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

292 EXACT SOLUTIONS AND SCALAR FIELDS IN GRAVITY
ing interior shell can produce an anti–dragging phenomenon, an example
of which was also given in [7]. But all these effects are only caused by
the somewhat unphysical properties of the massless, charged shell, which
e.g. violates most energy conditions.
4.3. RESULTS EXACT IN MASS M AND
CHARGE Q
As already remarked, the explicit formulas for the magnetic fields B
and for the dragging functions A in the case of general values M and
are too complicated for extracting much obvious physical interpretation.
Therefore we restrict ourselves here to a discussion of only two special,
physically interesting cases.
We observe that in the case II all 8 integration constants are proportional
to the expression appearing in the energy
conditions (16). Therefore, the magnetic field and the dragging
function are zero for and change sign if changes sign,
e.g. change from dragging to anti–dragging. This emphasizes the importance
of the discussion of the energy conditions for the mass shell
in Sec. 2. A similar behavior shows up in the analysis of the Thirring
problem with cosmological boundary conditions [9].
The collapse of our two–shell system, i.e. the appearance of a horizon,
sets in for It turns out that then in both cases I and II
we have and We see that the important
results by Brill and Cohen [8] that inside a rotating collapsing mass
shell one has total dragging of the inertial systems, transfers also to our
highly charged two–shell system, and we have a complete realization
of Machian expectations: only the rotation relative to the “universe”
counts. Moreover, all “physical” magnetic fields vanish inside the mass
shell. In the exterior region the essential non–zero integration
constant in the collapse limit is and one gets exactly
the Kerr–Newman field in lowest order of
References
[1]
[2]
[3]
[4]
[5]
[6]
[7]
K.D. Hofmann, Z. Phys. 166 (1962) 567.
J. Cohen, Phys. Rev. 148 (1966) 1264.
J. Ehlers and W. Rindler, Phys. Lett. A32 (1970) 257.
J. Ehlers and W. Rindler, Phys. Rev. D4 (1971) 3543.
J. Cohen, J. Tiomno, and R. Wald, Phys. Rev. D7 (1973) 998.
M. King and H. Pfister, Phys. Rev. D (to be published).
C. Briggs, J. Cohen, G. DeWoolfson, and L. Kegeles, Phys. Rev. D23 (1981)
1235.