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Lyapunov functional approach to raiative metrics (1984)

Lukács, B. ; Perjés, Z. ; Porter, J. ; [et al.]

Springer

General relativity and gravitation 16 (1984), S. 691-701

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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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