Physics Letters B 772 (2017) 542–546
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
Hawking radiation of five-dimensional charged black holes with scalar
fields
Yan-Gang Miao
∗
, Zhen-Ming Xu
School of Physics, Nankai University, Tianjin 300071, China
a r t i c l e i n f o a b s t r a c t
Article history:
Received
28 April 2017
Received
in revised form 19 June 2017
Accepted
10 July 2017
Available
online 14 July 2017
Editor:
N. Lambert
Keywords:
Hawking
radiation
Greybody
factor
Scalar
field
We investigate the Hawking radiation cascade from the five-dimensional charged black hole with a scalar
field coupled to higher-order Euler densities in a conformally invariant manner. We give the semi-analytic
calculation of greybody factors for the Hawking radiation. Our analysis shows that the Hawking radiation
cascade from this five-dimensional black hole is extremely sparse. The charge enhances the sparsity of
the Hawking radiation, while the conformally coupled scalar field reduces this sparsity.
© 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
Black holes, as a fascinating and elegant object, are increasingly
popular in classical and quantum gravity theories. In particular,
in virtue of semi-classical quantum field theory, Hawking [1] re-
vealed
that black holes are actually characterized by thermally
distributed emission spectra, not completely black. This intriguing
phenomenon, known as the Hawking radiation, is now considered
as certainly one of the theoretical topics of primary importance in
fundamental physics. Meanwhile, a plenty of works [2–19] devote
to calculating the Hawking radiation in order to explore a convinc-
ing
insight into a possible quantum gravity theory.
In
this paper, we make some efforts to discuss the Hawking
radiation for a charged black hole associated with a scalar field
coupled to higher-order Euler densities in a conformally invariant
manner in a five-dimensional spacetime [20–23]. In the situation
of the scalar field conformally coupling to the Einstein gravity, the
well-known no-hair theorem forbids [24,25] the existence of scalar
hairy black holes, especially in D > 4 dimensions. However, the
recent research shows [26–28] that the existence of scalar hairy
black holes is becoming possible in arbitrary D > 4dimensions
when a scalar field couples conformally to higher-order Euler den-
sities.
This gravity theory is the most general scalar field/gravity
coupling theory whose field equations are of second order for both
*
Corresponding author.
E-mail
addresses: miaoyg@nankai.edu.cn (Y.-G. Miao),
xuzhenm@mail.nankai.edu.cn (Z.-M. Xu).
gravity and matter, and it can be regarded as a generalization of
the Horndeski theory [29,30]. Hence, it is meaningful and nec-
essary
in this sense to study a five-dimensional black hole as a
banner of high dimensional black holes with a scalar field con-
formally
coupled to higher-order Euler densities. Here we mainly
focus on the investigation of the sparsity of the Hawking radiation
flow in order to capture the physical picture of the Hawking ra-
diation
out of the five-dimensional black hole with a scalar field.
Taking a specific situation (see eq. (2.1)) in ref. [27] as our starting
point, we calculate semi-analytically the Hawking radiation, and
our result indicates that the Hawking radiation cascade from this
five-dimensional charged black hole with a scalar field is extremely
sparse. Specifically, the charge enhances the sparsity of the Hawk-
ing
radiation, while the conformally coupled scalar field reduces
this sparsity.
The
paper is organized as follows. In section 2, we give a
brief review of the analytic solution of the charged black hole
with a scalar field in five dimensions. In section 3, we calcu-
late
the total Hawking radiation power and the greybody factor
for this five-dimensional black hole. We then analyze the sparsity
of the Hawking radiation cascade in section 4. Finally, we devote
to a brief summary in section 5. Note that the geometric units,
¯
h = c =k
B
= G = 1, are adopted throughout this paper.
2. A brief review of the charged black hole with a scalar field in
five dimensions
We proceed to reviewing the five-dimensional charged black
hole associated with a scalar field coupled to higher-order Euler
http://dx.doi.org/10.1016/j.physletb.2017.07.023
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
.