The use of generalized functions and distributions in general relativity

By R. Steinbauer, J. Vickers. 2006

154 citations recorded by the source corpus.

We review the extent to which one can use classical distribution theory in describing solutions of Einstein's equations. We show that there are a number of physically interesting cases which cannot be treated using distribution theory but require a more general concept. We describe a mathematical theory of nonlinear generalized functions based on Colombeau algebras and show how this may be applied in general relativity. We end by discussing the concept of singularity in general relativity and show that certain solutions with weak singularities may be regarded as distributional solutions of Einstein's equations.

Subfields: Atomic and Molecular Physics, and Optics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/bf6fcffcc2c79a4b632c7a8a73542115000ef647

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In Atomic and Molecular Physics, and Optics

1. A. Pound
2. E. Poisson
3. I. Vega

In Geometry and Topology

1. A. Pound
2. E. Poisson
3. I. Vega

In Mathematical Physics

1. A. Pound
2. E. Poisson
3. I. Vega

Citations in the corpus

• The Motion of Point Particles in Curved Spacetime (2003, methodology): “It may be possible to overcome this limitation using more advanced methods such as Colombeau algebras [164], which allow for the multiplication of distributions, but little work has been done to that end.”