Aplikace algebraické klasifikace a příbuzných metod na problémy vícerozměrné relativity

Tintěra, Tomáš

In four-dimensional general relativity, the algebraic classification has played an important role in study of spacetimes, including, but not limited to the search for new solutions to the Einstein equation. In the present work, we study its recent generalization to higher dimensions, based on categorizing Weyl tensor frame components by their transformation properties under boosts. Specifically, we concentrate on its connection to two well-established concepts. Kaluza-Klein reduction can be regarded as a relation between spacetimes of different dimen- sionality. As such, it is desirable to be understood in the context of the higher-dimensional algebraic classification. We study algebraic properties of Weyl tensors related by Kaluza-Klein reduction. Specifically, we concentrate on reduction of vacuum spacetimes by one spatial Killing direction and investigate Weyl-alignment multiplicities of two related null directions that are parallel in a gauge where they are perpendicular to the Maxwell potential. We express rela- tions of various quantities of the related spacetimes, such as Riemann and Weyl tensors, optical matrices and non-geodeticities, revealing some interesting consequences regarding reduction of Kundt spacetimes and of spacetimes admitting a geodetic null direction. Based on this, we...

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