Selected topics in General RElativity

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

Syllabus

Martin Krššák:

1. Schwarzschild black hole reminder; coordinate systems for Schwarzschild black holes; maximally extended solution; Kruskal and Carter-Penrose conformal diagrams

2. Charged black holes: Reissner-Nordstrom solution; naked singularities; extremal black holes; Kruskal and conformal diagrams

3. Rotating black holes: Kerr solution; Laws of black hole mechanics, Smarr law; more general black hole solutions 

4. Geodesic congruences, energy conditions, Raychaudhuri equation, focusing theorem, null congruences

5. Hypersurfaces, normal vectors and induced metrics, Stokes’ theorem, Gauss-Codazzi equations and initial value problem

María José Guzmán:

References

1. C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation, W. H. Freeman,1973

2. S. Carroll, Spacetime and Geometry, CUP 2004

3. E. Poisson, A Relativist’s Toolkit: The Mathematics of Black-Hole Mechanics, CUP 2009

4. H. Reall, Black Holes, Math Tripos pIII Cambridge notes

5. R. Wald, General Relativity, University of Chicago Press, 1984

6. T. Padmanabhan, Gravitation: Foundations and frontiers, CUP, 2014

7. P. K. Townsend, Black Holes, ArXiv:gr-qc/9707012