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Geometry of isolated horizons
Flandera, Aleš ; Scholtz, Martin (advisor)
While the formalism of isolated horizons is known for some time, only quite recently the near horizon solution of Einstein's equations has been found in the Bondi-like coordinates by Krishnan in 2012. In this framework, the space-time is regarded as the characteristic initial value problem with the initial data given on the horizon and another null hypersurface. It is not clear, however, what ini- tial data reproduce the simplest physically relevant black hole solution, namely that of Kerr-Newman which describes stationary, axisymmetric black hole with charge. Moreover, Krishnan's construction employs the non-twisting null geodesic congruence and the tetrad which is parallelly propagated along this congruence. While the existence of such tetrad can be easily established in general, its explicit form can be very difficult to find and, in fact it has not been provided for the Kerr-Newman metric. The goal of this thesis was to fill this gap and provide a full description of the Kerr-Newman metric in the framework of isolated horizons. In the theoretical part of the thesis we review the spinor and Newman-Penrose formalism, basic geometry of isolated horizons and then present our results. Thesis is complemented by several appendices.
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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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Geometry of isolated horizons
Flandera, Aleš ; Scholtz, Martin (advisor)
While the formalism of isolated horizons is known for some time, only quite recently the near horizon solution of Einstein's equations has been found in the Bondi-like coordinates by Krishnan in 2012. In this framework, the space-time is regarded as the characteristic initial value problem with the initial data given on the horizon and another null hypersurface. It is not clear, however, what ini- tial data reproduce the simplest physically relevant black hole solution, namely that of Kerr-Newman which describes stationary, axisymmetric black hole with charge. Moreover, Krishnan's construction employs the non-twisting null geodesic congruence and the tetrad which is parallelly propagated along this congruence. While the existence of such tetrad can be easily established in general, its explicit form can be very difficult to find and, in fact it has not been provided for the Kerr-Newman metric. The goal of this thesis was to fill this gap and provide a full description of the Kerr-Newman metric in the framework of isolated horizons. In the theoretical part of the thesis we review the spinor and Newman-Penrose formalism, basic geometry of isolated horizons and then present our results. Thesis is complemented by several appendices.
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Geometry of isolated horizons
Flandera, Aleš ; Scholtz, Martin (advisor) ; Acquaviva, Giovanni (referee)
While the formalism of isolated horizons is known for some time, only quite recently the near horizon solution of Einstein's equations has been found in the Bondi-like coordinates by Krishnan in 2012. In this framework, the space-time is regarded as the characteristic initial value problem with the initial data given on the horizon and another null hypersurface. It is not clear, however, what ini- tial data reproduce the simplest physically relevant black hole solution, namely that of Kerr-Newman which describes stationary, axisymmetric black hole with charge. Moreover, Krishnan's construction employs the non-twisting null geodesic congruence and the tetrad which is parallelly propagated along this congruence. While the existence of such tetrad can be easily established in general, its explicit form can be very difficult to find and, in fact it has not been provided for the Kerr-Newman metric. The goal of this thesis was to fill this gap and provide a full description of the Kerr-Newman metric in the framework of isolated horizons. In the theoretical part of the thesis we review the spinor and Newman-Penrose formalism, basic geometry of isolated horizons and then present our results. Thesis is complemented by several appendices.
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