Journal ArticleDOI
On the Time-evolution of the Robinson-trautman Solutions
TLDR
In this paper, an algorithm for solving the field equation of the Robinson-Trautman metrics is presented, in the linear approximation, to the line elements which evolve from an axially symmetric initial surface.Abstract:
An algorithm is presented for solving, by a power expansion, the field equation of the Robinson-Trautman metrics It is applied, in the linear approximation, to the line elements which evolve from an axially symmetric initial surface The special case of the ellipsoid of revolution is explicitly treatedread more
Citations
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Existence and asymptotic properties of global solutions of the Robinson-Trautman equation
TL;DR: In this article, it was shown that given antipodally symmetric initial data on the sphere S2 which are sufficiently small in an appropriate norm, there exists a global solution of the Robinson-Trautman equation with those initial data and moreover this solution decays exponentially to a constant value, corresponding to the Schwarzschild solution.
Journal ArticleDOI
Existence of solutions of the Robinson-Trautman equation and spatial infinity
TL;DR: The existence of solutions of the Robinson-Trautman equation has been established in this article, and if solutions exist global in time, they describe spacetimes with negative ADM mass and C ∞ scri±.
Journal ArticleDOI
Apparent Horizons in Vacuum Robinson-Trautman Spacetimes ∗
E. W. M. Chow,Anthony W-C Lun +1 more
TL;DR: In this article, the authors describe a method of locating the past apparent horizon in the Robinson-Trautman spacetimes, and discuss the properties of the horizon, showing that the horizon is non-timelike and that its surface area is a decreasing function of the retarded time.
Journal ArticleDOI
Past horizons in Robinson-Trautman spacetimes with a cosmological constant
Jiri Podolsky,Otakar Svítek +1 more
TL;DR: In this paper, past horizons in the class of type II Robinson-Trautman vacuum spacetimes with a cosmological constant were studied and the existence, uniqueness, location, and character of the past horizon was investigated.
Journal ArticleDOI
Study of the Robinson-Trautman metrics in the asymptotic future
TL;DR: In this paper, a systematic study of the Robinson-Trautman metrics in the asymptotic future is presented, and a technique that could be used for determining existence of solutions of the RTA equation is found.
References
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Journal ArticleDOI
Some spherical gravitational waves in general relativity
Isaac Robinson,Andrzej Trautman +1 more
TL;DR: In this paper, the class of metrics which admit a family of hypersurface-orthogonal, non-shearing, diverging null curves is studied. But their solutions admit no Killing field whatsoever.