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- Title
The Einstein-Maxwell Equations and Conformally Kähler Geometry.
- Authors
LeBrun, Claude
- Abstract
Page's Einstein metric on $${{\mathbb{CP}}_2\#\overline{\mathbb{CP}}_2}$$ is conformally related to an extremal Kähler metric. Here we construct a family of conformally Kähler solutions of the Einstein-Maxwell equations that deforms the Page metric, while sweeping out the entire Kähler cone of $${{\mathbb{CP}}_2\#\overline{\mathbb{CP}}_2}$$ . The same method also yields analogous solutions on every Hirzebruch surface. This allows us to display infinitely many geometrically distinct families of solutions of the Einstein-Maxwell equations on the smooth 4-manifolds $${S^2 \times S^2}$$ and $${{\mathbb{CP}}_2\#\overline{\mathbb{CP}}_2}$$ .
- Subjects
EINSTEIN-Maxwell equations; MAXWELL equations; KAHLERIAN manifolds; CONFORMAL geometry; METRIC geometry; MATHEMATICAL physics
- Publication
Communications in Mathematical Physics, 2016, Vol 344, Issue 2, p621
- ISSN
0010-3616
- Publication type
Article
- DOI
10.1007/s00220-015-2568-5