Four-force

About: Four-force is a research topic. Over the lifetime, 3459 publications have been published within this topic receiving 87308 citations.

A Note on General Relativity, Energy Conservation, and Noether’s Theorems

Abstract: The subject of this note has been a small historical thread in the long and complex story of the status of energy conservation in General Relativity, concerning two related claims made by Klein and Hilbert: that the energy conservation law is an identity in generally covariant theories, and that this marks a contrast with other (earlier) theories. Both these claims were disputed by Einstein. We have seen how three theorems proved by Noether and Klein can be brought to bear on this disagreement, showing that: (1) Klein’s worry over the physical significance of the energy conservation law in General Relativity was perhaps not adequately addressed by Einstein, even though in the end we side with Einstein against Klein, and (2) the possibility of re-writing the energy conservation law in the form that so worried Klein does indeed depend upon the local symmetry structure of General Relativity.

Quantization of general relativity

Abstract: Several theories of quantum general relativity have been formulated. Each of these theories has elements of arbitrariness and ambiguity as well as technical difficulty which make it less than satisfactory. However, the construction of these theories has revealed much about the structure of general relativity as a dynamical system and has spurred the development of new approaches to quantum theory. Canonical, sum-over-histories and source theory approaches to the quantization of the gravitational field in the absence of matter are reviewed in terms of a unified notation. Discussions of quantum theory and general relativity are provided to make the review self-contained for readers with a general physics background. The quantization of open space-time geometries (graviton scattering) is treated in sufficient detail to reveal the basic mathematical structure of the formalism. The quantization of closed universes (quantum cosmology) is discussed with particular attention to the superspace concept and the construction of finite-dimensional model quantum theories. Superspace, the domain manifold of the quantum state functional in general relativity, is also discussed separately.

On hypermomentum in general relativity. III - Coupling hypermomentum to geometry

Abstract: Abstract In Part I1 of this series we presented the notion of the material hypermomentum current and motivated its introduction into general relativity. In Part II2 we showed that a general, linearly connected manifold with symmetric metric (L4, g) is the appropriate geometrical framework for such an introduction. The present paper completes the picture by giving dynamical definitions for energy-momentum and hypermomentum for a minimally coupled material Lagrangian. We derive and discuss the field equations of a new metricaffine gravitational theory which embodies these notions.

Tensors, Relativity, and Cosmology

Abstract: Tensors, Relativity, and Cosmology, Second Edition, combines relativity, astrophysics, and cosmology in a single volume, providing a simplified introduction to each subject that is followed by detailed mathematical derivations. The book includes a section on general relativity that gives the case for a curved space-time, presents the mathematical background (tensor calculus, Riemannian geometry), discusses the Einstein equation and its solutions (including black holes and Penrose processes), and considers the energy-momentum tensor for various solutions. In addition, a section on relativistic astrophysics discusses stellar contraction and collapse, neutron stars and their equations of state, black holes, and accretion onto collapsed objects, with a final section on cosmology discussing cosmological models, observational tests, and scenarios for the early universe.