Institute of Theoretical Physics · Faculty of Mathematics and Physics, Charles University
Class. Quantum Grav. 15(0), 1539-1555 (1998)
Scalar curvature invariants are studied in type-N solutions of the vacuum Einstein equations with, in general, a non-vanishing cosmological constant . Zeroth-order invariants, which include only the metric and Weyl (Riemann) tensor, either vanish or are constants depending on . All higher-order invariants containing covariant derivatives of the Weyl (Riemann) tensor are also shown to be trivial if a type-N spacetime admits a non-expanding and non-twisting null geodesic congruence. However, in the case of expanding type-N spacetimes we discover a non-vanishing scalar invariant, which is quartic in the second derivatives of the Riemann tensor. We use this invariant to demonstrate that both the linearized and third-order type-N twisting solutions recently discussed in literature contain singularities at large distances and thus cannot describe radiation fields outside bounded sources.
General Relativity
@article{UTF238,
author = {Bičák, J. and Pravda, V.},
title = {{Curvature invariants in type-N spacetimes.}},
journal = {Class. Quantum Grav.},
volume = {15},
number = {0},
pages = {1539-1555},
year = {1998},
eprint = {gr-qc/9804005},
archivePrefix = {arXiv},
url = {http://www.iop.org/EJ/abstract/0264-9381/15/6/011/},
}