NONISOMETRIC VACUUM EXTENSIONS OF VACUUM MAXIMAL GLOBALLY HYPERBOLIC SPACETIMES

We discuss a number of familes of maximal globally hyperbolic vacuum spacetimes-Taub, Misner, and polarized Gowdy-and their nonglobally hyperbolic extensions. We show that many of the familiar extensions are isometric, but we also show that in the Taub and Gowdy familes there are nonisometric maximal extensions. In the latter family, we show there are spacetimes that have an arbitrarily large number of nonisometric maximal extensions.