ISSN 0202-2893, Gravitation and Cosmology, 2017, Vol. 23, No. 3, pp. 261–272.
Pleiades Publishing, Ltd., 2017.
A Thin Dust Shell Falling to a Reissner-Nordstr
om Black Hole
as Seen by a Freely Falling Observer
Reutov, Moscow region, Russia
Received March 22, 2017; in ﬁnal form, May 15, 2017
Abstract—We study the observation of a thin dust shell, radially freely falling to a Reissner-Nordstr
black hole, by an observer who is also freely and radially falling into this black hole. Considered and resolved
are several common paradoxes and fallacies peculiar for such problems. The results of this analytical
study are written as a numerical code that allows for calculating all related eﬀects of this model. The
numerical result have been presented in a few synthesized videos, making a colorful, quantitative and
detailed description of the occurring astrophysical phenomena, both above and below the horizon.
Recently, my colleagues repeatedly encountered
with misunderstanding and confusion in matters of
hypothetically-possible observations of some eﬀects
from black holes. Moreover, this misunderstand-
ing was sometimes originated by even professional
astrophysicists. This concerns visual eﬀects which
accompany an observer freely falling into a black hole.
Of course, all these arguments are pure fantasy,
in the sense of a possible technical implementation
of such observations, but no doubt this subject is of
methodological interest. This interest is related to
understanding important eﬀects of general relativity
(GR) which accompany such hypothetic observa-
tions. This led to the idea to write an article in which
these hypothetic observations would be described in
detail and, most importantly, correctly.
In addition to the methodological study, descrip-
tion and calculation of this model, I have also made
some virtual animations in which I tried to show
exactly the real visual eﬀects that must be seen by a
freely falling observer (in theory). These videos are
under open internet access. So, this work (with the
videos) can be used for eﬀective student learning as
well as for all those interested in the subject.
Brieﬂy about the model:
1. Let us imagine an observer freely falling into
a black hole in vacuum, along the radius, and he is
always in weightlessness.
2. In addition, a dust sphere fall into the black hole
too, and the observer sees this sphere, which is closer
to the black hole than the observer.
3. All dust particles of this sphere are at the same
distance from the black hole at the same time. All
dust particles also fall radially and freely.
4. The inﬂuence of the dust particles and the
observer on the black hole is neglected.
A few words on the misconceptions. The main
misconception, to be refuted in this paper, is that
the observer should see an inﬁnite red shift from the
dust particles when the sphere reaches the black hole
The next misconception is that the observer will no
longer see the radiation (the intensity tends to zero)
when the sphere reaches the black hole horizon.
Let me brieﬂy explain the cause of the above mis-
conceptions. For photons near the horizon it is, in a
sense, diﬃcult to escape to inﬁnity, it requires more
time than far away from the horizon. Therefore an
observer ﬂying closer and closer to the horizon sees
the photons that broke oﬀ the shell when it was
only approaching the horizon, but the shell itself is
at the same time already below the horizon. After
crossing the black hole horizon, the observer falls
to the center
faster than for the photons from the
dust, which are still “trying to get out,” but gravity
“pulls” them to the center. And the observer, during
the fall, still “comes across” these photons. For this
reason the observer will not see any peculiarities when
observing the photons from the shell, everything will
look smooth and continuous!
Another common misconception is that under
the horizon of a black hole we cannot use the
Here and below, by the term “center” I mean a smaller radial
coordinate r than the location discussed.