2015 is the centennial of Einstein General Relativity. On this occasion, we examine the General Relativity and Quantum Cosmology (GRQC) field of research by analysing 38291 papers uploaded on the electronic archives arXiv.org from 2000 to 2012. We establish a map of the countries contributing to GRQC in 2012. We determine the main journals publishing GRQC papers and which countries publish in which journals. We find that more and more papers are written by groups (instead of single) of authors with more and more international collaborations. There are huge differences between countries. Hence Russia is the country where most of papers are written by single authors whereas Canada is one of the countries where the most of papers imply international collaborations. We also study authors mobility, determining how some groups of authors spread worldwide with time in different countries. The largest mobilities are between USA-UK and USA-Germany. Countries attracting the most of GRQC authors are Netherlands and Canada whereas those undergoing a brain drain are Italy and India. There are few mobility between Europe and Asia contrarily to mobility between USA and Asia.

18 pages, 14 figures, to be published in Scientometrics