新发现：旋转Dilaton黑弦与指数非线性电动力学的耦合解
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更新于2024-09-04
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本文研究了一类新颖的带电旋转黑弦解，它是在Liouville型狄拉顿场的背景下，结合指数非线性电动力学的特殊情形。狄拉顿黑弦是一种在广义相对论中重要的对象，它们是引力理论与额外场相互作用的结果，特别是当考虑狄拉顿场时，可以产生与标准黑洞不同的物理特性。作者Ahmad Sheykhi及其团队在 Shiraz University 和 RIAAM (Research Institute for Astronomy and Astrophysics of Maragha) 进行了这项研究。
旋转黑弦模型中，关键的创新在于引入了指数非线性电动力学，这使得理论的电场行为不再局限于传统的线性麦克斯韦方程。这种非线性性可能源自于量子效应或者在高能量物理中的其他物理现象。通过构造新的解，他们探讨了狄拉顿场如何影响空间时间结构，特别是其渐近行为不再是平坦宇宙(Minkowski)或德西特宇宙(A)dS空间，而是受到狄拉顿场影响的独特形式。
文章的核心部分包括对这些新解的详尽分析，包括但不限于计算守恒量和热力学性质。守恒量如质量、角动量和电荷等对于理解黑洞的物理稳定性和基本性质至关重要。热力学第一定律的验证则展示了这些黑弦解在热力学上的合理性，即能量守恒原则在极端条件下依然成立。
当非线性参数β2趋近于无穷大时，这些解退化为经典的爱因斯坦-麦克斯韦-狄拉顿引力中的黑色弦解，表明了非线性效应在特定条件下的消失以及理论之间的连续性。这不仅展示了理论的普适性，也为未来的黑洞物理研究提供了新的可能性，即探索非线性效应如何影响基本物理规律。
总结来说，这篇研究文章深入探讨了狄拉顿黑弦在指数非线性电动力学环境下的性质，对引力理论和电磁理论的融合产生了新的见解。它的开放获取属性使得学术界可以无障碍地访问和研究这一前沿领域的研究成果，促进了物理学知识的共享与进展。
Advances in High Energy Physics 3
already studied in [5] and the corresponding black string
solutions were investigated [5]. e lagrangian proposed in
(3) is the quite one generalization of lagrangian [5]toinclude
the dilaton scalar eld.
For latter convenience we write the lagrangian as
(
,Φ
)
=4
2
2𝛼Φ
L
(
)
,
(5)
where we have dened
L
(
)
=exp
(
−
)
−1,
=
−4𝛼Φ
2
4
2
.
(6)
In this paper, we consider action (2)withaLiouvilletype
potential,
(
Φ
)
=2Λ
2𝛼Φ
,
(7)
where Λis a constant which may be referred to as the
cosmological constant, since in the absence of the dilaton
eld (Φ=0) the action (2)reducestotheactionof
EN electrodynamics in Einstein gravity in the presence of
cosmological constant [5]. e equations of motion can
be obtained by varying the action (2)withrespecttothe
gravitational eld
𝜇]
,thedilatoneldΦ,andthegaugeeld
𝜇
which yields the following eld equations:
R
𝜇]
=2
𝜇
Φ
]
Φ+
1
2
𝜇]
(
Φ
)
−2
−2𝛼Φ
×
𝑌
L
(
)
𝜇𝜂
𝜂
]
+2
2
2𝛼Φ
×2
𝑌
L
(
)
−L
(
)
𝜇]
,
(8)
∇
2
Φ=
1
4
Φ
+2
2
2𝛼Φ
2
𝑌
L
(
)
−L
(
)
,
(9)
∇
𝜇
−2𝛼Φ
𝑌
L
(
)
𝜇]
=0. (10)
In case of linear electrodynamics we have L()=−,and
the system of (8)–(10) reduce to the well-known equations of
Einstein-Maxwell-dilaton (EMd) gravity [36].
Our aim here is to construct charged rotating black string
solutions of the eld equations (8)–(10) and investigate their
properties. e metric of four-dimensional rotating solution
with cylindrical or toroidal horizons can be written as [60, 61]
2
=−
(
)
Ξ−
2
+
2
2
(
)
2
−Ξ
2
+
2
(
)
+
2
2
2
(
)
2
,
(11)
where Ξ=
1+
2
/
2
and is the rotation parameter as
we will see later. e functions ()and ()should be
determined and has the dimension of length which is related
to the constant Λby the relation
2
=−3/Λ.etwo
dimensional space, =constantand=constant,canbe(i)
the at torus model
2
with topology
1
×
1
and 0≤<2,
0≤<2, (ii) the standard cylindrical model with topology
×
1
and 0≤<2, −∞<<∞, and (iii) the innite
plane
2
with −∞<<∞and −∞<<∞.Wewillfocus
upon (i) and (ii).
e modied Maxwell equation (10)canbeintegrated
immediately to give
𝑡𝑟
=
Ξ
2𝛼Φ
2
2
(
)
exp −
1
2
𝑊
2
2
4
4
(
)
,
(12)
𝜙𝑟
=−
Ξ
𝑡𝑟
,
(13)
where is an integration constant which is related to the elec-
tric charge of the black string, and
𝑊
()=Lambert()is
the Lambert function which satises [62, 63]
𝑊
(
)
𝐿
𝑊
(𝑥)
=,
(14)
and it has the following series expansion:
𝑊
(
)
=−
2
+
3
2
3
−
8
3
4
+⋅⋅⋅.
(15)
Clearly, series (15)convergesfor|| < 1. e expansion of
(12)forlarge(or large )isgivenby
𝑡𝑟
=
Ξ
2𝛼Φ
(
)
2
−
Ξ
2
2
3
2𝛼Φ
(
)
6
+
5Ξ
8
4
5
2𝛼Φ
(
)
10
+
1
6
.
(16)
In the absence of the dilaton eld ( = 0,() = 1),(12)
reduces to
𝑡𝑟
=
Ξ
2
exp −
1
2
𝑊
2
2
4
,
(17)
while its expansion (16)reducesto
𝑡𝑟
=
Ξ
2
−
3
Ξ
2
2
6
+
5
5
Ξ
8
4
10
+
1
6
,
(18)
Now, we want to solve the system of (8)and(9)forthree
unknown functions (), (),andΦ().Tothisend,we
make the suitable ansatz [41]
(
)
=
𝛼Φ
.
(19)
Using (19), the electromagnetic elds (12)and(13) and metric
(11), aer some mathematic calculations, we can show that (8)
and (9)havesolutionoftheform
(
)
=
Λ+2
2
2
+1
2
𝛾
2
−3
2−𝛾
−
1−𝛾
−
2
1−𝛾
2
+1
𝛾
×
−𝛾
𝑊
−
1
𝑊
,
Φ
(
)
=
2
+1
ln
,
(20)
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