Quo Vadis, Mathematical General Relativity?

We provide an introduction to selected recent advances in the mathematical understanding of Einstein's theory of gravitation.

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.

This Resource Letter provides some guidance on issues that arise in teaching general relativity at both the undergraduate and graduate levels. Particular emphasis is placed on strategies for presenting the mathematical material needed for the formulation of general relativity.

This is the centenary year of general relativity, it is therefore natural to reflect on what perspective we have evolved in 100 years. I wish to share here a novel perspective, and the insights and directions that ensue from it.

In this report, which is an extended version of that appearing in the Proceedings of GR16, I will give a summary of the main topics covered in Session A.3. on mathematical relativity at GR16, Durban. The summary is mainly based on extended abstracts submitted by the speakers. I would like to thank all participants for their contributions and help with this summary.

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

This text aims to explain general relativity to geometers who have no knowledge about physics. Using handwritten notes by Michel Vaugon, we construct the bases of the theory.

Einstein's general relativity is increasingly important in contemporary physics on the frontiers of both the very largest distance scales (astrophysics and cosmology) and the very smallest(elementary particle physics). This paper makes the case for a `physics first' approach to introducing general relativity to undergraduate physics majors.