We assume and ignore
the region
for which the singularity at
is naked, for any value of
. Two cases are to be distinguished:
As the net charge of all known celestial bodies is close to zero, the naked-singularity case 2 is usually thought to be of little astrophysical relevance.
By switching to isotropic coordinates, one can
describe light propagation in the Reissner-Nordström metric by an
index of refraction (see, e.g., [105]). The resulting Fermat
geometry (optical geometry) is discussed, in terms of embedding
diagrams for the black-hole case and for the naked-singularity
case, in [191, 3]
(cf. [160]). The visual
appearance of a background, as distorted by a Reissner-Nordström
black hole, is calculated in [222].
Lensing by a charged neutron star, whose exterior is modeled by the
Reissner-Nordström metric, is the subject of [68, 69]. The lensing
properties of a Reissner-Nordström black hole are qualitatively
(though not quantitatively) the same as that of a Schwarzschild
black hole. The reason is the following. For a Reissner-Nordström
black hole, the metric coefficient
has one local
minimum and no other extremum between horizon and infinity, just as
in the Schwarzschild case (recall Figure 9
). The minimum of
indicates an unstable light sphere towards which
light rays can spiral asymptotically. The existence of this
minimum, and of no other extremum, was responsible for all
qualitative features of Schwarzschild lensing. Correspondingly,
Figures 15
, 16
, and 17
also qualitatively
illustrate lensing by a Reissner-Nordström black hole. In
particular, there is an infinite sequence of images for each light
source, corresponding to an infinite sequence of light rays whose
limit curve asymptotically spirals towards the light sphere. One
can consider the “strong-field limit” [39
, 37
] of lensing for a
Reissner-Nordström black hole, in analogy to the Schwarzschild case
which is indicated by the asymptotic straight line in the middle
graph of Figure 15
. Bozza [37
] investigates
whether quantitative features of the “strong-field limit”, e.g.,
the slope of the asymptotic straight line, can be used to
distinguish between different black holes. For the
Reissner-Nordström black hole, image positions and magnifications
have been calculated in [96], and travel times
have been calculated in [290]. In both
cases, the authors use the “almost exact lens map” of Virbhadra and
Ellis [337
] (recall
Section 4.3) and analytical methods of Bozza et
al. [39, 37
, 40].