An intrinsic characterization of 2 + 2 warped spacetimes

Joan Josep Ferrando (1) , Juan Antonio Sáez (2)

1 Departament d'Astronomia i Astrofsica, Universitat de València
2 Departament de Matemàtiques per a l'Economia i l'Empresa

We give several equivalent conditions that characterize the 2+2 warped spacetimes: imposing the existence of a Killing-Yano tensor A subject to complementary algebraic restrictions ; in terms of the projector v (or of the canonical 2-form U) associated with the 2-planes of the warped product. These planes are principal planes of the Weyl and/or Ricci tensors and can be explicitly obtained from them. Therefore, we obtain the necessary and sufficient (local) conditions for a metric tensor to be a 2+2 warped product. These conditions exclusively involve explicit concomitants of the Riemann tensor. We present a similar analysis for the conformally 2+2 product spacetimes and give an invariant classification of them. The warped products correspond to two of these invariant classes. The more degenerate class is the set of product metrics which are also studied from an invariant point of view.

Keywords: Physical Sciences

Joan Josep Ferrando, Juan Antonio Sáez. An intrinsic characterization of 2 + 2 warped spacetimes. Classical and Quantum Gravity, 2010, 27 (20), pp.205023. ⟨10.1088/0264-9381/27/20/205023⟩. ⟨hal-00634383⟩