ISSN:
1572-9532
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract 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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00767861
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