Advanced General Relativity
by Sergei Winitzki
Publisher: Google Sites 2007
Number of pages: 193
Topics include: Asymptotic structure of spacetime, conformal diagrams, null surfaces, Raychaudhury equation, black holes, the holographic principle, singularity theorems, Einstein-Hilbert action, energy-momentum tensor, Noether's theorem, tetrad (vierbein) formalism, spinor fields in curved spacetime, Hamiltonian formulation of GR, quantum cosmology.
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by Matthias Blau - Universitaet Bern
The first half of the book is dedicated to developing the machinery of tensor calculus and Riemannian geometry required to describe physics in a curved space time. We will then turn to various applications of General Relativity.
by Edmund Bertschinger - MIT
Working with GR requires some understanding of differential geometry. In this text we will develop the essential mathematics needed to describe physics in curved spacetime. These notes assume familiarity with special relativity.
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This text reviews the development of Einstein's thought on general covariance (the fundamental physical principle of GTR), its relation to the foundations of general relativity and the evolution of the continuing debate over his viewpoint.
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Starting from Newton's gravitational theory, we give a general introduction into the spherically symmetric solution of Einstein's vacuum field equation, the Schwarzschild solution, and into one specific stationary solution, the Kerr solution.