FPFVA051 Relativistic Physics and Astrophysics II

Faculty of Philosophy and Science in Opava
Summer 2022
Extent and Intensity
4/2/0. 8 credit(s). Type of Completion: zk (examination).
Teacher(s)
Roman Konoplya, Ph.D. (lecturer)
Roman Konoplya, Ph.D. (seminar tutor)
Guaranteed by
doc. RNDr. Jan Schee, Ph.D.
Institute of physics in Opava
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 (in Czech)
Studenti budou během semestru vypracovávat seminární práci na zadané téma. Na závěr kurzu budou studenti písemně řešit zadané úlohy v určeném, limitovaném čase.
Syllabus
  • 1. Gravitational lens and raytracinng in curved spacetimes
  • a. WKB approximation and geometric optics. Lens equation and deflection angle.
  • b. Magnification factor and theorem, critical points, caustics, Schwarzchild lens.
  • c. Perturbed gravitational lens, gravitational lens in the expanding Universe.
  • 2. Perturbation of black holes
  • a. Discussion of quasinormal modes, simple examples in classical mechanics
  • b. Derivation of Regge-Wheeler and Zerllini equations. Solutions of temporal evolution of scalar fields perturbations.
  • c. Solutions of electromagnetic and gravitational perturbation. Discussion of exponential dumping.
  • d. Discussing the stability of the Schwarzchild black hole in terms of perturbation theory.
  • 3. Alternative teories of gravity
  • a. Randal-Sundrum model of braneworlld universe, Hiearchy-problem resolution. Projection of 5D Einstein's equations onto 3D-brane. Hořava gravity, action of the Hořava field, violation of the Lorentz invariance at Planck scale level,
  • b. Braneworld black holes - static braneworld Reissner-Nordstrom and stationary braneworld Kerr-Newman solutions, branewold tidal-charge parameter. Kehagias-Sfetsos black hole, Hořava parameter.
  • c. Motion of test particles a test fields in the fields of braneworld and KS black holes. Structure of circular orbits.
  • 4. Wormholes.
  • a. Kruskal-Szekeres extension of the Schwarzchild solution. Einstein-Rosen bridge and its stability/instability.
  • b. Construction of traversible wormhole. Properties of the stress-energy tensor required by traversible wormhole. Energetic conditions and examples of their their violations.
Literature
    required literature
  • M. Morris and K. Thorne, Wormholes in spacetime and their use for interstellar travel: A tool for teaching general relativity , American Journal of Physics, 56(5), pp. 395-412 (1988)
  • J. Schee, P. Slaný, and F. Blaschke, Problem set: Relativistic physics and Astrophysics, live e-form (2019)
  • L. Randall a R. Sundrum: An Alternative to Compactification, Phys. Rev. Lett, 83(23) (1999)
  • P.Hořava: Quantum gravity at a Lifshitz point, Phys. Rev. D, 79, 8 (2009)
  • A. Kehagios a K. Sfetsos: The black hole and FRW geometries in non-relativistic gravity, Phys. Lett. B, 678(1) (2009)
  • Ch. W. Misner, K.S. Thorne, and J. A. Wheeler. Gravitation. W.H.Freeman and Company, 1973. info
    recommended literature
  • M. Visser: Lorentzian Wormholes: From Einstein to Hawking, AIP (1996)
  • P. Schneider, J. Ehlers and E. E. Falco. Gravitational lenses. Springer, 1999. info
  • S Chandrasekhar. The Mathematical Theory of Black Holes. Oxford University Press, 1998. info
Language of instruction
English
Further Comments
Study Materials
The course is also listed under the following terms Summer 2021, Summer 2023.
  • Enrolment Statistics (Summer 2022, recent)
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