Finding and using exact solutions of the Einstein equations
Abstract
The evolution of the methods used to find solutions of Einstein's field equations during the last 100 years is described. Early papers used assumptions on the coordinate forms of the metrics. Since the 1950s more invariant methods have been deployed in most new papers. The uses to which the solutions found have been put are discussed, and it is shown that they have played an important role in the development of many aspects, both mathematical and physical, of general relativity.
 Publication:

A Century of Relativity Physics: ERE 2005
 Pub Date:
 June 2006
 DOI:
 10.1063/1.2218172
 arXiv:
 arXiv:grqc/0601102
 Bibcode:
 2006AIPC..841..129M
 Keywords:

 04.20.Jb;
 04.25.g;
 Exact solutions;
 Approximation methods;
 equations of motion;
 General Relativity and Quantum Cosmology
 EPrint:
 15 pages, LaTeX2e, aipproc.cls, invited lecture to appear in the Proceedings of ERE05 (the Spanish Relativity Meeting), Oviedo, September 2005, to be published by the American Institute of Physics. v2: Remarks on black hole entropy corrected. Other minor changes