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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 Hamiltonian for general relativity obtained in a previous paper furnishes a definition of energy whose physical interpretation is direct, and which fulfills the conditions required of the energy in other physical systems as mentioned in this paper.
Abstract: The Hamiltonian for general relativity obtained in a previous paper furnishes a definition of energy whose physical interpretation is direct, and which fulfills the conditions required of the energy in other physical systems. The energy can be expressed as a surface integral at spacial infinity in terms of the spacial components of the covariant metric tensor at any given time. Thus, the energy depends only on the minimal initial Cauchy data and may be evaluated in any coordinate system, provided this system can be made asymptotically rectangular. These statements remain valid when particles are coupled to the gravitational field. The criteria for existence of gravitational radiation are formulated in terms of the canonical variables and the stress-tensor. These criteria are identical to those used in electromagnetic theory. Some applications are discussed.
186 citations
185 citations
184 citations
TL;DR: In this paper, a modified Regge calculus for general relativity on a triangulated four-dimensional Riemannian manifold is introduced, where the fundamental variables are areas and a certain class of angles.
Abstract: We introduce a modified Regge calculus for general relativity on a triangulated four-dimensional Riemannian manifold where the fundamental variables are areas and a certain class of angles. These variables satisfy constraints which are local in the triangulation. We expect the formulation to have applications to classical discrete gravity and non-perturbative approaches to quantum gravity.
179 citations