Pseudo-Kahler-Einstein geometries

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Amer Physical Soc
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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 Kahler 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.
© 2022 Amer Physical Soc This work was partially supported by the MICINN (Ministerio de Ciencia e Innovacion, Spain) Project No. PID2019-107394GB-I00 (AEI/FEDER, UE) . J. A. R. C. acknowledges support by Institut Pascal at Universite Paris-Saclay during the Paris-Saclay Astroparticle Symposium 2021, with the support of the P2IO (Physics of the two infinities and Origins) Laboratory of Excellence (program "Investissements d'avenir" ANR-11-IDEX-0003-01 Paris-Saclay and ANR-10-LABX-0038) , the P2I (Physics of the two infinities) axis of the Graduate School Physics of Universite Paris-Saclay, as well as IJCLab (Laboratoire de Physique des 2 Infinis Ire`ne Joliot-Curie) , CEA (Commissariat a` l'energie atomique) , IPhT (Institute of Theoretical Physics) , APPEC (Astroparticle physics Consortium) , the IN2P3 (Institut national de physique nucleaire et de physique des particules) master projet UCMN and EuCAPT (European Consortium for Astroparticle Theory) . This research was supported by the Munich Institute for Astro-and Particle Physics (MIAPP) which is funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy-EXC-2094-390783311.
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