2 research outputs found
Duality between Electric and Magnetic Black Holes
A number of attempts have recently been made to extend the conjectured
duality of Yang Mills theory to gravity. Central to these speculations has been
the belief that electrically and magnetically charged black holes, the solitons
of quantum gravity, have identical quantum properties. This is not obvious,
because although duality is a symmetry of the classical equations of motion, it
changes the sign of the Maxwell action. Nevertheless, we show that the chemical
potential and charge projection that one has to introduce for electric but not
magnetic black holes exactly compensate for the difference in action in the
semi-classical approximation. In particular, we show that the pair production
of electric black holes is not a runaway process, as one might think if one
just went by the action of the relevant instanton. We also comment on the
definition of the entropy in cosmological situations, and show that we need to
be more careful when defining the entropy than we are in an asymptotically-flat
case.Comment: 23 pages, revtex, no figures. Major revision: two sections on the
electric Ernst solution adde
Cosmological production of charged black hole pairs
We investigate the pair creation of charged black holes in a background with
a positive cosmological constant. We consider metrics with a cosmological
constant, and show that the conical singularities in the metric only disappear
when it reduces to the Reissner-Nordstr\"om de Sitter metric. We construct an
instanton describing the pair production of extreme black holes and an
instanton describing the pair production of non-extreme black holes from the
Reissner-Nordstr\"om de Sitter metric, and calculate their actions. There are a
number of striking similarities between these instantons and the Ernst
instantons, which describe pair production in a background electromagnetic
field. We also observe that the type I instanton in the ordinary metric
with zero cosmological constant is actually the Reissner-Nordstr\"om solution.Comment: 29 pages, latex, 3 figures in a seperate uuencoded compressed file.
Discussion of the significance of the instantons enlarged, and minor
emendation