Blue-shift surfaces and the stability of white holes.
Abstract
The eikonal, or geometric-optics, approximation is used to investigate the situation in which frequency shifts measured along a timelike geodesic approach a diverging blue shift. Those points of the approximation which are essential to a consideration of the present problem are reviewed, conditions under which a diverging blue shift will arise in the approximation are examined, and such a situation is illustrated in a conformal diagram. It is shown that a variety of stable inhomogeneous cosmological models can be constructed in the framework of the eikonal approximation. The specific example of a stable pressure-free inhomogeneity in a spherical expansion is considered, and it is found that the stability of an inhomogeneity of this type requires that the inner boundary of a pressure-free homogeneous external universe with positive spatial curvature originate from a curvature singularity at r = 0 (in general terms, a big-bang universe).
- Publication:
-
Nuovo Cimento Lettere
- Pub Date:
- May 1976
- Bibcode:
- 1976NCimL..16...17L
- Keywords:
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- Astronomical Models;
- Big Bang Cosmology;
- Eikonal Equation;
- Frequency Shift;
- White Holes (Astronomy);
- Geodesic Lines;
- Optics;
- Schwarzschild Metric;
- Universe;
- Astrophysics