Infinitesimal relative position vector fields for observers in a reference frame and applications to conformally stationary spacetimes

  • Magdalena CaballeroEmail author
  • Daniel de la Fuente
  • Rafael M. Rubio


We introduce and analyze the concept of infinitesimal relative position vector field between “infinitesimally nearby” observers, showing the equivalence between different definitions. Through the Fermi–Walker derivative of infinitesimal relative position vector fields along an observer in a reference frame, we characterize spacetimes admitting an umbilic foliation. Sufficient and necessary conditions for those spacetimes to be a conformally stationary spacetime are given. Finally, the important class of cosmological models known as generalized Robertson–Walker spacetimes is characterized.


Irrotational vector fields Conformal Killing vector fields Spatially conformal Killing vector fields Observers Fields of observers 

Mathematics Subject Classification

53C50 53B50 83C99 


Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Authors and Affiliations

  1. 1.Departamento de MatemáticasUniversidad de CórdobaCórdobaSpain
  2. 2.Departamento de MatemáticasUniversidad de OviedoGijónSpain

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