Special relativity (alternative formulations)

About: Special relativity (alternative formulations) is a research topic. Over the lifetime, 3102 publications have been published within this topic receiving 55015 citations.

The initial value problem and the dynamical formulation of general relativity

Abstract: In this chapter we discuss some of the interrelationships between the initial value problem, the canonical formalism, linearization stability and the space of gravitational degrees of freedom. In the last decade, these topics have experienced a resurgence of interest as more advanced mathematical methods and viewpoints have begun to show the intimate relationships among these topics. At present, the literature regarding these areas of general relativity is a rapidly expanding body of knowledge. Our purpose here is to present the current state of affairs from our own point of view. We shall use geometric methods developed by the authors to establish various conn~ctions between the above-mentioned topics. The main tools we shall use to develop this material are nonlinear functional analysis, an adjoint formalism for Hamiltonian field theories, and infinite-dimensional symplectic geometry. As we shall see, these tools and the topics we shall consider are naturally related. For a more complete picture of the current state of affairs, the reader is urged to consult Choquet-Section 4.1 develops the Hamiltonian formalism for the dynamics of general relativity, usually called the ADM (Arnowitt, Deser and Misner) formalism. This is done using invariant concepts and the adjoint formalism developed by the authors. We show how to write the Einstein dynamical system explicitly in the compact form

On the positivity of energy in general relativity

Abstract: We show that the positive energy argument of Geroch for time‐symmetric initial data sets can be generalized to general initial data sets

Spacetime physics : introduction to special relativity

Abstract: Edwin Taylor and John A. Wheeler-one of this century's most distinguished physicists - have completely reorganised this popular and well known book to make it accessible to an even wider audience. New topics, imaginative problems, and exceptionally clever illustrations, combined with a compelling narrative and intellectual authority make this a classic text. It is an ideal text for undergraduate courses in special relativity and modern physics.

An introduction to general relativity

Abstract: This textbook provides an introduction to general relativity for mathematics undergraduates or graduate physicists. After a review of Cartesian tensor notation and special relativity the concepts of Riemannian differential geometry are introducted. More emphasis is placed on an intuitive grasp of the subject and a calculational facility than on a rigorous mathematical exposition. General relativity is then presented as a relativistic theory of gravity reducing in the appropriate limits to Newtonian gravity or special relativity. The Schwarzchild solution is derived and the gravitational red-shift, time dilation and classic tests of general relativity are discussed. There is a brief account of gravitational collapse and black holes based on the extended Schwarzchild solution. Other vacuum solutions are described, motivated by their counterparts in linearised general relativity. The book ends with chapters on cosmological solutions to the field equations. There are exercises attached to each chapter, some of which extend the development given in the text.