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Four-force
About: Four-force is a research topic. Over the lifetime, 3459 publications have been published within this topic receiving 87308 citations.
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TL;DR: The initial value equations of general relativity are formulated as a system of four coupled quasilinear elliptic equations as discussed by the authors, which result from a covariant orthogonal decomposition of symmetric tensors and a generalized technique of conformal deformation.
Abstract: The initial-value equations of Einstein's theory of general relativity are formulated as a system of four coupled quasilinear elliptic equations. These equations result from a covariant orthogonal decomposition of symmetric tensors and a generalized technique of conformal deformation of initial data. Mathematical properties and global integrability conditions of the equations are discussed. Physical interpretation of the independent and dependent data is given for both spatially closed and asymptotically flat initial-data sets. In the latter case, the four dependent functions constitute long-range scalar and vector potentials which determine the total mass and total linear and angular momenta of an isolated system. The definitions of linear and angular momenta suggest a unique extension to asymptotically flat three-spaces of the group of translations and rotations of flat three-space. In turn, the "almost symmetries" thus defined lead to Gaussian theorems expressing the equality of certain surface and volume integrals for total linear and angular momenta. An interpretation of the scalar and vector potentials for closed three-spaces is also given. In the Appendix we treat the special case of conformally flat initial data.
157 citations
TL;DR: In this article, different kinds of self-similarity in general relativity are discussed, with special emphasis on similarity of the ''first'' kind, corresponding to spacetimes admitting a homothetic vector.
Abstract: The different kinds of self-similarity in general relativity are discussed, with special emphasis on similarity of the `first' kind, corresponding to spacetimes admitting a homothetic vector. We then survey the various classes of self-similar solutions to Einstein's field equations and the different mathematical approaches used in studying them. We focus mainly on spatially homogenous and spherically symmetric self-similar solutions, emphasizing their possible roles as asymptotic states for more general models. Perfect fluid spherically symmetric similarity solutions have recently been completely classified, and we discuss various astrophysical and cosmological applications of such solutions. Finally, we consider more general types of self-similar models.
157 citations
TL;DR: For many decades, the view has prevailed that no particle could possibly travel with a velocity greater than the velocity of light in vacuum, c = 3×108 m/sec as mentioned in this paper.
Abstract: FOR MANY DECADES now the view has prevailed that no particle could possibly travel with a velocity greater than the velocity of light in vacuum, c = 3×108 m/sec. It is generally held that this limitation is a direct consequence of the special theory of relativity. Albert Einstein himself has said so in his original paper on relativity.
153 citations
TL;DR: In this paper, it is argued that Minkowski space-time cannot serve as the deep structure within a "constructive" version of the special theory of relativity, contrary to widespread opinion in the philosophical community.
Abstract: It is argued that Minkowski space-time cannot serve as the deep structure within a “constructive” version of the special theory of relativity, contrary to widespread opinion in the philosophical community. This paper is dedicated to the memory of Jeeva Anandan.
153 citations
TL;DR: In this article, a static vacuum line element is derived which represents the field of a collinear set of spherically symmetric masses and a limiting process applied to this line-element yields an explicit global solution of a problem first considered by Bondi.
Abstract: A static vacuum line-element is derived which represents the field of a collinear set of spherically symmetric masses. A limiting process applied to this line-element yields an explicit global solution of a problem first considered by Bondi: the field of two symmetrically placed mass-dipoles moving in radially opposite directions.
152 citations