A joint course between Bratislava and Tartu
Lecturers: Martin Krššák, María José Guzmán, Sotirios Karamitsos
Coordinates: Wednesday 13:10-15:40 CET, 26/2-14/5 2025, Room (Bratislava) F2-125 + Zoom
Martin Krššák:
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
María José Guzmán:
C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation, W. H. Freeman,1973
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
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