We define spacetimes that are asymptotically flat, except for a deficit solid angle 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.
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Nucamendi et al. (1997) studied this question.
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