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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: In this paper, the authors present a series of papers on complex spaces and their use in complex relativity, and discuss a number of important properties which arise in the development of the basic equations and key concepts, these properties being mainly ones which are not apparent in standard real formulations.
Abstract: This is the first of a series of papers on complex spaces and their use in complex relativity. The basic aim is to develop the theory of complex relativity but only insofar as it helps in obtaining, and understanding, real solutions of Einstein's vacuum equations as slices of complex solutions. In this first paper, specific aims of the whole series are first presented. The basic equations and key entities, which are used later, are presented. The basic relativistic language used is that of Newman and Penrose. Included is a discussion of a number of important properties which arise in the development of the basic equations and key concepts, these properties being mainly ones which are not apparent in standard real formulations.
44 citations
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TL;DR: The relation between the Newton-Cartan theory, Newton's clasical gravitational theory and General Relativity is discussed in this article, where it is shown that the limit c→∞ of GRL becomes identical with the Newton Cartan theory provided the so-called time function, defined as proportional to the singular part of the covariant Einsteinian metric in the transition c→ ∞, satisfies a certain boundary condition at spatial infinity.
Abstract: The relations between the Newton-Cartan theory, Newton's clasical gravitational theory and General Relativity are discussed. It is shown that the limit c→∞ of General Relativity becomes identical with the Newton-Cartan theory, provided the so-called time function ― defined as proportional to the singular part of the covariant Einsteinian metric in the transition c→∞ ― satisfies a certain boundary condition at spatial infinity. Using this limiting process, one obtains an asymptotic representation of Einsteinian fields near the Newtonian limit. This should allow us to identify post-Newtonian corrections for the Newton-Cartan theory
44 citations
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TL;DR: In this article, the kinematic results of the special theory of relativity are derived using only the first (Galilean) postulate and the results of one simple thought experiment.
Abstract: The kinematic results of the special theory of relativity are derived using only the first (Galilean) postulate and the results of one simple thought experiment. Our method is mathematically simple and, therefore, can be used in an algebra based introductory physics course. It is also pedagogically attractive because the relativistic results follow as a natural extension of the familiar Newtonian ones.
44 citations