conservation laws play in different classical contexts. In such contexts we find conservation laws to be useful, but often not…
The particles of a classical relativistic gas are supposed to move under the influence of a quasilinear (in the particle four-momenta), self-interacting force inbetween elastic, binary collisions. This force which is completely fixed by the…
We propose a gravitational energy-momentum tensor of the general relativity obtained using Noethers theorem. It transforms as a tensor under general coordinate transformations. One of the two indices of the gravitational energy-momentum…
Our investigation of differential conservation laws in Lagrangian field theory is based on the first variational formula which provides the canonical decomposition of the Lie derivative of a Lagrangian density by a projectable vector field…
We present the derivation of second-order relativistic viscous hydrodynamics from an effective Boltzmann equation for a system consisting of quasiparticles of a single species. We consider temperature-dependent masses of the quasiparticles…
The interplay between the action-reaction principle and the energy-momentum conservation law is revealed by the examples of the Maxwell-Lorentz and Yang-Mills-Wong theories, and general relativity. These two statements are shown to be…
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…
We derive the Noether identities and the conservation laws for general gravitational models with arbitrarily interacting matter and gravitational fields. These conservation laws are used for the construction of the covariant equations of…
For systems of partial differential equations in three spatial dimensions, dynamical conservation laws holding on volumes, surfaces, and curves, as well as topological conservation laws holding on surfaces and curves, are studied in a…
We extend the derivation of second-order relativistic viscous hydrodynamics to incorporate the effects of baryon current, a non-vanishing chemical potential, and a realistic equation of state. Starting from a microscopic quantum theory, we…
Symmetries and conservation laws are studied for a generalized Westervelt equation which is a nonlinear partial differential equation modelling the propagation of sound waves in a compressible medium. This nonlinear wave equation is widely…
A new representation of electromagnetic gyrokinetic Vlasov-Maxwell theory is presented in which the gyrocenter equations of motion are expressed solely in terms of the perturbed electric and magnetic fields. In this representation, the…
Based on a general variational principle, Noether's theorem is revisited. It is shown that the so called pseudotensor problem of the gravitational energy-momentum is a result of mis-reading Noether's theorem, and in fact, all the Noether's…
We extend the quasilocal formalism of Brown and York to include electromagnetic and dilaton fields and also allow for spatial boundaries that are not orthogonal to the foliation of the spacetime. The extension allows us to study the…
Several energy-momentum "tensors" of gravitational field are considered and compared in the lowest approximation. Each of them together with energy-momentum tensor of point-like particles satisfies the conservation laws when equation of…
Although there is no known meaningful notion of the energy density of the gravitational field in general relativity, a few notions of quasi-local energy of gravity associated to extended but finite domains have been proposed. In this paper,…
In a wide range of physical phenomena, we find propagating surfaces {\Omega}t which need mathematical treatment. In this article, we review the theory of the system of kinematical conservation laws (KCL), which govern the evolution of these…