The form of Killing vectors in expanding ℋℋ spaces
Copyright policy )The form of Killing vectors in expanding ℋℋ spaces
The Killing vector structure of those spaces of complexified general relativity known as expanding hyperheavens is investigated using the methods of spinor calculus. The Killing equations for all left-algebraically degenerate Einstein vacuum spaces are completely integrated. Using the available gauge freedom, the resulting homothetic and isometric Killing vectors are classified in an invariant way according to Petrov–Penrose type. A total of four distinct kinds of isometric Killing vectors and three distinct kinds of homothetic Killing vectors are found. A master Killing vector equation is found which gives the form that the Lie derivative of the metric potential function W must take in order that it admit a given Killing vector.
- University of New Mexico United States
metric potential function, Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.), gauge freedom, 2-spinors, HH spaces, complex general relativity, space of the most general algebraically degenerate solutions of the complex Einstein field equations, Petrov-Penrose types, Schwarzschild metric, Einstein's equations (general structure, canonical formalism, Cauchy problems), Applications of manifolds of mappings to the sciences, Applications of global differential geometry to the sciences, Killing equation, Killing vectors
metric potential function, Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.), gauge freedom, 2-spinors, HH spaces, complex general relativity, space of the most general algebraically degenerate solutions of the complex Einstein field equations, Petrov-Penrose types, Schwarzschild metric, Einstein's equations (general structure, canonical formalism, Cauchy problems), Applications of manifolds of mappings to the sciences, Applications of global differential geometry to the sciences, Killing equation, Killing vectors
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