Type D conformal initial data

Preprint

Type D conformal initial data

Alfonso García-Parrado

Abstract

For a vacuum initial data set of the Einstein field equations it is possible to carry out a conformal rescaling or conformal compactification of the data giving rise to an initial data set
for the Friedrich vacuum conformal equations. When will the data development with respect to the conformal equations of this set be a conformal extension of a type D solution? In this
work we provide a set of necessary and sufficient conditions on a set of initial data for the conformal equations that guarantees that the data development of the conformal equations has a subset that is conformal to a vacuum type D solution of the Einstein’s equations. In particular we find the conditions under which this vacuum solution corresponds to the Kerr solution. Using our results we are able to show that there are no obstructions to extend the Petrov type of the physical spacetime to the unphysical spacetime if and only if the conformal data are hyperboloidal. In this case, the Weyl scalar of the rescaled Weyl tensor turns out to be a constant on the conformal boundary.

Supported by

GACR 14-37086G — Albert Einstein Center for Gravitation and Astrophysics

BibTeX

@misc{UTF786,
  author        = {Alfonso García-Parrado},
  title         = {{Type D conformal initial data}},
  year          = {2018},
  eprint        = {https://arxiv.org/abs/1809.06753},
  archivePrefix = {arXiv},
}