Brozos-Vázquez, MiguelMojón Álvarez, Diego2025-11-122025-11-122025-05-03Brozos-Vázquez, M., Mojón-Álvarez, D. The vacuum weighted Einstein field equations. Math. Z. 310, 44 (2025). https://doi.org/10.1007/s00209-025-03747-11432-1823https://hdl.handle.net/2183/46432Financiado para publicación en acceso aberto: Universidade da Coruña/CISUG[Abstract] On a spacetime (M, g) endowed with a density function h, we consider the vacuum weighted Einstein field equations: hρ − Hesh +hg = 0. First, it is shown that the equation characterizes critical metrics for an appropriate action. Then, after describing locally conformally flat solutions in arbitrary dimension, fourdimensional solutions with harmonic curvature are classified.engAttribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/Smooth metric measure spaceStationary actionWeighted Einstein field equationsKundt spacetimeMultiply warped productjournal articleopen accesshttps://doi.org/10.1007/s00209-025-03747-1