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Journal of Mathematical Physics / Volume 28 / Issue 1

J. Math. Phys. 28, 159 (1987); http://dx.doi.org/10.1063/1.527798 (6 pages)

On the physical properties of a nonquadratic solution for the McVittie metric

Henning Knutsen

Stavanger College of Engineering, Box 2527, Ullandhaug, 4001 Stavanger, Norway

(Received 17 March 1986; accepted 27 August 1986)

A particular class of McVittie’s new nonquadratic solutions is examined with respect to its physical characteristics. It is found that center regularity is not compatible with negative pressure and density gradients. These solutions also have the strange geometric feature that the physical radius is a decreasing function of comoving radial coordinate. Models for nonstatic ‘‘gaseous’’ spheres (i.e., the density ρ vanishes at the outer surface of the perfect fluid sphere together with the pressure p) have been constructed. The global motion is studied, and it has been found that pulsations are not possible. It is shown, however, that the density and pressure gradients are both negative. The pressure and the density are thus positive within the boundary of these ‘‘gaseous’’ spheres, and it is also seen that the density is increasing for contracting models. For the layers close to the outer boundary, it is shown that the pressure is increasing when the sphere is contracting. The speed of sound is thus real, and it is further seen that this speed is less than the speed of light. It is found that there exist bouncing models where the rate of change of circumference as measured by an observer riding on the boundary of the ‘‘gaseous’’ sphere is zero just at the moment when the sphere starts its reexpansion.

KEYWORDS and PACS

Keywords

SELF−GRAVITATING SYSTEMS, ANALYTICAL SOLUTION, GEOMETRY, COORDINATES, SPHERES, DENSITY, PULSATIONS, PRESSURE GRADIENTS, BOUNDARY CONDITIONS, BOUNDARY−VALUE PROBLEMS, EXPANSION, GRAVITATION, GRAVITATIONAL COLLAPSE, EINSTEIN FIELD EQUATIONS, GENERAL RELATIVITY THEORY

PACS

  • 04.20.Jb

    Exact solutions

  • 04.40.-b

    Self-gravitating systems; continuous media and classical fields in curved spacetime

  • 95.30.Sf

    Relativity and gravitation

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.527798

PUBLICATION DATA

ISSN

0022-2488 (print)  
1089-7658 (online)

For access to fully linked references, you need to log in.
    C. W. Misner and D. H. Sharp, Phys. Rev. 136, B571 (1964).


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