scholarly journals A Model for a Spherically Symmetric Space Generated by a Spherical Gravitational Source and a Gravitational Medium with Constant Mass Density

2013 ◽  
Vol 03 (02) ◽  
pp. 21-27
Author(s):  
Nikolaj N. Popov ◽  
Vladimir I. Tsurkov
Keyword(s):  
Symmetric Space ◽  
Mass Density ◽  
Spherically Symmetric ◽  
Constant Mass ◽  
Gravitational Source

Construction of singularity-free spherically symmetric space-time manifolds

1967 ◽  
Vol 297 (1449) ◽  
pp. 244-268 ◽  
Keyword(s):  
Symmetric Space ◽  
Coordinate System ◽  
Free Space ◽  
World Line ◽  
Mass Density ◽  
Space Time ◽  
Polar Coordinate System ◽  
Spherically Symmetric ◽  
Euclidean Topology ◽  
Polar Coordinate

A method for constructing globally defined, spherically symmetric space-time manifolds in general relativity is developed by making the ordinary polar coordinate system applicable in the large. This is achieved by considering space-time M as a kind of sphere bundle over a Lorentz-2-manifold M̃ (in general with boundary), the radius r of the spheres being regarded as a function on M̃ . The singularity of the polar coordinate system at r = 0 which occurs on the world line of a centre in M and on the boundary of M̃ is carefully studied, and it turns out that regularity of the metric near this world line implies that the latter is necessarily timelike. As an application of this method some simple examples of globally defined, complete and singularity-free space-time manifolds are constructed representing an exterior Schwarzschild field and a massive central body without point centre. It is shown that such models do exist with everywhere non-negative mass density, but that this change of the topology (at least for these simple models) requires very high tensions, namely: tension ≥ density ≥ 0. In particular, the latter condition together with the change from Euclidean topology seems to be a necessary requirement for the construction of singularity-free space-times containing ‘collapsing’ regions.

ISOMETRY HORIZONS IN SPHERICALLY SYMMETRIC SPACE–TIMES

2006 ◽  
Vol 03 (05n06) ◽  
pp. 1263-1271
Author(s):  
J. SZENTHE
Keyword(s):  
Symmetric Space ◽  
Spherically Symmetric ◽  
Isometric Action ◽  
Event Horizons ◽  
Killing Horizons

Some event horizons in space–times that are invariant under an isometric action, considered first by Carter, are called isometry horizons, especially Killing horizons. In this paper, isometry horizons in spherically symmetric space–times are considered. It is shown that these isometry horizons are all Killing horizons.

scholarly journals PROPER CURVATURE COLLINEATIONS IN NONSTATIC SPHERICALLY SYMMETRIC SPACE–TIMES

2008 ◽  
Vol 23 (05) ◽  
pp. 749-759 ◽  
Author(s):  
GHULAM SHABBIR ◽  
M. RAMZAN
Keyword(s):  
Symmetric Space ◽  
Vector Fields ◽  
Killing Vector ◽  
Spherically Symmetric ◽  
Killing Vector Fields ◽  
Infinite Dimensional ◽  
Riemann Matrix ◽  
Integration Techniques ◽  
Curvature Collineations ◽  
Proper Curvature

A study of nonstatic spherically symmetric space–times according to their proper curvature collineations is given by using the rank of the 6×6 Riemann matrix and direct integration techniques. Studying proper curvature collineations in each case of the above space–times it is shown that when the above space–times admit proper curvature collineations, they turn out to be static spherically symmetric and form an infinite dimensional vector space. In the nonstatic cases curvature collineations are just Killing vector fields.

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