2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/182891We consider global monopoles as well as black holes with global monopole hair in Einstein-Goldstone model with a cosmological constant in four spacetime dimensions. Similar to the $Λ=0$ case, the mass of these solutions defined in the standard way diverges. We use a boundary counterterm subtraction method to compute the mass and action of $Λ\neq 0$ configurations. The mass of the asymptotically de Sitter solutions computed in this way turns out to take positive values in a specific parameter range and, for a relaxed set of asymptotic boundary conditions, yields a counterexample to the maximal mass conjecture.18 pages, 7 figures; v2: references added, typos corrected, extended discussion on mass computationHigh Energy Physics - TheoryGeneral Relativity and Quantum Cosmologytext