Four-force

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

On quadratic lagrangians in General Relativity

Abstract: Theories of gravitation similar to General Relativity but with an additionalR2 term in the Lagrangian are explored. The Schwarzschild metric is not the exterior solution that can be continued to the interior of the body to give a positive definite mass distribution. The experimental consequences ofR2 terms are investigated. Furthermore, it is shown that a theory with anR2 term only possesses an interesting singular dependence on the coupling constant.

Unimodular relativity and cosmological constant

Abstract: Unimodular relativity is a theory of gravity and space–time with a fixed absolute space–time volume element, the modulus, which we suppose is proportional to the number of microscopic modules in that volume element. In general relativity an arbitrary fixed measure can be imposed as a gauge condition, while in unimodular relativity it is determined by the events in the volume. Since this seems to break general covariance, some have suggested that it permits a nonzero covariant divergence of the material stress-energy tensor and a variable cosmological “constant.” In Lagrangian unimodular relativity, however, even with higher derivatives of the gravitational field in the dynamics, the usual covariant continuity holds and the cosmological constant is still a constant of integration of the gravitational field equations.

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 Origins of the Special Theory of Relativity

Abstract: Einstein's early work on relativity theory is found to be related to his other work at that time (e.g., in subject matter and style). In addition to this element of internal continuity one finds also—as a key to a new evaluation of the significance of Einstein's contribution—an external continuity with the classic, Newtonian tradition governing restrictions on permissible hypotheses. On the other hand, Einstein's work is shown to have been, in important respects, more independent of other contemporary work in this field than has recently been proposed.These continuities and discontinuities are set forth to make the point that philosophical studies of scientific work should proceed on historically valid ground. Some guiding principles are indicated for dealing with conflicting source materials for such studies.

Instability of closed spaces in general relativity

Abstract: There are strong restrictions on the solutions of the initial value constraints of General Relativity when the spatial hypersurface is closed. In particular, closed flat space is unstable: not all solutions of the linearized constraints correspond to nearby solutions of the constraints themselves. For example, no nearby solutions whatever exist which are time symmetric. Other restrictions, which limit perturbations of non-flat closed initial solutions, are also exhibited.