An algorithmic classification of geometries in general relativity

ABSTRACT

The complicated coordinate transformations in general relativity make coordinate invariant classification schemes extremely important. A computer program, written in SHEEP, performing an algorithmic classification of the curvature tensor and a number of its derivatives is presented. The output is a complete description of the geometry. The problem to decide whether or not two solutions of Einstein's equations describe the same gravitational field can be solved if the (non-) existence of a solution to a set of algebraic equations can be established. The classification procedure has been carried through for a number of fields, and solutions previously believed to describe physically different situations have been shown to be equivalent. We exemplify with a physically interesting class of geometries.

REFERENCES

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INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.1 SYMBOLIC AND ALGEBRAIC MANIPULATION
      I.1.3 Languages and Systems

Additional Classification:
  I. Computing Methodologies
  I.3 COMPUTER GRAPHICS
      I.3.5 Computational Geometry and Object Modeling
          Subjects: Hierarchy and geometric transformations

  J. Computer Applications
  J.2 PHYSICAL SCIENCES AND ENGINEERING
      Subjects: Physics

General Terms:
Algorithms, Design, Languages, Theory