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The topology of the solutions derived in Part I [J. Math. Phys. 28, 1118 (1987)] is discussed in detail using suitable topological embeddings. It is found that these solutions are homeomorphic to S3×R, R4, or S2×R2. Singularities and boundaries in these manifolds are examined within a global framework. One of these boundaries (mentioned but not examined in Part II) is regular (though unphysical), and is associated with an ‘‘asymptotically de Sitter’’ behavior characterized by an exponential form of the Hubble scale factor. Solutions with S2×R2 topology lack a center of symmetry [fixed point of SO(3)] and present a null boundary at an infinite affine parameter distance along hypersurfaces orthogonal to the four-velocity. This boundary, which in most cases is singular, can be identified as a null I surface arising as an asymptotical null limit of timelike hypersurfaces. Solutions with this topology, matched to a Schwarzschild or Reissner–Nordstro\m region, describe collapsing fluid spheres whose ‘‘surface’’ (as seen by observers in the vacuum region) has finite proper radius, but whose ‘‘interior’’ is a fluid region of cosmological proportions. In the case when the null boundary of the fluid region is singular, it behaves as a sort of ‘‘white hole.’’ Uniform density solutions which are not conformally flat are all homeomorphic to S2×R2. Conformally flat solutions are also examined in detail. Their global structure has common features with those of FRW and de Sitter solutions. The static limits of all nonstatic solutions are discussed. In particular, under suitable parameter restrictions, some of these static solutions, together with the nonstatic conformally flat subclass, are the less physically objectionable of all solutions. Hence, it is suggested that kinetic theory models could be applied to them. Possible cosmological... [ABSTRACT FROM AUTHOR]

Geometrical and physical properties of the solutions derived and classified in Part I [J. Math. Phys. 28, 1118 (1987)] are examined in detail. It is shown how the imposition of zero shear restricts the possible choices of equations of state. Two types of singular boundaries arising in these solutions are examined by verifying the local behavior of causal curves approaching these boundaries. For this purpose, a criterion due to C. J. S. Clarke (private communication) is given, allowing one to test the completeness of arbitrary accelerated timelike curves in terms of their acceleration and proper time. One of these boundaries is a spacelike singularity at which causal curves terminate as pressure diverges but matter-energy and charge densities remain finite. At the other boundary, which is timelike if the expansion Θ is finite, proper volume of local fluid elements vanishes as all state variables diverge but causal curves are complete. If Θ diverges at this boundary, a null singularity arises as the end product of the collapse of a twosphere generated by a given class of timelike curves. The gravitational collapse of bounded spheres matched to a Schwarzschild or Reissner-Nordstrøm exterior is also examined in detail. it is shown that the spacelike singularity mentioned above could be naked under certain parameter choices. Solutions presenting the other boundary produce very peculiar black holes in which the "surface" of the sphere collapses into the above mentioned null singularity, while the "interior" fluid layers avoid this singularity and evolve towards their infinite future. [ABSTRACT FROM AUTHOR]

A class of solutions describing a wide variety of nonstatic, spherically symmetric, charged, shear-free perfect fluid configurations is derived. It is presented in the form of Jacobian elliptic functions characterized by seven free parameters: five constants and two arbitrary functions of time. This class of solutions is the most general charged version of the class derived by Kustaanheimo and Qvist [Comment. Phys. Math. Helsingf. 13, 12 (1948); Exact Solutions of Einstein’s Field Equations (Cambridge U. P., Cambridge, 1980), Chap. 12, Sec. 2]. It is found that many of the charged particular solutions expressible by elementary functions are new. Particular solutions, including neutral and uniform density solutions, are classified in detail. The physical interpretation of these solutions, including the study of their singularity structure, will be presented in a subsequent paper (Part II). [ABSTRACT FROM AUTHOR]