FPFVA051 Relativistic Physics and Astrophysics II

Filozoficko-přírodovědecká fakulta v Opavě
léto 2023
Rozsah
4/2/0. 8 kr. Ukončení: zk.
Vyučující
Roman Konoplya, Ph.D. (přednášející)
Roman Konoplya, Ph.D. (cvičící)
Garance
doc. RNDr. Jan Schee, Ph.D.
Fyzikální ústav v Opavě
Omezení zápisu do předmětu
Předmět je nabízen i studentům mimo mateřské obory.
Mateřské obory/plány
Cíle předmětu
Studenti budou během semestru vypracovávat seminární práci na zadané téma. Na závěr kurzu budou studenti písemně řešit zadané úlohy v určeném, limitovaném čase.
Osnova
  • 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.
Literatura
    povinná literatura
  • 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
    doporučená literatura
  • 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
Vyučovací jazyk
Angličtina
Předmět je zařazen také v obdobích léto 2021, léto 2022.
  • Statistika zápisu (nejnovější)
  • Permalink: https://is.slu.cz/predmet/fpf/leto2023/FPFVA051