Comment on " Boundary Conditions for the Scalar Field in the Presence of Signature Change "

Fundamental errors exist in the above-mentioned article, which attempts to justify previous erroneous claims concerning signature change. In the simplest example, the authors’ proposed “solutions” do not satisfy the relevant equation, as may be checked by substitution. These “solutions” are also different to the authors’ originally proposed “solutions”, which also do not satisfy the equation. The variational equations obtained from the authors’ “actions” are singular at the change of signature. The authors’ “distributional field equations” are manifestly ill defined. Several years ago, Dray et al. (1991) reported solutions to the wave equation across a change of signature which do not satisfy the usual junction conditions, namely that the momentum fields vanish at the change of signature. These conditions are well known in quantum cosmology, where signature-changing solutions are known as real tunnelling solutions (e.g. Gibbons & Hartle 1990). The junction conditions were also derived by various purely classical methods (Hayward 1992, 1993, Kossowski & Kriele 1993, 1994). However, Dray et al. (1993) later claimed to have justified their original claims, and Hellaby & Dray (1994) went on to claim that matter conservation is violated at a change of signature. Some of the mistakes behind these claims have been identified already (Hayward 1993, 1995), but have not been accepted by the authors concerned. Nevertheless, it was recently shown that though the “solutions” of Dray et al. do not satisfy the relevant field equation, they could be re-interpreted as weak solutions, if the equation were written in a certain form (Hayward 1994). Dray et al. (1995) have rejected this re-interpretation and again attempted to justify their previous claims. This latest article is considered in the following. It contains several fundamental errors, some of which had already been identified in the articles cited above. It also seriously misrepresents some of these articles. The authors’ own equation numbering and section heading will be used. Example. The authors’ first substantive claim, concerning the equation