Kerr-NUT-AdS prostorčasy a jejich zobecnění

• Název práce v češtině: Kerr-NUT-AdS prostorčasy a jejich zobecnění
• Název v anglickém jazyce: Kerr-NUT-AdS spacetimes and their generalizations
• Klíčová slova: gravitace|vícedimenzionální prostoročasy|černé díry|skryté symetrie|integrabilita a separabilita
• Klíčová slova anglicky: gravity|higher-dimensional spacetimes|black holes|hidden symmetries|integrability and separability
• Akademický rok vypsání: 2021/2022
• Typ práce: disertační práce
• Ústav: Ústav teoretické fyziky (32-UTF)
• Vedoucí / školitel: prof. RNDr. Pavel Krtouš, Ph.D.

Zásady pro vypracování

The project will study rotating black holes with spherical topology of horizon, with possible additional sources on the axis, generalized to an arbitrary dimension. These are described by so called Kerr-NUT-(A)dS spacetimes. The most of their properties stems from their high symmetry which is encoded by the principal tensor. It guarantees the existence of the tower of Killing tensors and Killing vectors, which imply that the geodesic motion is integrable and the basic field equations are separable.

Recently, the separability of the electromagnetic and massive vector field in these spacetimes has been widely discussed. One of the tasks would be clarification of some issues related to this separability, using, e.g., a comparison with the standard separation methods in four dimension or by studying limits to known cases of the Schwarzschild and Minkowski spacetime.
Similarly, one can study also the separability of gravitational perturbations.

Another open problem of higher-dimensional black holes is the absence of a charged solution, as well as of an analogy of the C-metric solution (accelerated black holes). In four dimensions it is known that these solutions are of the Petrov type D, but the C-metric does not possesses the principal tensor, just the conformal Killing-Yano tensor. Therefore, it would be interesting to look for higher-dimensional metrics having just the conformal Killing-Yano tensor and try to employ such metrics for identifications of a solution with accelerated black holes.

Seznam odborné literatury

[1] Frolov V. P., Krtouš P., Kubizňák D.: Black holes, hidden symmetries, and complete integrability, Living Rev. Relat. 20 (2017) 6
[2] Krtouš P., Frolov V. P., Kubizňák D.: Separation of Maxwell equations in Kerr-NUT-(A)dS spacetimes, Nucl. Phys. B 934 (2018) 7

the comprehensive overview of the references can be found in [1]

Předběžná náplň práce v anglickém jazyce

In past decades black holes have become standard objects used both in theoretical research and as astrophysical sources. They have been observed by different methods, investigated from many points of view and generalized to various situations.

In this project we will be interested in rotating black holes with spherical topology of horizon, with possible additional sources on the axis, generalized to an arbitrary dimension. These are described by so called Kerr-NUT-(A)dS spacetimes. The most of their properties stems from their high symmetry [Living Rev. Relat. 20 (2017) 6]. It has been demonstrated that this symmetry is encoded by the principal tensor (the non-degenerated closed conformal Killing-Yano tensor of rank 2). It guarantees the existence of the tower of Killing tensors and Killing vectors, which imply that the geodesic motion is integrable and the basic field equations are separable.

The separability has been shown for the scalar, Dirac, electromagnetic and massive vector field. It is still an open problem for the gravitational perturbations. Also an interpretation of all modes for the electromagnetism is still not completely finished [Nucl. Phys. B 934 (2018) 7]. One of the tasks in this research would be clarification of the separability for the electromagnetic field: e.g., a comparison with the standard methods in four dimension, limits to known cases of the Schwarzschild and Minkowski spacetime, etc.

Another open problem of higher dimensional black hole is the absence of a charged solution, as well as of an analogy of the C-metric solution (accelerated black holes). In four dimensions it is known that these solutions are of the Petrov type D, but the C-metric does not possesses the principal tensor, just the conformal Killing-Yano tensor. Therefore, it would be interesting to look for higher-dimensional metrics having just the conformal Killing-Yano tensor and try to employ such metrics for identifications of a solution with accelerated black holes.