5 papers
Conformally weighted Einstein manifolds: the uniqueness problem
Miguel Brozos-Vázquez, Eduardo García-Río, Diego Mojón-Álvarez
We discuss smooth metric measure spaces admitting two weighted Einstein representatives of the same weighted conformal class. First, we describe the local geometries of such manifo…
The vacuum weighted Einstein field equations
M. Brozos-Vázquez, D. Mojón-Álvarez
On a spacetime endowed with a density function , we consider the vacuum weighted Einstein field equations: \[hρ-\operatorname{Hes}_h+Δh g=0.\] First, it is shown that th…
The vacuum weighted Einstein field equations on pr-waves
Miguel Brozos-Vázquez, Diego Mojón-Álvarez
We classify solutions of the vacuum weighted Einstein field equations on smooth metric measure spacetimes of dimension 4, where the underlying manifold i…
Rigidity of weighted Einstein smooth metric measure spaces
Miguel Brozos-Vázquez, Diego Mojón-Álvarez
We study the geometric structure of weighted Einstein smooth metric measure spaces with weighted harmonic Weyl tensor. A complete local classification is provided, showing that eit…
Vacuum Einstein field equations in smooth metric measure spaces: the isotropic case
Miguel Brozos-Vázquez, Diego Mojón-Álvarez
On a smooth metric measure spacetime , we define a weighted Einstein tensor. It is given in terms of the Bakry-Émery Ricci tensor as a tensor which is symmetri…