Quasi-asymptotically flat spacetimes and their ADM mass

We define spacetimes that are asymptotically flat, except for a deficit solid angle 0264-9381/14/5/031/img5 and present a definition of their `ADM' mass, which is finite for this class of spacetimes, and, in particular, coincides with the value of the parameter M of the global monopole spacetime studied by Vilenkin and Barriola. Moreover, we show that the definition is coordinate independent, and explain why it can, in some cases, be negative.