Gravitating monopole and its black hole solution in Brans-Dicke theory

We find a self-gravitating monopole and its black hole solution in Brans-Dicke (BD) theory. We mainly discuss the properties of these solutions in the Einstein frame and compare the solutions with those in general relativity (GR) on the following points. From the field distributions of the generic type of self-gravitating monopole solutions, we find that the Yang-Mills potential and the Higgs field hardly depend on the BD parameter for most of the solution. There is an upper limit of the vacuum expectation value of the Higgs field to which a solution exists, as in GR. Since the BD scalar field has the effect of lessening an effective gauge charge, the upper limit in BD theory (in the $\omega =0\mathrm{}$ case) becomes about $30\%$ larger than in GR. In some parameter ranges, there are two nontrivial solutions with the same mass, one of which can be regarded as the excited state of the other. This is confirmed by the analysis by catastrophe theory, which states that the excited solution is unstable. We also find that the BD scalar field varies more for solutions of smaller horizon radii, which can be understood from the differences of the nontrivial structure outside the horizon. A scalar mass and the thermodynamical properties of new solutions are also examined. Our analysis may give insight into solutions in other theories of gravity; particularly, a theory with a dilaton field may show similar effects because of its coupling to a gauge field.