Some exact inhomogeneous solutions of Einstein's equations with symmetries on the hypersurfaces t = const

Journal Article · Sun Dec 01 04:00:00 EST 1985 · J. Math. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1063/1.526691· OSTI ID:6333594

Argueeso, F; Sanz, J L

The solution of Einstein's field equations is studied for a metric written in the form (deltanot =..gamma..)ds/sup 2/ = -..cap alpha../sup 2/(t,r,theta,phi)dt/sup 2/ +e/sup( 2betat/,r) dr/sup 2/+e/sup( 2gammat/,r) dtheta/sup 2/ +e/sup( 2deltat/,r)M/sup 2/(theta)dphi/sup 2/. A perfect fluid, which flows orthogonally to the hypersurfaces t = const is considered as matter content. These hypersurfaces admit a translational Killing vector, which will not be, in general, a Killing vector of the whole space-time. All the possible solutions are obtained when ..cap alpha.. depends on the variable phi. These solutions represent either a perfect fluid without expansion or vacuum with a cosmological constant ..lambda..0. Some particular inhomogeneous solutions are obtained for ..cap alpha.. independently of phi. These solutions are physical, the fluid obeys an equation of state p = rho (stiff matter), and the space-time admits, apparently, only a group G/sub 2/ of isometries. A vacuum family is also obtained in this case.

• Research Organization: Departamento de Fisica Teorica, Facultad de Ciencias, Universidad de Santander, 39005 Santander, Spain
• OSTI ID: 6333594
• Journal Information: J. Math. Phys. (N.Y.); (United States), Journal Name: J. Math. Phys. (N.Y.); (United States) Vol. 26:12; 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
COSMOLOGICAL CONSTANT
COSMOLOGY
EINSTEIN FIELD EQUATIONS
EQUATIONS
EQUATIONS OF STATE
FIELD EQUATIONS
FIELD THEORIES
FLUID FLOW
GENERAL RELATIVITY THEORY
GROUP THEORY
MATHEMATICS
METRICS
SYMMETRY