Mathematical Institute
Topic
Schwarzschild metric and its generalization
PhD. program
Mathematics (PF UPJŠ, Mathematics (1113))
Year of admission
2026
Name of the supervisor
doc. RNDr. Karol Nemoga, CSc.
Contact:
Receiving school
Faculty of Science, Pavol Jozef Šafárik University Košice
Annotation
supervisor: doc. RNDr. Ján Brajerčík, PhD., MI SAS, Košice (external supervisor),
e-mail: jan.brajercik@unipo.sk
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The thesis deals with the mathematical foundations of the general relativity. The starting point is the structure of the Schwarzschild metric and the underlying geometric structures of the general relativity. The goal is to obtain assertions on the generalization of the Schwarzschild metric to metric dependent on velocities (Finsler metric) invariant to the action of the Lie groups of general relativity.
References:
[1] De Felice, F.; Clarke, C.J.S. Relativity on Curved Manifolds. In Cambridge Monographs on Mathematical Physics; Cambridge University Press: Cambridge, UK, 1990.
[2] D. Krupka, Introduction to Global Variational Geometry, Atlantis Studies in Variational Geometry, D. Krupka, H. Sun (Eds.), Atlantis Press, 2015.
[3] D. Krupka, J. Brajerčík, Schwarzschild Spacetimes: Topology. Axioms 2022, 11 (12) 693. https://doi.org/10.3390/axioms11120693
e-mail: jan.brajercik@unipo.sk
==
The thesis deals with the mathematical foundations of the general relativity. The starting point is the structure of the Schwarzschild metric and the underlying geometric structures of the general relativity. The goal is to obtain assertions on the generalization of the Schwarzschild metric to metric dependent on velocities (Finsler metric) invariant to the action of the Lie groups of general relativity.
References:
[1] De Felice, F.; Clarke, C.J.S. Relativity on Curved Manifolds. In Cambridge Monographs on Mathematical Physics; Cambridge University Press: Cambridge, UK, 1990.
[2] D. Krupka, Introduction to Global Variational Geometry, Atlantis Studies in Variational Geometry, D. Krupka, H. Sun (Eds.), Atlantis Press, 2015.
[3] D. Krupka, J. Brajerčík, Schwarzschild Spacetimes: Topology. Axioms 2022, 11 (12) 693. https://doi.org/10.3390/axioms11120693