Bogomolnyi Bound with a Cosmological Constant

Abstract

Bogomolnyi-type bound is constructed for the topological solitons in O(3) nonlinear $\sigma$ model coupled to gravity with a negative cosmological constant. Spacetimes made by self-dual solutions form a class of Gödel-type universe. In the limit of a spinless massive point particle, the obtained stationary metric does not violate the causality and it is a new point particle solution different from the known static hyperboloid and black hole. We also showed that static Nielsen-Olesen vortices saturate Bogomolnyi-type bound only when the cosmological constant vanishes.

11 pages, RevTeX

References in corpus (3)

• Reply to Comment on ``Spinning Cosmic Strings and Quantization of Energy''
• Global Vortex and Black Cosmic String
• Charged Black Cosmic String

Cited by in corpus (2)

• Gravitating Self-dual Chern-Simons Solitons
• Black Brane World from Gravitating Half $\sigma$-lump