Spacetime groups
Copyright policy )Spacetime groups
A spacetime group is a connected 4-dimensional Lie group G endowed with a left invariant Lorentz metric h such that the connected component of the isometry group of h is G itself. The Newman–Penrose formalism is used to give an algebraic classification of spacetime groups, that is, we determine a complete list of inequivalent spacetime Lie algebras, which are pairs (g,η), with g being a 4-dimensional Lie algebra and η being a Lorentzian inner product on g. A full analysis of the equivalence problem for spacetime Lie algebras is given, which leads to a completely algorithmic solution to the problem of determining when two spacetime Lie algebras are isomorphic. The utility of our classification is demonstrated by a number of applications. The results of a detailed study of the Einstein field equations for various matter fields on spacetime groups are given, which resolve a number of open cases in the literature. The possible Petrov types of spacetime groups that, generically, are algebraically special are completely characterized. Several examples of conformally Einstein spacetime groups are exhibited. Finally, we describe some novel features of a software package created to support the computations and applications of this paper.
- Utah State University United States
High Energy Physics - Theory, General Relativity, Computer Algebra, and Gravity, Newman-Penrose formalism, Equivalence Problem, 115, FOS: Physical sciences, General Relativity and Quantum Cosmology (gr-qc), Spinor and twistor methods in general relativity and gravitational theory; Newman-Penrose formalism, General Relativity and Quantum Cosmology, Lie Group, Relativity, Applications of differential geometry to physics, Einstein Field Equations, Spacetime, Petrov types, Einstein's equations (general structure, canonical formalism, Cauchy problems), Lie Algebra, Lie Algebras, Mathematical Physics, Physics, Applied Mathematics, Classes of solutions; algebraically special solutions, metrics with symmetries for problems in general relativity and gravitational theory, General properties and structure of real Lie groups, PDEs in connection with relativity and gravitational theory, Mathematical Physics (math-ph), Einstein Equations, Lie Groups, Cosmology, spacetime group, Lie group, Elementary Particles and Fields and String Theory, Algebra, Lorentzian Geometry, High Energy Physics - Theory (hep-th), Structure and representation of the Lorentz group, left invariant Lorentz metric, Computational methods for problems pertaining to relativity and gravitational theory, Geometry and Topology, Mathematics
High Energy Physics - Theory, General Relativity, Computer Algebra, and Gravity, Newman-Penrose formalism, Equivalence Problem, 115, FOS: Physical sciences, General Relativity and Quantum Cosmology (gr-qc), Spinor and twistor methods in general relativity and gravitational theory; Newman-Penrose formalism, General Relativity and Quantum Cosmology, Lie Group, Relativity, Applications of differential geometry to physics, Einstein Field Equations, Spacetime, Petrov types, Einstein's equations (general structure, canonical formalism, Cauchy problems), Lie Algebra, Lie Algebras, Mathematical Physics, Physics, Applied Mathematics, Classes of solutions; algebraically special solutions, metrics with symmetries for problems in general relativity and gravitational theory, General properties and structure of real Lie groups, PDEs in connection with relativity and gravitational theory, Mathematical Physics (math-ph), Einstein Equations, Lie Groups, Cosmology, spacetime group, Lie group, Elementary Particles and Fields and String Theory, Algebra, Lorentzian Geometry, High Energy Physics - Theory (hep-th), Structure and representation of the Lorentz group, left invariant Lorentz metric, Computational methods for problems pertaining to relativity and gravitational theory, Geometry and Topology, Mathematics
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