JHEP12(2015)139
The AdS-RN solution together with the gauge field is given by:
ds
2
= −f(r)dt
2
+
dr
2
f(r)
+ r
2
(dθ
2
+ sin
2
θdφ
2
) , (2.2)
f(r) = 1 −
2M
r
+
Q
2
r
2
+
r
2
L
2
, (2.3)
A = Q
1
r
+
−
1
r
dt , (2.4)
where M is the mass, Q is the electric charge and L is the AdS lengthscale. The additive
constant in A
t
was chosen to be
Q
r
+
so that the norm of the vector potential A
2
is regular
at the horizon. The black hole temperature and entropy are:
T =
3r
4
+
+ L
2
(r
2
+
− Q
2
)
4πL
2
r
3
+
, (2.5)
S = πr
2
+
, (2.6)
where r
+
is the horizon (the largest root of f(r
+
) = 0). From (2.5) and (2.6), we can easily
eliminate the parameter r
+
to obtain the function T (S, Q):
T (S, Q) =
1
4π
3
L
2
r
S
π
+
r
π
S
− Q
2
π
3/2
S
3/2
!
. (2.7)
From the function T (S, Q) above, one can plot the isocharges on the T − S plane. The
plot is presented on the right panel of figure 1. As can be seen from the plot, the curve is
monotonic for sufficiently large Q. As Q decreases, the curve has an inflection point when
Q reaches a threshold value Q
c
. One can solve for the position of the inflection point by:
∂T
∂S
Q
=
∂
2
T
∂S
2
Q
= 0 . (2.8)
We find the critical entropy S
c
, critical charge Q
c
and critical temperature T
c
to be:
S
c
=
π
6
L
2
, (2.9)
Q
c
=
L
6
, (2.10)
T
c
=
r
2
3
1
πL
. (2.11)
Finally, when Q < Q
c
, the curve becomes oscillatory, and there is a small portion with
negative heat capacity:
T
∂S
∂T
Q
≤ 0 . (2.12)
Like in the case of the liquid-gas transition, this portion is believed to be thermodynam-
ically unstable, and should be replaced by an isotherm T = T
∗
according to Maxwell’s
prescription. The value of T
∗
can be obtained in two different (but equivalent) ways: by
the equal area condition, or from the Helmholtz free energy. The first method, the equal
area condition, states that T
∗
is the unique temperature which divides the oscillatory part
of the curve T (S) into two regions with equal area. We will find T
∗
from the second method,
i.e. using the Helmholtz free energy, and check numerically that it is equivalent to the first.
– 3 –
剩余16页未读，继续阅读
付出余切
- 粉丝: 200
- 资源: 912
我的内容管理
展开
最新资源
- 计算机人脸表情动画技术发展综述
- 关系数据库的关键字搜索技术综述：模型、架构与未来趋势
- 迭代自适应逆滤波在语音情感识别中的应用
- 概念知识树在旅游领域智能分析中的应用
- 构建is-a层次与OWL本体集成：理论与算法
- 基于语义元的相似度计算方法研究：改进与有效性验证
- 网格梯度多密度聚类算法：去噪与高效聚类
- 网格服务工作流动态调度算法PGSWA研究
- 突发事件连锁反应网络模型与应急预警分析
- BA网络上的病毒营销与网站推广仿真研究
- 离散HSMM故障预测模型：有效提升系统状态预测
- 煤矿安全评价：信息融合与可拓理论的应用
- 多维度Petri网工作流模型MD_WFN：统一建模与应用研究
- 面向过程追踪的知识安全描述方法
- 基于收益的软件过程资源调度优化策略
- 多核环境下基于数据流Java的Web服务器优化实现提升性能
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
