Further applications of harmonic mappings of Riemannian manifolds to gravitational fields

Journal Article · Fri Apr 01 04:00:00 EST 1977 · J. Math. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1063/1.523311· OSTI ID:7119998

Eris, A

We consider static, spherically-symmetric and stationary, axially-symmetric gravitational fields in the framework of harmonic mappings of Riemannian manifolds. In this approach the emphasis is on a correspondence between the solution of the Einstein field equations and the geodesics in an appropriate Riemannian configuration space. Using Hamilton--Jacobi techniques, we obtain the geodesics and construct the resulting space--time geometries. For static space--times with spherical symmetry we obtain the well-known solutions of Schwarzschild, Reissner--Nordstroem, and Janis--Newman--Winicour, where in the latter two cases the source for the geometry is the static, source-free Maxwell field and the massless scalar field respectively. When we consider the source to be a triad of massless scalar fields with the internal symmetry SU(2) x SU(2), we find that the space--time geometry is once again that of Janis--Newman--Winicour. Finally we formulate the stationary, axisymmetric gravitational field problem in terms of composite mappings and obtain the Weyl, Papapetrou, and the generalized Lewis and van Stockum classes of axisymmetric solutions.

• Research Organization: Department of Physics, Middle East Technical University, Ankara, Turkey
• OSTI ID: 7119998
• Journal Information: J. Math. Phys. (N.Y.); (United States), Journal Name: J. Math. Phys. (N.Y.); (United States) Vol. 18:4; ISSN JMAPA
• Country of Publication: United States
• Language: English

Related Subjects

657003* -- Theoretical & Mathematical Physics-- Relativity & Gravitation
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
EINSTEIN FIELD EQUATIONS
EQUATIONS
FIELD EQUATIONS
FIELD THEORIES
GENERAL RELATIVITY THEORY
GEODESICS
GRAVITATIONAL FIELDS
LIE GROUPS
MATHEMATICAL SPACE
RIEMANN SPACE
SPACE
SU GROUPS
SU-2 GROUPS
SYMMETRY GROUPS
TOPOLOGICAL MAPPING
TRANSFORMATIONS