Fuchsian analysis of singularities in Gowdy spacetimes beyond analyticity. (English) Zbl 0967.83021
Summary: Fuchsian equations provide a way of constructing large classes of spacetimes whose singularities can be described in detail. In some of the applications of this technique only the analytic case could be handled up to now. This paper develops a method of removing the undesirable hypothesis of analyticity. This is applied to the specific case of the Gowdy spacetimes in order to show that analogues of the results known in the analytic case hold in the smooth case. As far as possible the likely strengths and weaknesses of the method, as applied to more general problems are displayed.
MSC:
83C75 | Space-time singularities, cosmic censorship, etc. |
35Q75 | PDEs in connection with relativity and gravitational theory |
83C15 | Exact solutions to problems in general relativity and gravitational theory |