Abstract
Solutions to vacuum Einstein field equations with cosmological constants, such as the de Sitter space and the anti–de Sitter space, are basic in different cosmological and theoretical developments. It is also well known that complex structures admit metrics of this type. The most famous example is the complex projective space endowed with the Fubini-Study metric. In this work, we perform a systematic study of Einstein complex geometries derived from a logarithmic Kähler potential. Depending on the different contribution to the argument of such logarithmic term, we shall distinguish among direct, inverted and hybrid coordinates. They are directly related to the signature of the metric and determine the maximum domain of the complex space where the geometry can be defined.
- Received 17 December 2021
- Accepted 16 February 2022
DOI:https://doi.org/10.1103/PhysRevD.105.065006
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.
Published by the American Physical Society