New metrics admitting the principal Killing–Yano tensor

Article

New metrics admitting the principal Killing–Yano tensor

Frolov,V. P.; Krtouš, P.; Kubizňák, D.

Phys. Rev. D 97, 104071 (2018)

Abstract

It is believed that in any number of dimensions the off-shell Kerr–NUT–(A)dS metric represents a
unique geometry admitting the principal (rank 2, non-degenerate, closed conformal Killing–Yano) tensor.
The original proof relied on the Euclidean signature and therein natural assumption that the eigenvalues of
the principal tensor have gradients of spacelike character. In this paper we evade this common wisdom and
construct new classes of Lorentzian (and other signature) off-shell metrics admitting the principal tensor
with “null eigenvalues,” uncovering so a much richer structure of spacetimes with principal tensor in four
and higher dimensions. A few observations regarding the Kerr–Schild ansatz are also made.

Institute authors

Krtouš, Pavel

Supported by

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

BibTeX

@article{UTF676,
  author        = {Frolov,V. P. and Krtouš, P. and Kubizňák, D.},
  title         = {{New metrics admitting the principal Killing–Yano tensor}},
  journal       = {Phys. Rev. D},
  volume        = {97},
  pages         = {104071},
  year          = {2018},
  doi           = {10.1103/PhysRevD.97.104071},
  eprint        = {1712.08070},
  archivePrefix = {arXiv},
}