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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 scalar-tensor formalism is implicitly embodied in the theory of general relativity, thus illustrating the considerable freedom available in specifying the nature and physical content of the "matter tensor" in the Einstein equation.
Abstract: The various versions of the scalar-tensor theory (e.g., the theories of Jordan, Hoyle, and Brans-Dicke) are derived from a general variational principle. It is shown that scalar-conformal transformations not only interconvert the various current versions of the scalar-tensor theory (i.e., Brans-Dicke theory \ensuremath{\rightleftarrows} Hoyle steady-state theory), but also convert the scalar-tensor variational principle into the variational principle of general relativity. The scalar-tensor formalism is therefore implicitly embodied in the theory of general relativity, thus illustrating the considerable freedom available in specifying the nature and physical content of the "matter tensor" in the Einstein equation.
26 citations
TL;DR: In this paper, a reformulation of the Arnowitt-Deser-Misner equations in general relativity, which has dramatically improved the stability properties of numerical implementations, has a direct analogue in classical electrodynamics.
Abstract: We show that a reformulation of the Arnowitt-Deser-Misner equations in general relativity, which has dramatically improved the stability properties of numerical implementations, has a direct analogue in classical electrodynamics. We numerically integrate both the original and the revised versions of Maxwell's equations, and show that their distinct numerical behavior reflects the properties found in linearized general relativity. Our results shed further light on the stability properties of general relativity, illustrate them in a very transparent context, and may provide a useful framework for further improvement of numerical schemes.
26 citations
TL;DR: In this article, a curve shortening method was used to obtain the Morse relations for light rays joining an event with a smooth timelike curve in a Lorentzian manifold with boundary.
Abstract: In this paper we use a general version of Fermat’s principle for light rays in general relativity and a curve shortening method to write the Morse relations for light rays joining an event with a smooth timelike curve in a Lorentzian manifold with boundary The Morse relations are obtained under the most general assumptions and one can apply them to have a mathematical description of the gravitational lens effect in a very general context Moreover, Morse relations can be used to check if existing models are corrected
26 citations
TL;DR: The work in this paper is concerned with the charged analogue of Bayin's paper (1978) related to Tolman's type astrophysically interesting aspects of stellar structure, and is related to our work.
Abstract: The work is concerned with the charged analogue of Bayin's paper (1978) related to Tolman's type astrophysically interesting aspects of stellar structure.
26 citations
TL;DR: In this article, a discussion is presented which indicates that a stagnation point is being reached in the standard applications of symmetries (especially isometries) in general relativity, and an attractive alternative is suggested.
Abstract: A discussion is presented which indicates that a stagnation point is being reached in the standard applications of symmetries (especially isometries) in general relativity. In order to continue the advance of this area of research, an attractive alternative is suggested. This alternative involves the use of what are termed “intrinsic symmetries.” With this technique, emphasis is placed on underlying symmetries ofsubmanifolds. One particular set of symmetries gives rise to an invariant formulation of the Szekeres inhomogeneous cosmological models, and suggests quite natural generalizations.
26 citations