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The region beyond the Cauchy horizon has several surprising features.
The boundary of this set is the Cauchy horizon.
In all these solutions, the singularity that occurs when corresponds to a Cauchy horizon.
These modes exhibit a behaviour of ever-increasing frequency as the Cauchy horizon is approached.
A clear physical example of a Cauchy horizon is the second horizon inside a charged or rotating black hole.
All these have quasiregular singularities that are interpreted as Cauchy horizons on the surface.
Any slight variation in these functions would change the Cauchy horizon into a curvature singularity.
The Cauchy horizon is generated by closed null geodesics.
This result also applies to solutions which contain a Cauchy horizon rather than a curvature singularity.
If then there exists a Cauchy horizon between and regions of the manifold not completely determined by information on .
This provides an analytic extension beyond the Cauchy horizon which is another part of Kerr space-time.
A homogenous space-time with a Cauchy horizon is anti de Sitter space.
If the causality violation developed from a noncompact initial surface, the averaged weak energy condition must be violated on the Cauchy horizon."
This focusing singularity is normally a curvature singularity, but this may be replaced by a Cauchy horizon.
This only applies to initial conditions which are outside of the chronology-violating region of spacetime, which is bounded by a Cauchy horizon.
Under the averaged weak energy condition (AWEC), Cauchy horizons are inherently unstable.
A CTC therefore results in a Cauchy horizon, and a region of spacetime that cannot be predicted from perfect knowledge of some past time.
Inside the inner horizon, the Cauchy horizon, the singularity is visible and to predict the future requires additional data about what comes out of the singularity.
The larger of these roots determines the location of the event horizon, and the smaller determines the location of a Cauchy horizon.
On the other hand, when the Cauchy horizon corresponds to the outer Kerr horizon, the amplitude decays towards a quasiregular fold singularity.
A further class of exceptional vacuum solutions in which the curvature singularity is replaced by a Cauchy horizon has been obtained by Feinstein and Ibañez (1989).
Once having passed through the event horizon, the coordinate now behaves like a time coordinate, so it must decrease until the curve passes through the Cauchy horizon.
Although charged black holes with r r are similar to the Schwarzschild black hole, they have two horizons: the event horizon and an internal Cauchy horizon.
For this reason, Kerr and others suggest that a Cauchy horizon never forms, instead that the inner horizon is in fact a spacelike or timelike singularity.
It is along this way that Hawking succeeded in proving that time machines of a certain type (those with a "compactly generated Cauchy horizon") cannot appear without exotic matter.
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