Spherically symmetric space-times have attained considerable attention ever since the early beginnings of the theory of general relativity. In fact, they have appeared already in the papers of K. Schwarzschild [12] and W. De Sitter [5] which were published in 1916 and 1917 respectively soon after Einstein's epoch-making work [7] in 1915. The present survey is concerned mainly with recent results pertainig to the toplogy of spherically symmetric space-times. Definition. By space-time a connected time-oriented 4-dimensional Lorentz manifold is meant. If (M,<,>) is a space-time, and Φ: SO(3)×M→M an isometric action such that the maximal dimension of its orbits is equal to 2, then the action Φ is said to be spherical and the space-time is said to be spherically symmetric [8]; [11]. Likewise, isometric actions Ψ: O(3)×M→M are also considered ([10], p. 365; [4]) which will be called quasi-spherical if the maximal dimension of its orbits is 2 and then the space-time is said to be quasi-spherically symmetric here. Each quasi-spherical action yields a spherical one by restricting it to the action of SO(3); the converse of this statement will be considered elsewhere. The main results concerning spherically symmetric space-times are generally either of local character or pertaining to topologically restricted simple situations [14], and earlier results of global character are scarce [1], [4], [6], [13]. A report on recent results concerning the global geometry of spherically symmetric space-times [16] is presented below.
@article{bwmeta1.element.doi-10_2478_BF02475973,
author = {J. Szenthe},
title = {On the topology of spherically symmetric space-times},
journal = {Open Mathematics},
volume = {2},
year = {2004},
pages = {725-731},
zbl = {1116.53043},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_BF02475973}
}
J. Szenthe. On the topology of spherically symmetric space-times. Open Mathematics, Tome 2 (2004) pp. 725-731. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_BF02475973/
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[16] J. Szenthe: “On the global geometry of spherically symmetric space-times”, Math. Proc. Camb. Phil. Soc., Vol. 137, (2004), pp. 297–306. http://dx.doi.org/10.1017/S030500410400790X | Zbl 1065.53056