Book ChapterDOI
Variational Principles In General Relativity
A. H. Taub
- pp 205-300
TLDR
In this paper, the authors derive the Einstein field and the equations of motion for uncharged and charged self- gravitating fluids from variational principles, and show how singular hyper-surfaces (shock waves) and the equation governing their behavior may be treated by means of these principles.Abstract:
In these lectures we shall derive the Einstein field and the equations of motion for uncharged and charged self- gravitating fluids from variational principles. We shall also see how singular hyper-surfaces (shock waves) and the equations governing their behavior may be treated by means of these principles. In addition we shall show how the “second variation” problem is related to the discussion of the stability of the solutions of the Einstein field equations.read more
Citations
More filters
Book
Lectures on geometric methods in mathematical physics
TL;DR: Infinite-Dimensional Hamiltonian Systems Elasticity as a Hamiltonian System Symmetry and Reduction Applications of Reduction Two Completely Integrable Systems Bifurcations of a Forced Beam The Traction Problem in Elastostatics Bifurlcations for Momentum Mappings The Space of Solutions of Einstein's Equations Regular and Singular Points as mentioned in this paper
Book Chapter
Stress-Energy-Momentum Tensors and the Belinfante-Rosenfeld Formula
Mark J. Gotay,Jerrold E. Marsden +1 more
TL;DR: In this paper, the authors presented a new method of constructing a stress-energy-momentum tensor based on covariance considerations and Noether theory, which is uniquely determined as well as gauge-covariant, and depends only upon the divergence equivalence class of the Lagrangian.
Journal ArticleDOI
Weyl geometry and the nonlinear mechanics of distributed point defects
Arash Yavari,Alain Goriely +1 more
TL;DR: In this paper, the residual stress field of a nonlinear elastic solid with a spherically symmetric distribution of point defects is obtained explicitly using methods from differential geometry, where the residual tensors of the body are computed using Cartan's moving frames.
Journal ArticleDOI
Higgs inflation in the Palatini formulation with kinetic terms for the metric
TL;DR: In this paper, the authors consider scalar field inflation in the Palatini formulation of general relativity and show that by tuning the coefficients of the new terms, they can generate various effective inflationary potentials, including quadratic, hilltop-type, and inflection point.
References
More filters
Journal ArticleDOI
The Dynamical Instability of Gaseous Masses Approaching the Schwarzschild Limit in General Relativity.
TL;DR: In this article, the theory of the infinitesimal, baryon-number conserving, adiabatic, radial oscillations of a gas sphere is developed in the framework of general relativity.