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282 EXACT SOLUTIONS AND SCALAR FIELDS IN GRAVITY
respectively corresponding angular momenta and We provide
explicit solutions of the relevant coupled Einstein–Maxwell equations
exactly in M/R and and in first order of the angular velocities.
By performing the additional approximations pertaining to refs. [1, 5],
we generally confirm their mathematical results but we find, in contrast
to [4], that all results are in complete agreement with Machian expectations.
Furthermore we calculate some new interaction effects between
strong gravitational and electromagnetic fields, and we consider in detail
the collapse limit of the two–shell system.
2. THE STATIC TWO–SHELL MODEL
Mathematically, our models of two concentric spherically symmetric
shells are given by three pieces of the Reissner–Nordström metric
with and one for the
region outside the exterior shell, one for the region between both shells,
and one for the interior region, for which both parameters and
have to be zero in order to guarantee regularity at the origin
However, a matching of these Reissner–Nordström metrics with different
mass– and charge–parameters obviously would not be continuous at the
shell positions. A global continuous metric is however desirable for the
physical interpretation of the dragging effects, and was also used in the
papers [2] and [4]. It can be reached by a transformation of the metric
(1) to the isotropic form
Identification of (2) and (1) results in
with an arbitrary constant D. In the following we often change between
the variable (in which the field equations and their solutions are simplest)
and the variable (necessary for the conditions at the shells and
for the physical interpretation of the results). In the exterior region
we choose identify with and set If we then
use the dimensionless variables