Surveys in Differential Geometry

Volume 20 (2015)

Geons and the instability of anti-de Sitter spacetime

Pages: 321 – 335



Gary T. Horowitz (Department of Physics, University of California at Santa Barbara)

Jorge E. Santos (Department of Physics, Stanford University, Stanford, California, U.S.A.; and Department of Applied Mathematics and Theoretical Physics, University of Cambridge, England)


We briefly review the evidence that anti-de Sitter spacetime is nonlinearly unstable, and the perturbative arguments that there should exist geons—nonsingular solutions to Einstein’s equation with a helical symmetry. We then explicitly construct these geons numerically and discuss some of their properties. We conclude with some open questions.


anti-de Sitter spacetime, geons, instability, geons, numerical relativity

2010 Mathematics Subject Classification

35Q76, 83C05

Published 7 July 2015