TFNRAF0002 Relativistic Physics and Astrophysics II

Institute of physics in Opava
summer 2025
Extent and Intensity
4/2/0. 8 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Jan Schee, Ph.D. (lecturer)
Mgr. Dmitriy Ovchinnikov (seminar tutor)
Guaranteed by
doc. RNDr. Jan Schee, Ph.D.
Institute of physics in Opava
Timetable
Tue 8:55–10:30 B4, Wed 8:55–10:30 B4
  • Timetable of Seminar Groups:
TFNRAF0002/A: Mon 14:45–16:20 B4, D. Ovchinnikov
Prerequisites
(FAKULTA(FU) && TYP_STUDIA(N))
Prerequisite to this subject is successful successful mastery of the subject Relativistic physics and Astrophysics I.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
This subject let students to learn advanced parts of relativistic physics and astrophysics.
Learning outcomes
Graduating from this subject student will earn following capabilities: - analyse local and global properties of curved spacetimes
- analyse and solve problems connected with black hole perturbations and the stability analysis of particular black hole solutions of Einstein equations
- solve physical problems in framework of alternative theories of gravity (braneworld theory, Hořava gravity)
- find wormhole solutions and analyze associated fundamental physical phenomena (stress-energy tensor properties, closed time-like curves)
Syllabus
The key topics of the subject are:
- Other black hole solutions of Einstein equations: Reissner- Nordström, Kerr and Kerr-Newman black holes.
- Carter equations, test particle motion in the field of Kerr black hole.
- Black holes thermodynamics, Penrose process of energy extraction from rotating black hole, ergosphere, Hawking radiation and black hole evaporation, „no-hair” theorem.
- Penrose-Carter diagrams, Cauchy horizont.
- Black hole perturbation: Regge-Wheeler and Zerllini equations derivation, temporal evolution of gravitational field perturbations and exponenciální dumping. Schwarzschild black hole stability and quasinormal modes condition.
- Alternativne teory of gravity: Randal-Sundrum braneworld model, braneworld black hole solutions, nonlocal effects and braneworld parameter.
- Alternativne teory of gravity: Hořava gravity, ultra-relativistic violation of Lorentz structure, Kehagias-Sfetsos (KS) black hole, Hořava parameter.
- Test particle and physical fields motion in the fields of braneworld and KS black holes.
- Energetic conditions and examples of their violation.
- Wormhole history, Einstein-Rosen bridge and its stability.
- Construction of traversible wormhole, necessary stress-energy tensor conditions for traversible wormhole.
- Wormholes and closed time-like curves. Time-machine and time-paradoxes.
Literature
    recommended literature
  • Misner, C. W., Thorne, K. S., Wheeler, J. A. Gravitation, Freeman, San Francisco, 1973 (2017)
  • Schneider, P., Ehlers, J., Falco, E., E. Gravitational Lenses, A&A Library, Springer, 2009,
  • S Chandrasekhar. The Mathematical Theory of Black Holes. Oxford University Press, 1998. info
  • Visser, M. Lorentzian Wormholes: From Einstein to Hawking, AIP, 1996
  • Hořava, P. Quantum gravity at a Lifshitz point, Phys. Rev. D, 79, 8, 2009
  • Randall, L., Sundrum, R. An Alternative to Compactification, Phys. Rev. Lett, 83(23), 1999
  • Kehagios, A., Sfetsos, K. The black hole and FRW geometries in non-relativistic gravity, Phys. Lett. B, 678, 2009
Teaching methods
lectures, discussion, seminar, essay
Assessment methods
oral exam, written test
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is also listed under the following terms summer 2021, summer 2022, summer 2023, summer 2024.
  • Enrolment Statistics (recent)
  • Permalink: https://is.slu.cz/course/fu/summer2025/TFNRAF0002