On spherically symmetric shear-free perfect fluid configurations (neutral and charged). III. Global view

Journal Article · Sun May 01 04:00:00 EDT 1988 · J. Math. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1063/1.527962· OSTI ID:5371007

Sussman, R A

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 S/sup 3/ x R, R/sup 4/, or S/sup 2/ x R/sup 2/. 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 S/sup 2/ x R/sup 2/ 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-script surface arising as an asymptotical null limit of timelike hypersurfaces. Solutions with this topology, matched to a Schwarzschild or Reissner--Nordstrapprox. =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 S/sup 2/ x R/sup 2/. 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.

• Research Organization: School of Mathematical Sciences, Queen Mary College, Mile End Road, London E1 4NS, England
• OSTI ID: 5371007
• Journal Information: J. Math. Phys. (N.Y.); (United States), Journal Name: J. Math. Phys. (N.Y.); (United States) Vol. 29:5; ISSN JMAPA
• Country of Publication: United States
• Language: English

Related Subjects

657003* -- Theoretical & Mathematical Physics-- Relativity & Gravitation
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ANALYTICAL SOLUTION
EINSTEIN FIELD EQUATIONS
EQUATIONS
EQUATIONS OF STATE
FIELD EQUATIONS
FIELD THEORIES
FLUID FLOW
GENERAL RELATIVITY THEORY
GLOBAL ANALYSIS
GRAVITATION
IDEAL FLOW
MATHEMATICS
METRICS
SINGULARITY
SYMMETRY