Higher-dimensional spacetimes
Advisor: Marcello Ortaggio (IM CAS)
Funding: Fully funded. Basic stipend will be supplemented to net 20 000 CZK/month with grants and institution funds.
Contact: ortaggio@math.cas.cz

Gravity in more than four spacetime dimensions is an area of active theoretical research, 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 Lorentzian spaces is of interest also from a purely geometrical viewpoint.

Several qualitatively new higher-dimensional features have been revealed in recent years. These range from uniqueness and stability properties of black holes, to the asymptotic behavior of gravitational and electromagnetic fields and extensions of the Goldberg-Sachs theorem.

This project will aim at answering some remaining open questions about asymptotic properties of (electro)vacuum solutions in higher dimensions, such as a characterization of the space of solutions which satisfies certain boundary conditions (typically asymptotically flat or (A)dS with some restrictions on the Weyl tensor or on matter fields). These results can be employed in various directions (e.g., a study of radiative fields [1,2] or the "uniqueness" of certain black holes solution within algebraically special spacetimes [3-5]). Within this context, the precise focus of the thesis can be determined also depending on the student's interests. Analytic techniques developed by our group and collaborators in the past few years will be a useful tool for this investigation [6].

[1] M. Ortaggio, A. Pravdová, Asymptotic behaviour of the Weyl tensor in higher dimensions, Phys. Rev. D90 (2014) 104011
[2] M. Ortaggio, Asymptotic behavior of Maxwell fields in higher dimensions, Phys.Rev. D90 (2014) 124020.
[3] M. Ortaggio, V. Pravda, A. Pravdová, On asymptotically flat algebraically special spacetimes in higher dimensions, Phys. Rev. D 80, 084041 (2009).
[4] G. Bernardi de Freitas, M. Godazgar, H. S. Reall, Uniqueness of the Kerr–de Sitter Spacetime as an Algebraically Special Solution in Five Dimensions, Commun. Math. Phys. 340 (2015) 291-323
[5] M. Ortaggio, On the uniqueness of the Myers-Perry spacetime as a type II(D) solution in six dimensions, JHEP 1706 (2017) 042.
[6] M. Ortaggio, V. Pravda and A. Pravdová, Algebraic classification of higher dimensional spacetimes based on null alignment, 2013 Class. Quantum Grav. 30 013001