Gravitational waves in vacuum space-times with cosmological constant. 2. Deviation of geodesics and interpretation of nontwisting type N solutions

Jul, 1999
16 pages
Published in:
  • J.Math.Phys. 40 (1999) 4506-4517
e-Print:

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19992005201120172023012345
Abstract: (arXiv)
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.
  • gravitational radiation
  • Einstein equation: vacuum state
  • Einstein equation: solution
  • cosmological constant
  • polarization
  • space-time: Minkowski
  • space-time: de Sitter
  • space-time: anti-de Sitter
  • amplitude analysis