Institute of Theoretical Physics · Faculty of Mathematics and Physics, Charles University
J. Math. Phys. 40(0), 4506-4517 (1999)
In a suitably chosen essentially unique frame tied to a given observer in a general spacetime, the equation of geodesic deviation can be decomposed into a sum of terms describing specific effects: isotropic (background) motions associated with the cosmological constant, transverse motions corresponding to the effects of gravitational waves, longitudinal motions, and Coulomb-type effects. Conditions under which the frame is parallelly transported along a geodesic are discussed. Suitable coordinates are introduced and an explicit coordinate form of the frame is determined for spacetimes admitting a non-twisting null congruence. Specific properties of all non-twisting type N vacuum solutions with cosmological constant Lambda (non-expanding Kundt class and expanding Robinson-Trautman class) are then analyzed. It is demonstrated that these spacetimes can be understood as exact transverse gravitational waves of two polarization modes "+" and "x", shifted by pi/4, which propagate "on" Minkowski, de Sitter, or anti-de Sitter backgrounds. It is also shown that the solutions with Lambda>0 may serve as exact demonstrations of the cosmic "no-hair" conjecture in radiative spacetimes with no symmetry.
Gravity Waves: Space-Time
@article{UTF151,
author = {Bičák, J and Podolský, J.},
title = {{Gravitational waves in vacuum spacetimes with cosmological constant. II. Deviation of geodesics and interpretation of nontwisting type N solutions.}},
journal = {J. Math. Phys.},
volume = {40},
number = {0},
pages = {4506-4517},
year = {1999},
doi = {10.1063/1.532982},
eprint = {gr-qc/9907049},
archivePrefix = {arXiv},
url = {http://jmp.aip.org/resource/1/jmapaq/v40/i9/p4506\_s1},
}