旋转狄拉顿黑黄铜的热力学与对数非线性电动力学研究
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更新于2024-09-03
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"这篇研究文章探讨了在对数非线性电动力学背景下带电旋转Dilaton黑黄铜的热力学性质。作者构建了一类新的旋转黑黄铜解，这些解具有完整的任意维度旋转参数集。解决方案的视界拓扑被描述为平坦的，而狄拉顿场的存在使得其渐近行为既非平坦也非(A)dS空间。通过应用AdS/CFT对应反条件方法，计算了时空质量和角动量，进一步确定了与视界相关的温度、电势和熵。研究还涉及了热力学第一定律在黑黄铜视界上的适用性。此外，作者分析了正则和大正则集合中的解的热稳定性，揭示了旋转参数、非线性电动力学以及狄拉顿场对热稳定性条件的影响。特别是，当狄拉顿-电磁耦合常数α小于1时，解可能出现不稳定相。"
文章详细阐述了在带电旋转Dilaton黑黄铜的研究中引入对数非线性电动力学的新颖理论框架。这种框架允许在不同维度下探索具有完整旋转参数的解，扩展了我们对非平凡时空结构的理解。狄拉顿场是本文的关键要素，它改变了黑黄铜的视界性质和渐近行为，使其区别于传统的平坦或(A)dS空间。
作者通过AdS/CFT（Anti-de Sitter/Conformal Field Theory）对应反条件方法来确定物理量，这是一种强大的工具，能将高维引力理论与低维量子场论联系起来。他们计算了黑黄铜的热力学特性，包括温度、电势和熵，这些都是理解系统热行为的基础。此外，对热力学第一定律的验证确保了这些解的热力学一致性。
在热稳定性分析部分，作者关注了解在不同参数组合下的稳定性。旋转参数、非线性电动力学效应以及狄拉顿场的存在都可能影响热稳定性。特别指出的是，当狄拉顿-电磁耦合常数α小于1时，系统的稳定性受到挑战，这可能导致不稳定的相态出现。这一发现对于理解和预测高能物理环境中复杂系统的动态行为至关重要。
这篇开放获取的文章提供了对带电旋转Dilaton黑黄铜热力学性质的深入洞察，特别是在非线性电动力学环境中的新见解。研究结果有助于推动对强耦合量子场论、黑洞物理学以及广义相对论与量子场论交叉领域的理解。
Advances in High Energy Physics
By varying action () with respect to the gravitational eld
𝜇]
,thedilatoneldΦ,andthegaugeeld
𝜇
,wend
R
𝜇]
=
4
−2
𝜇
Φ
]
Φ+
1
4
𝜇]
(
Φ
)
+2
−4𝛼Φ/(𝑛−2)
𝑌
L
(
)
𝜇𝜂
]
𝜂
−
8
2
−2
4𝛼Φ/(𝑛−2)
2
𝑌
L
(
)
−L
(
)
𝜇]
,
()
∇
2
Φ
=
−2
8
Φ
−4
2
4𝛼Φ/(𝑛−2)
2
𝑌
L
(
)
−L
(
)
,
()
∇
𝜇
−4𝛼Φ/(𝑛−2)
𝑌
L
(
)
𝜇]
=0.
()
In the limiting case where →∞,wehaveL() = .In
this case the system of eld equations ()–() restore the well-
knownequationsofEMdgravity[–],asexpected.
2.1. Finite Action in Canonical and Grand-Canonical Ensem-
bles. In general, the total action given in () is divergent
when evaluated on a solution. One way of dealing with the
divergences of the action is adding some counterterms to
action (). e counterterms should contain a part which
removes the divergence of the gravity part of the action and
a part for dealing with the divergence of the matter action.
Since the horizon of our solution is at, the counterterm
which removes the divergence of the gravity part should be
proportional to
−. e counterterm for the matter part of
theactioninthepresenceofthedilatonisgivenby
ct
=−
1
8
𝜕M
𝑛−1
−
−2
e
+
deriv
,
()
where
e
is given by () and
deriv
is a collection of terms
involving derivatives of the boundary elds that could involve
the curvature tensor constructed from the boundary metric.
Sinceinourcasetheboundaryisatso
deriv
is zero on the
boundary. e variation of the total action (
tot
=+
ct
)about
the solutions of the equations of motion is
tot
=
𝑛−1
𝑎𝑏
𝑎𝑏
−
1
16
𝑛−1
−
−4𝛼Φ/(𝑛−2)
𝑌
L
(
)
𝑎
𝑎𝑏
𝑏
,
()
where
𝑎𝑏
=
−
16
Θ
𝑎𝑏
−Θ
𝑎𝑏
+
−2
e
𝑎𝑏
.
()
Equation()showsthatthevariationofthetotalaction
with respect to
𝑎
will only give the equation of motion of
the nonlinear massless eld
𝑎
provided the variation is at
xed nonlinear massless gauge potential on the boundary.
us, the total action,
tot
=+
ct
, given in () is appropriate
for the grand-canonical ensemble, where
𝑎
=0on the
boundary. But in the canonical ensemble, where the electric
charge [−
−4𝛼Φ/(𝑛−2)
𝑌
L()
𝑎
𝑎𝑏
]is xed on the boundary,
the appropriate action is
tot
=+
ct
+
1
16
⋅
𝜕M‘
𝑛−1
−
−4𝛼Φ/(𝑛−2)
𝑌
L
(
)
𝑎
𝑎𝑏
𝑏
.
()
e last term in () is the generalization of the boundary
term introduced by Hawking and Ross for linear electromag-
netic eld [] and the results of [, ] for the nonlinear
Lifshitz black holes to the exponential nonlinear gauge eld
coupledtothedilatoneld.us,bothincanonicaland
grand-canonical ensemble, the variation of total action about
the solutions of the eld equations is
tot
=
𝑛−1
𝑎𝑏
𝑎𝑏
. ()
at is, the nonlinear gauge eld is absent in the variation
of the total action both in canonical and grand-canonical
ensembles.
In order to obtain the conserved charges of the space-
time,weusethecountertermmethod[–]inspiredby
(A)dS/CFT correspondence. For asymptotically AdS solu-
tions this method works very well [–]. However, in
our paper we have the scalar dilaton eld with a Liouville
potential. It was argued that the presence of Liouville-type
dilaton potential, which is regarded as the generalization of
the cosmological constant, changes the asymptotic behavior
of the solutions to be neither asymptotically at nor (A)dS. It
has been shown that no dilaton dS or AdS black hole solution
exists with the presence of only one Liouville-type dilaton
potential [–]. But, as in the case of asymptotically AdS
spacetimes, according to the domain-wall/QFT (quantum
eld theory) correspondence [–], there may be a suitable
counterterm for the stress-energy tensor which removes the
divergences. In this paper, we deal with the spacetimes with
zero curvature boundary [
𝑎𝑏𝑐𝑑
() = 0], and therefore the
counterterm for the stress-energy tensor should be propor-
tional to
𝑎𝑏
. We nd the nite stress-energy tensor in -
dimensional Einstein-dilaton gravity with Liouville-type in
the form [, ]
𝑎𝑏
=
1
8
Θ
𝑎𝑏
−Θ
𝑎𝑏
+
−2
e
𝑎𝑏
,
()
where
e
is given by
2
e
=
(
−2
)
2
−+1
2Λ
−4𝛼Φ/(𝑛−2)
.
()
In the particular case =0,theeective
2
e
of ()
reduces to
2
= −(−1)(−2)/2Λof the AdS spacetimes.
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