Mathematical general relativity: a sampler

A review of selected topics in mathematical general relativity

Einstein's general relativity is the best available theory of gravity. In recent years, spectacular proofs of Einstein's theory have been conducted, which have aroused interest that goes far beyond the narrow circle of specialists. The aim of this work is to offer an elementary introduction to general relativity. In this first part, we introduce the geometric concepts that constitute the basis of Einstein's theory. In the second part we will use these concepts to explore the ...

These lectures notes contain an introduction to General Relativity. They are addressed to a general mathematical audience with no specific background in physics. The goal is to motivate and explain Einstein's theory of gravity and discuss some of the fundamental examples.

Lecture notes written for a one-semester course in mathematical relativity aimed at mathematics and physics students. Not meant as an introduction to general relativity, but rather as a complementary, more advanced text.

We report on selected oral contributions to the A2 session "Mathematical relativity and other progress in classical gravity theory" of "The 20th International Conference on General Relativity and Gravitation (GR20)" in Warsaw.

To commemorate the 100th anniversary of general relativity, the International Society on General Relativity and Gravitation (ISGRG) commissioned a Centennial Volume, edited by the authors of this article. We jointly wrote introductions to the four Parts of the Volume which are collected here. Our goal is to provide a bird's eye view of the advances that have been made especially during the last 35 years, i.e., since the publication of volumes commemorating Einstein's 100th bi...

This is Chapter 1 in the book General Relativity and Gravitation: A Centennial Perspective, Edited by Abhay Ashtekar (Editor in Chief), Beverly Berger, James Isenberg, Malcolm MacCallum. Publisher: Cambridge University Press (June, 2015). It gives a survey of themes that have been developed during the 100 years of progress in general relativity theory.

These are lectures on General Theory of Relativity that were given to students of the Mathematical Faculty of the Higher School of Economics in Moscow.

The aim of this work is to use the notions of Riemann's geometry introduced in Part I, to analyze the foundations of Einstein's theory of general relativity.

These notes represent approximately one semester's worth of lectures on introductory general relativity for beginning graduate students in physics. Topics include manifolds, Riemannian geometry, Einstein's equations, and three applications: gravitational radiation, black holes, and cosmology.