Brozos-Vázquez, MiguelMojón Álvarez, Diego2024-07-052024-07-052022Brozos-Vázquez, M., Mojón-Álvarez, D., 2022. Vacuum Einstein field equations in smooth metric measure spaces: the isotropic case. Class. Quantum Grav. 39, 135013. https://doi.org/10.1088/1361-6382/ac72e91361-6382http://hdl.handle.net/2183/37740Accepted manuscript[Abstract] On a smooth metric measure spacetime (M, g, e−fdvolg), we define a weighted Einstein tensor. It is given in terms of the Bakry–Émery Ricci tensor as a tensor which is symmetric, divergence-free, concomitant of the metric and the density function. We consider the associated vacuum weighted Einstein field equations and show that isotropic solutions have nilpotent Ricci operator. Moreover, the underlying manifold is a Brinkmann wave if it is two-step nilpotent and a Kundt spacetime if it is three-step nilpotent. More specific results are obtained in dimension 3, where all isotropic solutions are given in local coordinates as plane waves or Kundt spacetimes.engThis Accepted Manuscript is available for reuse under a CC BY-NC-ND licence after the 12 month embargo period provided that all the terms of the licence are adhered to. https://creativecommons.org/licenses/by-nc-nd/4.0/http://creativecommons.org/licenses/by-nc-nd/3.0/es/Smooth metric measure spaceVacuum Einstein eld equationsBakry-Émery Ricci tensorKundt spacetimeBrinkmann wavePP-wavePlane wavejournal articleopen accesshttps://doi.org/10.1088/1361-6382/ac72e9