Gravity of a noncanonical global monopole: conical topology and compactification

TL;DR

This paper derives solutions for the gravitational field of noncanonical global monopoles with a cosmological constant, revealing new compactification channels influenced by nonlinear kinetic terms, with implications for topological inflation.

Contribution

It introduces new solutions for noncanonical global monopoles, including black holes with conical topology and novel compactification channels affected by kinetic nonlinearity.

Findings

Noncanonical kinetic terms do not alter the critical symmetry-breaking scale.

Existence of black hole solutions with conical global topology.

Identification of new compactification channels influenced by nonlinearity.

Abstract

We 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, $\eta_{crit}$, 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; ${\mathcal Y}_4\rightarrow {\mathcal Z}_2\times S^2$, with ${\mathcal Y}, {\mathcal Z}$ 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 $\Lambda=0$ four-dimensional geometry, we conjecture that these compactification channels are their (possible) non-static super-critical states, right before they undergo topological inflation.