ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
Solutions of Einstein's equations are examined when a particular class of closed three-form fields is taken as a source. The choice of source is motivated by developments in particle physics indicating the possible existence of physical fields described by three-forms. After summarizing basic dynamical equations and some properties, attention is focused on two particular configurations: (1) static, spherically symmetric, self-gravitating, three-form fields; and (2) homogeneous and isotropic geometries coupled to three-forms. For the spherically symmetric case, there exists two mutually exclusive sets of effective equations, solutions which describe static, spherically symmetric, self-gravitating axion fields. For the one class of the effective equations, a two-parameter family of asymptotically flat solutions of the Einstein axion field equations have been constructed. The axionic black hole solution of Bowick et al. [Phys. Rev. Lett. 61, 2823 (1988)] is also recovered as a special case of this class. For the other set of equations, only a special solution has been constructed. Its properties and global structure are discussed at length. For the case of axions coupled to homogeneous and isotropic geometries, explicit solutions of the relevant equations have also been constructed. In particular, for the case where the hypersurfaces of homogeneity are either flat or characterized by negative curvature, a global solution is obtained. It represents an ever expanding universe originating from a spacelike curvature singularity. For the case of a closed universe, local solutions have been constructed, which in principle can be patched to yield a global solution. Nevertheless, by employing them, the singularity structure of this solution was able to be analyzed. It behaves in the same manner as the previous two cases.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.529174
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