Exact Solutions and Scalar Fields in Gravity - Instituto Avanzado de ...

124 EXACT SOLUTIONS AND SCALAR FIELDS IN GRAVITY
authors and became a starting point for different multidimensional generalizations.
Here we consider a more general class of exact solutions in a D–
dimensional model with scalar fields and fields of forms, inspired by
modern unified models. Such generalization is intended to study general
gravitational and cosmological properties of these models. Clear, that
most of their symmetries are not preserved in arbitrary dimensions, but
are recovered in 10 or 11. Among our solutions, there are solutions with
harmonic functions obtained by the null–geodesic method suggested by
G. Neugebauer and D. Kramer in [2]. We also consider exact spherically
symmetric, cosmological and black hole configurations with
All of them have a general structure since minor restrictions on parameters
of the model are imposed. We also present PPN parameters for
4–dimensional section of the metric with the aim of studying new observational
windows to unified models and extra dimensions [3, 4, 5].
2. THE MODEL
We consider the model governed by the action
where is the metric on the manifold M, dim M = D,
is a vector from dilatonic scalar fields, is a non–
degenerate matrix
is a on a D–dimensional manifold M,
is a cosmological constant and is a 1–form on
In (0) we denote
where is some finite set.
In the models with one time all when the signature of the
metric is (–1, +1,..., +1).
2.1. ANSATZ FOR COMPOSITE P-BRANES
Let us consider the manifold and metric as