We revisit our calculations in [1] and found that there are some mistakes in the solutions of power-law global monopole black holes and compactification channels. We hereby present the following erratum correcting our error and modifying our conclusions. * Electronic address: ilham.prasetyo51@ui.ac.id † Electronic address: hramad@ui.ac.id
AbstractWe obtain solutions of Einstein's equations describing gravitational field outside a noncanonical global monopole with cosmological constant. In particular, we consider two models of k-monopoles: the Dirac-Born-Infeld (DBI) and the power-law types, and study their corresponding exterior gravitational fields. For each model we found two types of solutions. The first of which are global k-monopole black hole with conical global topology. These are generalizations of the Barriola-Vilenkin solution of global monopole. The appearance of noncanonical kinetic terms does not modify the critical symmetry-breaking scale, η crit , but it does affect the corresponding horizon(s).The second type of solution is compactification, whose topology is a product of two 2-dimensional spaces with constant curvatures; Y 4 → Z 2 × S 2 , with Y, Z can be de Sitter, Minkowski, or Anti-de Sitter, and S 2 is the 2-sphere. We investigate all possible compactifications and show that the nonlinearity of kinetic terms opens up new channels which are otherwise non-existent. For Λ = 0 four-dimensional geometry, we conjecture that these compactification channels are their (possible) non-static super-critical states, right before they undergo topological inflation. * Electronic address: ilham.prasetyo51@ui.ac.id † Electronic address: hramad@ui.ac.id