Conservation Laws on Riemann-Cartan, Lorentzian and Teleparallel Spacetimes
نویسنده
چکیده
Using a Clifford bundle formalism, we examine: (a) the strong conditions for existence of conservation laws involving only the energy-momentum and angular momentum of the matter fields on a general Riemann-Cartan spacetime and the particular cases of Lorentzian and teleparallel spacetimes and (b) the conditions for the existence of conservation laws of energy-momentum and angular momentum for the matter and gravitational fields when this later concept can be rigorously defined. We examine in more details some statements concerning the issues of the conservation laws in General Relativity and Riemann-Cartan (including the particular case of the teleparallel ones) theories.
منابع مشابه
Nongeodesic motion of spinless particles in the teleparallel gravitational wave background
The motion of spinless particles in Riemann-Cartan (RC) U4 and teleparallel spacetimes is revisited on the light of gravitational waves hitting on the spinless test particles. It is shown that in the case Cartan contortion is totally skew-symmetric the spinless particles follow geodesics but if this symmetry is dropped they are able to follow nongeodesic worldlines in torsionic background. The ...
متن کاملSelf-similar solutions of the Riemann problem for two-dimensional systems of conservation laws
In this paper, a new approach is applied to study the self-similar solutions of 2×2 systems of nonlinear hyperbolic conservation laws. A notion of characteristic directions is introduced and then used to construct local and smooth solutions of the associated Riemann problem
متن کاملDifferential Forms on Riemannian (Lorentzian) and Riemann-Cartan Structures and Some Applications to Physics
In this paper after recalling some essential tools concerning the theory of differential forms in the Cartan, Hodge and Clifford bundles over a Riemannian or Riemann-Cartan space or a Lorentzian or Riemann-Cartan spacetime we solve with details several exercises involving different grades of difficult. One of the problems is to show that a recent formula given in [10] for the exterior covariant...
متن کاملHyperbolic conservation laws and spacetimes with limited regularity
Hyperbolic conservation laws posed on manifolds arise in many applications to geophysical flows andgeneral relativity. Recentworkby the author and his collaborators attempts to set the foundations for a study of weak solutions defined on Riemannian or Lorentzian manifolds and includes an investigation of the existence and qualitative behavior of solutions. The metric on the manifold may either ...
متن کاملLorentzian Spacetimes with Constant Curvature Invariants in Three Dimensions
In this paper we study Lorentzian spacetimes for which all polynomial scalar invariants constructed from the Riemann tensor and its covariant derivatives are constant (CSI spacetimes) in three dimensions. We determine all such CSI metrics explicitly, and show that for every CSI with particular constant invariants there is a locally homogeneous spacetime with precisely the same constant invarian...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008