Eur. Phys. J. C (2018) 78:662
https://doi.org/10.1140/epjc/s10052-018-6109-1
Regular Article - Theoretical Physics
Magnetoacoustic and Alfvénic black holes
A. Gheibi
1
, H. Safari
1,a
, D. E. Innes
2
1
Department of Physics, University of Zanjan, P. O. Box 45195-313, Zanjan, Iran
2
Max-Planck Institute for Solar System Research, 37077 Göttingen, Germany
Received: 21 May 2017 / Accepted: 30 July 2018
© The Author(s) 2018
Abstract We introduce analogue black holes (BHs) based
on ideal magnetohydrodynamic equations. Similar to acous-
tic BHs, which trap phonons and emit Hawking radiation
(HR) at the sonic horizon where the flow speed changes from
super- to sub-sonic, in the horizon of magnetoacoustic and
Alfvénic BHs, the magnetoacoustic and Alfvén waves will
be trapped and emit HR made of quantized vibrations simi-
lar to phonons which we call magnephonons and Alphonons.
We proposed that magnetoacoustic and Alfvénic BHs may
be created in the laboratory using a tube with variable cross
section embedded in a uniform magnetic field, and a super-
magnetoacoustic or a super-Alfvénic flow. We show that the
Hawking temperature for both BHs is a function of the back-
ground magnetic field, number density of fluid, and radius of
the tube. For a typical setup, the temperature is estimated to
be about 0.0266 K.
1 Introduction
In 1916 Schwarzschild gave a metric as a solution of the Ein-
stein field equation. Singularity of such a metric predicted a
gravitational BH with event horizon at Schwarzschild radius
[1]. Although, based on classical physics everything, even
light, is absorbed by BHs and cannot escape, in the context
of quantum field theory in curved space, Hawking showed
that BHs should emit black body radiation [2,3]. HR in the
universe has not been observed yet, but numerous attempts
have been done to simulate the interesting phenomena in the
laboratory. Unruh showed that HR is not only a character-
istic of gravitational BHs, it is also a characteristic of the
acoustic analogue BH [4,5]. After 1981, most of attempts
are proposed based on Bose–Einstein condensates of quan-
tum fluid, [6–10] quasi particles in superfluid [11], ultra-cold
fermions [12], in plasmas and ion rings, [13–17] slow light
in an atomic vapor, [18–21] in water [22,23], etc. Recently,
a
e-mail: safari@znu.ac.ir
observation of self-amplifying HR in an analogue BH laser
suggested a very promising experiment method for probing
the inside of a BH [24]. From a theoretical point of view, the
acoustic analogue BH models are developed in geometrical
acoustics and physical acoustics [25]. Using the linearized
hydrodynamic equations in the presence of initial material
flow, a wave equation for velocity potential was obtained.
Tensorial form of the wave equation results in an acoustic
metric. The acoustic metric is singular at a point where the
local sound speed is equal to the flow speed [26]. This was
interpreted as characteristic of a sonic BH [25,26].The effect
of magnetic field on the acoustic BH and HR has not been
studied, yet.
Alternatively, the idea for definition of acoustic BH can
be applied to introduce new analogue magnetoacoustic and
Alfvénic BHs in the magnetohydrodynamics (MHD) frame-
work. Magnetohydrodynamics (MHD) is an useful approach
to analyze characteristics (flow, wave and dissipation etc) of
the laboratory and astrophysical plasma [33]. After Alfvén
[34], MHD waves (Alfvén and magnetoacoustic) have been
detected, using the laboratory experiments Alfvén wave (e.g.
[35–37], in the earth-ionosphere and magnetic field [38,39],
a variety normal modes of the solar corona [40–44].
Here, first we treat the magnetoacoustic, Alfvén, and
acoustic waves based on Helmholtz theorem for a uniform
and stationary medium with constant background magnetic
field. Second, mimicking the definition of acoustic BH in
a nozzle, we introduce magnetoacoustic and Alfvénic BHs
with using a slightly variable cross section tube. We con-
clude that at the horizon of magnetoacoustic and Alfvénic
BHs should emit radiations made of the Magnephonon and
Alphonon, respectively. We define two quasi-particles Mag-
nephonon and Alphonon correspond to quantum of the mag-
netoacoustic and Alfvén waves, respectively.
This paper is organized as follows: Sect. 2 gives the proper-
ties of magnetoacoustic waves (fast, slow, and Alfvén waves)
using the Helmholtz decomposition and explains a derivation
of magnetoacoustic metric in the basis of linearized ideal
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