Asymptotic properties of electrovacuum spacetimes in higher dimensions

• Název práce v češtině: Asymptotic properties of electrovacuum spacetimes in higher dimensions
• Název v anglickém jazyce: Asymptotic properties of electrovacuum spacetimes in higher dimensions
• Akademický rok vypsání: 2024/2025
• Typ práce: diplomová práce
• Ústav: Ústav teoretické fyziky (32-UTF)
• Vedoucí / školitel: Marcello Ortaggio

Zásady pro vypracování

Topics of interest for a diploma work include the asymptotic behavior of the gravitational and electromagnetic fields at null infinity in General Relativity.

Earlier works have pointed out some qualitative new features when the number of spacetime dimensions is greater than four [1,2]. In particular, the "peeling-off" behavior has been studied for gravity [2,3] and test Maxwell fields [4].
One of the goals of the thesis will be an extension of [3,4] to include the back-reaction of the electromagnetic field as well as p-form fields. Higher-dimensional generalizations of the Newman-Penrose and Geroch-Held-Penrose formalisms and the boost-weight algebraic classification of tensors (cf. e.g. the review [5]) will be useful tools.

Seznam odborné literatury

[1] S. Hollands and R. M.Wald, Classical Quantum Gravity 21, 5139 (2004)
[2] M. Godazgar and H. S. Reall, Phys. Rev. D 85, 084021 (2012)
[3] M. Ortaggio and A. Pravdová, Phys. Rev. D 90, 104011 (2014)
[4] M. Ortaggio, Asymptotic behaviour of Maxwell fields in higher dimensions, Phys. Rev. D 90, 124020 (2014)
[5] M. Ortaggio, V. Pravda and A. Pravdová, Algebraic classification of higher dimensional spacetimes based on null alignment Class. Quantum Grav. 30, 013001 (2013)

Předběžná náplň práce

In recent years, there has been a significant increase in interest in the properties of gravity in more than four spacetime dimensions, motivated, e.g., by fundamental theories such as string theory, along with the idea of extra dimensions and braneworld models of TeV gravity. The study of higher-dimensional spacetimes, however, is of interest also from a purely geometrical viewpoint.

Several higher-dimensional solutions of classical General Relativity have been known for some time, and various techniques to study and classify exact solutions have been extended to an arbitrary number D of dimension. There are, however, general qualitatively new features when D>4. These concern, among others, radiative and asymptotic properties of gravitational and electromagnetic fields, which are relevant to the study of isolated systems. This will be the topic of the diploma work.

Předběžná náplň práce v anglickém jazyce

In recent years, there has been a significant increase in interest in the properties of gravity in more than four spacetime dimensions, motivated, e.g., by fundamental theories such as string theory, along with the idea of extra dimensions and braneworld models of TeV gravity. The study of higher-dimensional spacetimes, however, is of interest also from a purely geometrical viewpoint.

Several higher-dimensional solutions of classical General Relativity have been known for some time, and various techniques to study and classify exact solutions have been extended to an arbitrary number D of dimension. There are, however, general qualitatively new features when D>4. These concern, among others, radiative and asymptotic properties of gravitational and electromagnetic fields, which are relevant to the study of isolated systems. This will be the topic of the diploma work.