Global monopoles, cosmological constant and maximal mass conjecture

TL;DR

This paper investigates global monopoles and black holes with monopole hair in Einstein-Goldstone theory with a cosmological constant, revealing solutions that challenge the maximal mass conjecture in de Sitter space.

Contribution

It extends the analysis of monopole solutions to include a cosmological constant and demonstrates counterexamples to the maximal mass conjecture.

Findings

Mass of solutions can be positive in de Sitter space.

Counterexamples to the maximal mass conjecture are found.

Boundary counterterm method effectively computes mass and action.

Abstract

We 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 $\Lambda=0$ 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 $\Lambda \neq 0$ 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.