Lyapunov functional approach to radiative metrics.

Details Lyapunov functional approach to radiative metrics. Lyapunov functional approach to radiative metrics.

Jul 1984

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1984gregr..16..691l&link_type=abstract

General Relativity and Gravitation, Volume 16, Issue 7, pp.691-701

Mathematics

Logic

22

Gravitation Theory:Space-Time

Scientific paper

Lyapunov's second method is applied to the spherical radiative Robinson-Trautman vacuum space-times to prove that they asymptotically settle down to Schwarzschild space-time. This class of Robinson-Trautman metrics is characterized by the surfaceS being topologically a two-sphere, whereS is invariantly defined by the intersection of the hypersurfacesu=const andr=const. It is shown that ∝ S K 2 dσ is a Lyapunov functional, whereK is the Gaussian curvature anddσ is the invariant measure onS. The critical point occurs atK=0 or, equivalently, at ð2 K=0, which condition is shown to characterize Schwarzschild space-time.

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