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

On Electromagnetic Thirring Problems 285
The electromagnetic field tensor belonging to the Reissner–Nordström
metric (2) has only a radial component
where is the Heaviside function (the charge is concentrated
solely on the inner shell at ), and the potentials (5) or
(6) have to be inserted in the respective regions. The charge density
of the interior shell results from the inhomogeneous Maxwell equation
as
3. FIRST ORDER ROTATION OF THE
SHELLS
Rotations of the shells from Sec. 2 in first order of angular velocity
(denoting the velocity of the inner charged shell and/or the velocity
of the exterior mass shell) are described by an extension of the metric
(2):
with neglect of the By the very definition of an angular velocity,
a stationary rotating system is invariant under the common substitutions
and and since the metric functions U, V,
and A are independent of they have to be even functions of Therefore,
in first order of the functions U and V can be taken from Sec.
2, and the function A is the only new metric function.
(Centrifugal deformations of the spherical shells start only at order )
The relevant Einstein equation takes its simplest form in the variable
with Since there are no electric currents in the and
in our models, the magnetic field component is
zero, and there remains only one homogeneous Maxwell equation (with
• denoting the )