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Universal solutions in gravity, electrodynamics and nonabelian gauge theories
Kuchynka, Martin ; Pravdová, Alena (advisor) ; Hervik, Sigbjorn (referee) ; Švarc, Robert (referee)
The presented thesis spans over a number of related topics with a com- mon theme - the so-called universality. Classical fields exhibiting this property serve as exact solutions to virtually any higher-order theory irrespective of the particular form of the field equations, being thus of particular interest in ef- fective field theories. The aim of this work is to study various aspects of such solutions in the context of gravity, electrodynamics, as well as more general nonabelian gauge theories. The results are concentrated in four chapters, the first of which is devoted to what we call the almost universal spacetimes. Due to their nice curvature properties, these spacetimes provide an efficient method for simplifying and solving the field equations of higher-order gravity theories. We illustrate this feature of almost universal metrics by finding new vacuum solutions to quadratic gravity and six-dimensional conformal gravity. In the second chapter, we shift our attention towards electrodynamics. Following up on recent results on universal electromagnetic fields, we deal with Einstein- Maxwell fields which simultaneously solve also any higher-order modification of the Einstein-Maxwell theory. In particular, we identify solutions with this remarkable property as plane-fronted gravitational and...
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On type II universal spacetimes
Hervik, S. ; Málek, Tomáš ; Pravda, Vojtěch ; Pravdová, Alena
We briefly summarize our recent results on type II universal metrics of the Lorentzian signature. These metrics simultaneously solve all vacuum field equations of theories of gravity with the Lagrangian being a polynomial curvature invariant constructed from the metric, the Riemann tensor and its covariant derivatives of arbitrary order. It turns out that the results critically depend on the dimensionality of the spacetime. While we discuss examples of type II universal metrics for all composite number dimensions, we have no examples for prime number dimensions. Furthermore, we have proven the non-existence of type II universal spacetimes in five dimensions.
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