CR structures and twisting vacuum spacetimes with two Killing vectors and cosmological constant: type II and more special

DOI10.1088/0264-9381/30/11/115006zbMATH Open1271.83024arXiv1302.3275OpenAlexW3103878582MaRDI QIDQ2841441

Publication date: 25 July 2013

Published in: Classical and Quantum Gravity (Search for Journal in Brave)

Abstract: Based on the CR formalism of algebraically special spacetimes by Hill, Lewandowski and Nurowski, we derive a nonlinear system of two real ODEs, of which the general solution determines a twisting type II (or more special) vacuum spacetime with two Killing vectors (commuting or not) and at most seven real parameters in addition to the cosmological constant Lambda. To demonstrate a broad range of interesting spacetimes that these ODEs can capture, special solutions of various Petrov types are presented and described as they appear in this approach. They include Kerr-NUT, Kerr and Debney/Demia'{n}ski's type II, Lun's type II and III (subclasses of Held-Robinson), MacCallum and Siklos' type III (Lambda<0), and the type N solutions (Lambda<>0) we found in an earlier paper, along with a new class of type II solutions as a nontrivial limit of Kerr and Debney's type II solutions. Also, we discuss a situation in which the two ODEs can be reduced to one. However, constructing the general solution still remains an open problem.

Full work available at URL: https://arxiv.org/abs/1302.3275

zbMATH Keywords

cosmological constant Killing vectors CR structures twisting vacuum spacetimes

Mathematics Subject Classification ID

Classes of solutions; algebraically special solutions, metrics with symmetries for problems in general relativity and gravitational theory (83C20) Spinor and twistor methods in general relativity and gravitational theory; Newman-Penrose formalism (83C60) Exact solutions to problems in general relativity and gravitational theory (83C15) Embeddings of CR manifolds (32V30) CR functions (32V10)

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