On the local extension of Killing vector fields in electrovacuum spacetimes

Research paper by Elena Giorgi

Indexed on: 21 Mar '17Published on: 21 Mar '17Published in: arXiv - General Relativity and Quantum Cosmology

Abstract

We revisit the problem of extension of a Killing vector field in a spacetime which is solution to the Einstein equation with electromagnetic stress/energy tensor. This extension has been proven by Yu to be unique in the case of a Killing vector field which is normal to a bifurcate horizon. Here we generalize the extension of the vector field to a strong null convex domain in an electrovacuum spacetime, inspired by the same technique used by Ionescu and Klainerman in the setting of Ricci flat manifolds. Using their construction, we also prove a result concerning non-extendibility: we show that one can find local, stationary electrovacuum extension of a Kerr-Newman solution in a full neighborhood of a point of the horizon which admits no extension of the Hawking vector field.