新型带电膨胀BTZ黑洞的热力学分析与稳定性研究

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本文主要探讨了三维爱因斯坦-麦克斯韦理论在带有膨胀标量场的背景下，尤其是在考虑了两个Liouville型势线性组合的特殊情况下。作者M.Dehghani针对Ilam University的研究团队，对带电膨胀的BTZ黑洞进行了深入研究。BTZ黑洞是一种在三维广义相对论中的重要模型，它在量子引力和宇宙学中有潜在的应用。文章的核心内容聚焦在两类全新的带电膨胀BTZ黑洞的发现和分析上。这些黑洞被作为耦合标量、矢量和张量场方程的精确解，它们的特性包括电荷和质量，这些物理量通过高斯定律和Abbott-Deser提出的计算方法得到了精确的评估。研究者对比了从几何方法和热力学角度得到的温度和熵，以此验证了新黑洞的热力学第一定律的有效性。此外，论文还对这些黑洞的热稳定性进行了详尽的考察，通过典范积分方法分析了它们的相变行为。研究发现，当视界半径处于特定范围内时，黑洞被认为是局部稳定的，这涉及到第一类和第二类相变点。特别地，当视界半径等于相变点时，黑洞表现出不稳定性，需要经历第一或第二类型相变才能恢复到稳定状态。总结来说，这篇工作不仅提供了带电膨胀BTZ黑洞的新解，还深化了我们对这些黑洞的热力学性质和相变理解，这对于理解三维时空中的基本物理现象以及可能的宇宙学应用具有重要意义。由于文章发表在《物理学报B》上，且具有开放存取权限，这意味着其研究成果可以被广泛共享和讨论。

Physics Letters B 773 (2017) 105–111

Contents lists available at ScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

Thermodynamics of novel charged dilatonic BTZ black holes

M. Dehghani

Department of Physics, Ilam University, Ilam, Iran

a r t i c l e i n f o a b s t r a c t

Article history:

Received

9 July 2017

Received

in revised form 31 July 2017

Accepted

2 August 2017

Available

online 10 August 2017

Editor:

N. Lambert

Keywords:

Charged

BTZ black hole

Charged

black hole with scalar hair

Maxwell’s

theory of electrodynamics

Three-dimensional

dilatonic black holes

In this paper, the three-dimensional Einstein–Maxwell theory in the presence of a dilatonic scalar ﬁeld

has been studied. It has been shown that the dilatonic potential must be considered as the linear

combination of two Liouville-type potentials. Two new classes of charged dilatonic BTZ black holes, as

the exact solutions to the coupled scalar, vector and tensor ﬁeld equations, have been obtained and

their properties have been studied. The conserved charge and mass of the new black holes have been

calculated, making use of the Gauss’s law and Abbott–Deser proposal, respectively. Through comparison

of the thermodynamical extensive quantities (i.e. temperature and entropy) obtained from both, the

geometrical and the thermodynamical methods, the validity of the ﬁrst law of black hole thermodynamics

has been conﬁrmed for both of the new black holes we just obtained. A black hole thermal stability or

phase transition analysis has been performed, making use of the canonical ensemble method. Regarding

the black hole heat capacity, it has been found that for either of the new black hole solutions there are

some speciﬁc ranges in such a way that the black holes with the horizon radius in these ranges are

locally stable. The points of type one and type two phase transitions have been determined. The black

holes, with the horizon radius equal to the transition points are unstable. They undergo type one or type

two phase transitions to be stabilized.

(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP

1. Introduction

Although the Einstein’s tensorial theory of gravitation is in

agreement with a large amount of observational tests, but it fails

regarding some important issues [1–5]. Modiﬁcation of the Ein-

stein’s

theory of gravity is one of the main approaches to over-

come

the related failures. Among the various proposed modiﬁ-

cations

[6–13], the so-called scalar-tensor theories [14], as the

modiﬁcation arisen from string theory, have provided interesting

results [15]. The Einstein’s action is naturally modiﬁed by the

scalar-tensor superstring terms at the high energy regime. In the

low energy limit of the string theory, the Einstein’s theory of grav-

ity

is recovered which is coupled to a dilatonic scalar ﬁeld [16].

Black

holes with scalar hair are interesting solutions of Ein-

stein’s

theory of gravity and also of certain types of modiﬁed

gravity theories. These solutions have been investigated by theo-

retical

physicists in four and higher dimensional space times for

a long time (see [17] and references therein). The ﬁrst studies on

the three-dimensional black holes, as the interesting predictions

of Einstein’s theory of relativity in lower dimensional space times,

have been done by Banados, Teitelboim, and Zanelli (BTZ) [18].

E-mail address: m.dehghani@ilam.ac.ir.

Investigation of the three-dimensional black holes is one of the in-

teresting

subjects for recent gravitational studies [19]. Chan and

Mann [20], are the ﬁrst authors who investigated the charged

three-dimensional dilatonic black holes in the presence of a mini-

mally

coupled logarithmic dilaton ﬁeld.

is a commonly believed that study of three-dimensional so-

lutions

help us to ﬁnd a deeper insight into the fundamental ideas

in comparison to higher dimensional black holes. Also, according to

(A)dS/CFT correspondence, there is a dual between quantum grav-

ity

on A(dS) space and Euclidean conformal ﬁeld theory on the

lower dimensional space times [21,22]. From this point of view,

study of physics in (2 +1)-dimensional space times can be useful

for understanding of quantum ﬁeld theory on A(dS) spacetimes.

Although this subject area has been considered extensively [23], it

still has many unknown and interesting parts to be studied [24].

the other hand, after the discoveries of Bekenstein, Bardeen,

Carter and Hawking, it is well-known that black holes can be

considered as the thermodynamical systems with a temperature

proportional to the surface gravity and having pure geometrical

entropy equal to one-fourth of the horizon area [25–27]. When a

dilatonic scalar ﬁeld is coupled to the three-dimensional Einstein–

Maxwell

theory, it is expected to produce new and interesting

consequences for the black hole solutions. Thus, it is worth to ﬁnd

exact solutions of Einstein–Maxwell theory in the presence of a

http://dx.doi.org/10.1016/j.physletb.2017.08.003

0370-2693/

SCOAP

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