Physics Letters B 759 (2016) 115–120
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
Canonical structure of BHT massive gravity in warped AdS
3
sector
Davood Mahdavian Yekta
Department of Physics, Hakim Sabzevari University, P.O. Box 397, Sabzevar, Iran
a r t i c l e i n f o a b s t r a c t
Article history:
Received
3 April 2016
Received
in revised form 9 May 2016
Accepted
9 May 2016
Available
online 12 May 2016
Editor:
N. Lambert
We investigate the asymptotic structure of the three dimensional Warped Anti-de Sitter (WAdS
3
)
black holes in the Bergshoeff–Hohm–Townsend (BHT) massive gravity using the canonical Hamiltonian
formalism. We define the canonical asymptotic gauge generators, which produce the conserved charges
and the asymptotic symmetry group for the WAdS
3
black holes. The attained symmetry group is
described by a semi-direct sum of a Virasoro and a Ka
ˇ
c–Moody algebra. Using the Sugawara construction,
we obtain a direct sum of two Virasoro algebras. We show that not only the asymptotic conserved charges
satisfy the first law of black hole thermodynamics, but also they lead to the expected Smarr formula for
the WAdS
3
black holes. We also show that the black hole’s entropy obeys the Cardy formula of the dual
conformal field theory (CFT).
© 2016 The Author. 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
A theoretically physical issue in general relativity (GR) is the
existence of black hole solutions, which are naturally endowed
through the laws of black hole thermodynamics and accompa-
nied
by a macroscopic entropy [1,2]. However, we need a quantum
theory of GR to produce this entropy from counting the micro-
states
[3]. String theory is the most well-known candidate of
quantum theory of GR, which embraces two practical features: the
gauge/gravity duality [4], which is also called the AdS/CFT corre-
spondence,
and the black hole physics.
Three-dimensional
(3D) gravity is another candidate to study
the quantum theory of GR [5], which could also be appeared in
the lower dimensional solutions of string theories [6–8]. How-
ever,
3D gravity describing by the Einstein–Hilbert action has no
physical degrees of freedom [9,10], so it demands that we add
higher derivative correction terms to the action. The first odd-
parity
extension is the topologically massive gravity (TMG) in-
cluding
a gravitational Chern–Simons Lagrangian, which gives one
massive and two massless spin-2 gravitons [11,12]. The BHT mas-
sive
gravity theory is a unitary parity-preserving extension, which
includes higher curvature terms up to the forth order of deriva-
tives
[13]. Other extensions of this theory could be found in
Refs. [14–17].
E-mail address: d.mahdavian@hsu.ac.ir.
In this letter, we study the BHT massive gravity in the canon-
ical
first-order formalism [18] on the basis of WAdS
3
black holes,
which have introduced in Refs. [19] and [20]. A similar procedure
for the BTZ black holes [21] has made in Ref. [22]. In the first step,
we define the gauge generators based on a constrained Hamilto-
nian
theory. We calculate the energy and angular momentum of
the WAdS
3
black hole from the asymptotic structure of these gen-
erators
due to the gauge transformations. The Poisson bracket (PB)
algebra of the asymptotic generators describes the asymptotic sym-
metry
group (ASG) of the asymptotically warped backgrounds in
the BHT massive gravity. We show that these conserved charges
satisfy the black hole mechanics as the first law, the Smarr formula
[23], and the Cardy formula [24] in verification of the AdS/CFT cor-
respondence.
In
the investigation of the asymptotic symmetries, we use the
asymptotic boundary conditions (BCs) introduced by Compére and
Detournay in Refs. [25,26], just like the Brown–Henneaux BCs in
Ref. [27], which are introduced for the asymptotically AdS
3
so-
lutions
in 3D gravity theories. In the framework of gauge/gravity
duality, this is known as WAdS
3
/warped CFT
2
[28,29].
After
having briefly discussed the canonical structure of the
BHT massive gravity in Sect. 2, we will compute the asymp-
totic
conserved charges using the asymptotic gauge generators in
Sect. 3. We consider, in sect. 4, the WAdS
3
black hole as a solution
of the BHT equations of motion and then, derive the asymptotic
canonical algebra and thermodynamics. Finally, in sect. 5, we dis-
cuss
about the concluding results.
http://dx.doi.org/10.1016/j.physletb.2016.05.023
0370-2693/
© 2016 The Author. 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
.
下载后可阅读完整内容，剩余5页未读，立即下载
weixin_38688550
- 粉丝: 7
- 资源: 912
我的内容管理
展开
最新资源
- 李兴华Java基础教程：从入门到精通
- U盘与硬盘启动安装教程：从菜鸟到专家
- C++面试宝典：动态内存管理与继承解析
- C++ STL源码深度解析：专家级剖析与关键技术
- C/C++调用DOS命令实战指南
- 神经网络补偿的多传感器航迹融合技术
- GIS中的大地坐标系与椭球体解析
- 海思Hi3515 H.264编解码处理器用户手册
- Oracle基础练习题与解答
- 谷歌地球3D建筑筛选新流程详解
- CFO与CIO携手：数据管理与企业增值的战略
- Eclipse IDE基础教程：从入门到精通
- Shell脚本专家宝典：全面学习与资源指南
- Tomcat安装指南：附带JDK配置步骤
- NA3003A电子水准仪数据格式解析与转换研究
- 自动化专业英语词汇精华：必备术语集锦
资源上传下载、课程学习等过程中有任何疑问或建议，欢迎提出宝贵意见哦~我们会及时处理！
点击此处反馈
