The main objective of this course is to discuss some advanced topics in gravitational physics and its applications to high energy physics. Necessary mathematical tools will be introduced on the way. These mathematical tools will include a review of differential geometry (tensors, forms, Lie derivative), vielbeins and Cartan’s formalism, hypersurfaces, Gauss-Codazzi formalism, and variational principles (Einstein-Hilbert action & Gibbons-Hawking term). Several topics in black hole physics including the Kerr solution, black hole astrophysics, higher-dimensional black holes, black hole thermodynamics, Euclidean action, and Hawking radiation will be covered. Additional advanced topics will include domain walls, brane world scenarios, Kaluza-Klein theory and KK black holes, Gregory-Laflamme instability, and gravitational instantons
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