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Twistor equation on isolated horizons
 Matejov, Dávid ; Scholtz, Martin (advisor) ; Švarc, Robert (referee)
In the present work we investigate the solution of the univalent twistor equation on an isolated horizon that serves for the definition of the so-called Penrose mass. We start our discussion with the construction of adapted co- ordinates to the isolated horizon and summarizing the main results in this field that are needed for our work. We include a chapter devoted to the extre- mal isolated horizons and prove an important result concerning uniqueness of geometry therein. It is a generalization of the paper by Lewandowski and Pawlowski (Class. Quantum Grav. 31 (17), 2014), which states that the ex- tremal isolated horizons are necessarily isometric to the intrinsic geometry of the Kerr-Newmann black hole. Further we proceed to investigation of the twistor equation on the isolated horizon. We analyze conditions of integra- bility and derive the time dependent solution. Consequently we solve the 2-surface twistor equation and briefly discuss the general approach to the problem of defining the Penrose charge. 1
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