The vacuum weighted Einstein field equations

2024/07/26 by Brozos-Vázquez, M., Mojón-Álvarez, D.
#53B30 #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc)

paper · doi:10.48550/arxiv.2407.18791

Abstract

On a spacetime (M,g) endowed with a density function h, we consider the vacuum weighted Einstein field equations: hρ-Hes_h+Δh g=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, four-dimensional solutions with harmonic curvature are classified.

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