Physics Letters B 773 (2017) 639–643
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
Minimal surfaces in AdS C-metric
Hao 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
8 August 2017
Received
in revised form 1 September 2017
Accepted
13 September 2017
Available
online 19 September 2017
Editor:
M. Cveti
ˇ
c
We shed some light on the field theory interpretation of C-metric by investigating the minimal surfaces
which are homologous to the given boundary regions. The accelerating black holes change the asymptotic
structure of the space–time. We focus on the geometry features of the minimal surface and study how
deep it reaches into the bulk. The regularized area of the minimal surface is not well defined and we
introduce a new quantity D(m, θ
0
), defined as the minimal surface divided by the area of the given
boundary region, to study the system.
© 2017 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
.
AdS/CFT, or gauge/gravity correspondence, which was discov-
ered
by Maldacena in 1990s, relates the strongly coupled field
theory to the classical dynamics of gravity [1,2]. It asserts that the
non-gravitational QFT in d-dimensions are equivalently described
by gravitational interactions in one higher dimensions. AdS/CFT
correspondence provides us key insights into various systems and
has become a bridge connecting gravity and quantum theory.
The
prototype example of the AdS/CFT correspondence is that
the type IIB string theory on the product space AdS
5
× S
5
is equiv-
alent
to N = 4 supersymmetric Yang–Mills (SYM) theory on the
4-dimensional boundary. Generally, we may also have more exam-
ples
on d-dimensional CFTs which are dual to the classical gravity
models, by viewing the classical gravity as a low energy effective
field theory. Matter, which depends on the details of the dual field,
can also be allowed. The bulk space–time M
d+1
satisfies the Ein-
stein’s
equation, and the CFT
d
lives on its boundary B
d
= ∂ M
d+1
.
For the vacuums CFT
d
, it is dual to the vacuum AdS
d+1
space–time.
For the excited CFT
d
, it maps to the non-trivial asymptotically AdS
space–time determined by Einstein’s equation. The simplest case
is that the thermal CFT
d
is dual to a Schwarzschild-AdS
d+1
black
hole [3].
As
we have a dictionary between the field theory and asymp-
totically
AdS space–time, we can try to solve questions in field
theory from gravity side, and vice versa. Giving a holographic CFT
d
on the boundary B
d
, for a spatial region A at some particular in-
stant
in time, we can find a surface , which is codimensional-2
minimal in the bulk and share the same boundary ∂ A with A.
The minimal surface satisfies a homology constraint, which de-
mands
that is smoothly retractable to the boundary region A.
E-mail address: haoxu@mail.nankai.edu.cn.
In 2006, Ryu and Takayanagi proposed that the quantum entangle-
ment
entropy can be directly obtained from minimal surface [4,5].
The holography entanglement entropy (HEE) is given by the area
of the minimal surface in a manner similar to the black hole en-
tropy:
S
A
=
Area()
4G
, where G is the gravitational constant of the
bulk theory. This minimal surface also plays an important role in
“subregion–subregion” duality. See, e.g., [6–12] for reviews and ref-
erences.
It is natural to investigate the minimal surface in more unusual
gravity models, since it may provide some important information
about the dual field theory. There is an important model, known
as C-metric, which is a representative of a class of space–time with
boost-rotation symmetry [13–23]. It was originally found by Weyl
in 1917 and rediscovered many times [13]. In 1970, Kinnersley
and Walker showed that it describes a pair of black holes which
accelerate away from each other due to the existence of conical
singularities caused by cosmic strings or struts [14]. C-metric also
admits a non-vanishing value of a cosmological constant . These
solutions can be used to investigate the accelerating black holes in
dS and AdS backgrounds [15–20]. The global causal structure and
physical interpretation of parameters in the metric are investigated
in [21]. Recently, the authors of [22,23] addressed the problem of
describing the thermodynamics of a slowing charged accelerating
black hole in AdS space–time. C-metric also has been used to con-
struct
localized black holes on UV branes and plasma ball solutions
on IR branes [24–26].
However,
the field theory interpretation of C-metric are still,
to a large extent, open questions. In the present work we plan to
shed some light on these questions by studying the minimal sur-
faces
which are homologous to the given boundary regions. It is
worth emphasizing that it is still unclear about whether the min-
imal
surface can be interpreted as the HEE, since the accelerating
http://dx.doi.org/10.1016/j.physletb.2017.09.033
0370-2693/
© 2017 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
.
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