General Relativity and Gravitation

, Volume 28, Issue 11, pp 1401–1407

Comment on “smooth and discontinuous signature change in general relativity”

  • Tevian Dray
  • Charles Hellaby

DOI: 10.1007/BF02109530

Cite this article as:
Dray, T. & Hellaby, C. Gen Relat Gravit (1996) 28: 1401. doi:10.1007/BF02109530


Kossowski and Kriele derived boundary conditions on the metric at a surface of signature change. We point out that their derivation is based not only on certain smoothness assumptions but also on a postulated form of the Einstein field equations. Since there is no canonical form of the field equations at a change of signature, their conclusions are not inescapable. We show here that a weaker formulation is possible, in which less restrictive smoothness assumptions are made, and (a slightly different form of) the Einstein field equations are satisfied. In particular, in this formulation it is possible to have a bounded energy-momentum tensor at a change of signature without satisfying their condition that the extrinsic curvature vanish.

Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • Tevian Dray
    • 1
  • Charles Hellaby
    • 3
  1. 1.School of Physics & ChemistryLancaster UniversityLancasterUK
  2. 2.Department of MathematicsOregon State UniversityCorvallisUSA
  3. 3.Department of Applied MathematicsUniversity of Cape TownRondeboschSouth Africa