Physics Letters B 771 (2017) 257–263
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
Charged scalar quasi-normal modes for linearly charged
dilaton-Lifshitz solutions
M. Kord Zangeneh
a,b,c,d
, B. Wang
d,e
, A. Sheykhi
c,b
, Z.Y. Tang
d
a
Physics Department, Faculty of Science, Shahid Chamran University of Ahvaz 61357-43135, Iran
b
Research Institute for Astronomy and Astrophysics of Maragha (RIAAM), Maragha, P. O. Box: 55134-441, Iran
c
Physics Department and Biruni Observatory, Shiraz University, Shiraz 71454, Iran
d
Center of Astronomy and Astrophysics, Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
e
Center for Gravitation and Cosmology, College of Physical Science and Technology, Yangzhou University, Yangzhou 225009, China
a r t i c l e i n f o a b s t r a c t
Article history:
Received
17 March 2017
Received
in revised form 24 April 2017
Accepted
17 May 2017
Available
online 22 May 2017
Editor:
N. Lambert
Most available studies of quasi-normal modes for Lifshitz black solutions are limited to the neutral scalar
perturbations. In this letter, we investigate the wave dynamics of massive charged scalar perturbation
in the background of (3 + 1)-dimensional charged dilaton Lifshitz black branes/holes. We disclose the
dependence of the quasi-normal modes on the model parameters, such as the Lifshitz exponent z, the
mass and charge of the scalar perturbation field and the charge of the Lifshitz configuration. In contrast
with neutral perturbations, we observe the possibility to destroy the original Lifshitz background near
the extreme value of charge where the temperature is low. We find out that when the Lifshitz exponent
deviates more from unity, it is more difficult to break the stability of the configuration. We also study
the behavior of the real part of the quasi-normal frequencies. Unlike the neutral scalar perturbation
around uncharged black branes where an overdamping was observed to start at z = 2and independent
of the value of scalar mass, our observation discloses that the overdamping starting point is no longer
at z = 2and depends on the mass of scalar field for charged Lifshitz black branes. For charged scalar
perturbations, fixing m
s
, the asymptotic value of ω
R
for high z is more away from zero when the charge
of scalar perturbation q
s
increases. There does not appear the overdamping.
© 2017 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP
3
.
1. Introduction
In black hole physics, quasi normal mode (QNM) is a power-
ful
tool to study the evolution of perturbations in the exterior of
black holes [1–4]. The behavior of QNM can be used to identify the
black hole existence and disclose dynamical stability of black hole
configurations. Besides, QNM can serve as a testing ground of fun-
damental
physics. It is widely believed that QNM can give deeper
understandings of the AdS/CFT [4–8], dS/CFT [9] correspondences,
loop quantum gravity [10] and also phase transitions of black holes
[11] etc.
In
this letter we will examine the QNM of the linearly charged
dilaton-Lifshitz black brane solutions and try to disclose deep in-
fluences
of the model parameters on the perturbation wave dy-
namics
and examine the stability of the background configurations.
E-mail addresses: mkzangeneh@shirazu.ac.ir (M. Kord Zangeneh),
wang_b@sjtu.edu.cn (B. Wang), asheykhi@shirazu.ac.ir (A. Sheykhi),
tangziyu@sjtu.edu.cn (Z.Y. Tang).
Asymptotic Lifshitz black solutions are interesting duals to many
condensed matter systems [12]. They are duals to systems with
Schrodinger-like scaling symmetries i.e. t → λ
z
t,
x → λ
x, where
z is dynamical critical exponent. Lifshitz spacetime is not a vac-
uum
solution of Einstein gravity with or without cosmological
constant and some Lifshitz supporting fields are needed. Differ-
ent
Lifshitz supporting fields have been considered in literatures,
such as including higher curvature corrections [13–15], inserting
massive [16] and massless [17–22] Abelian gauge fields coupled to
dilaton and non-Abelian SU(2) Yang–Mills fields coupled to dila-
ton
[23] etc.
The
behavior of neutral scalar perturbations has been exten-
sively
studied for Lifshitz solutions in the presence of different
Lifshitz supporting fields. In [24,25], scalar and spinorial perturba-
tions
around (2 +1)-dimensional Lifshitz black holes with z =3in
the context of New Massive Gravity (which includes higher cur-
vature
terms) have been explored and it has been shown that
black holes are stable under both of these perturbations. Moreover,
it has been shown that higher-dimensional Lifshitz black branes
are stable under massive scalar perturbations in the presence of
http://dx.doi.org/10.1016/j.physletb.2017.05.050
0370-2693/
© 2017 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by
SCOAP
3
.