Geodetická deviácia a geometrický význam Riemannovho tenzora; kongruencie geodetík; expanxia, shear, a twist; Raychaudhuriho rovnica
A joint course between Bratislava and Tartu
Lecturers: Martin Krššák, María José Guzmán, Sotirios Karamitsos
Schwarzschild black hole reminder; coordinate systems for Schwarzschild black holes; maximally extended solution; Kruskal and Carter-Penrose conformal diagrams
Charged black holes: Reissner-Nordstrom solution; naked singularities; extremal black holes; Kruskal and conformal diagrams
Rotating black holes: Kerr solution; horizon and ergosphere; zero angular momentum and static observers; maximal extension of Kerr spacetime, Penrose diagram
Killing vectors and conserved quantities for particles; stationary observers in Kerr spacetime; Penrose process; irreducible mass; Smarr law; black hole mechanics and the analogy with thermodynamics
Conserved currents and quantities; hypersurfaces, normal vectors, induced metric; Komar mass, Schwarzchild example; covariant conservation laws as a consequence of diffeomorphism symmetry
S. Carroll, Spacetime and Geometry, CUP 2004
E. Poisson, A Relativist’s Toolkit: The Mathematics of Black-Hole Mechanics, CUP 2009
H. Reall, Black Holes, Math Tripos pIII Cambridge notes
C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation, W. H. Freeman,1973
R. Wald, General Relativity, University of Chicago Press, 1984
T. Padmanabhan, Gravitation: Foundations and frontiers, CUP, 2014
P. K. Townsend, Black Holes, ArXiv:gr-qc/9707012