极端Kerr-Newman黑洞的短标量毛发现象
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"极度Kerr–Newman黑洞，带极短的标量头发"
这篇研究文章主要探讨了关于黑洞“无短发”定理的一个反例，该定理通常认为球对称静态黑洞的外部场必须在黑洞的光子圈之外。然而，作者Shahar Hoda通过分析Kerr-Newman黑洞的特性，展示了非球对称的有毛黑洞结构可能违反这一界限。Kerr-Newman黑洞是带有电荷和角动量的旋转黑洞，其外部区域可以支持线性化的固定带电标量配置。
文章中，作者特别关注了中心黑洞参数{M，Q，J}（质量、电荷和角动量）以及线性标量场参数{μ，q}（质量和电荷耦合常数）的关系。通过研究这些参数，他们发现在特定情况下，标量场的有效长度（半径）可以非常小，甚至接近于黑洞的视界半径rH。这表明存在一种非球对称的非静态配置，使得带电标量场的“云”可以极其紧凑地存在于极端Kerr-Newman黑洞的外部时空。
更具体地说，当线性化的大质量带电标量场的无量纲比例q / μ达到某个临界值时，其峰值位置rfield可以非常接近黑洞视界，即rfield→rH。这样的情况违反了无短发定理，因为在这种极端配置下，标量头发并未延伸到光子圈之外。
此外，研究还证明了这些非常紧凑的稳定场配置与黑洞的无量纲角动量有直接关联，这意味着这些极端的标量头发现象不仅理论上可能存在，而且在某些条件下是物理上可实现的。这为理解黑洞的复杂性和可能的外部场结构提供了新的视角。
文章最后，作者指出这些发现可能对未来的黑洞物理学研究产生重要影响，尤其是在黑洞信息悖论、黑洞辐射和宇宙学等领域。通过提供这样的非典型黑洞模型，科学家们能够更好地探索宇宙中这些奇特天体的未知特性。
Physics Letters B 751 (2015) 177–183
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
Extremal Kerr–Newman black holes with extremely short
charged
scalar hair
Shahar Hod
a,b,∗
a
The Ruppin Academic Center, Emeq Hefer 40250, Israel
b
The Hadassah Institute, Jerusalem 91010, Israel
a r t i c l e i n f o a b s t r a c t
Article history:
Received
7 September 2015
Received
in revised form 13 October 2015
Accepted
14 October 2015
Available
online 20 October 2015
Editor:
M. Cveti
ˇ
c
The recently proved ‘no short hair’ theorem asserts that, if a spherically-symmetric static black hole
has hair, then this hair (the external fields) must extend beyond the null circular geodesic (the
“photonsphere”) of the corresponding black-hole spacetime: r
field
> r
null
. In this paper we provide
compelling evidence that the bound can be violated by non-spherically symmetric hairy black-hole
configurations. To that end, we analytically explore the physical properties of cloudy Kerr–Newman
black-hole spacetimes – charged rotating black holes which support linearized stationary charged scalar
configurations in their exterior regions. In particular, for given parameters {M, Q , J } of the central
black hole, we find the dimensionless ratio q/μ of the field parameters which minimizes the effective
lengths (radii) of the exterior stationary charged scalar configurations (here {M, Q , J} are respectively
the mass, charge, and angular momentum of the black hole, and {μ, q} are respectively the mass and
charge coupling constant of the linearized scalar field). This allows us to prove explicitly that (non-
spherically
symmetric non-static) composed Kerr–Newman-charged-scalar-field configurations can violate
the no-short-hair lower bound. In particular, it is shown that extremely compact stationary charged scalar
‘clouds’, made of linearized charged massive scalar fields with the property r
field
→r
H
, can be supported
in the exterior spacetime regions of extremal Kerr–Newman black holes (here r
field
is the peak location of
the stationary scalar configuration and r
H
is the black-hole horizon radius). Furthermore, we prove that
these remarkably compact stationary field configurations exist in the entire range s ≡ J /M
2
∈ (0, 1) of the
dimensionless black-hole angular momentum. In particular, in the large-mass limit they are characterized
by the simple dimensionless ratio q/μ = (1 −2s
2
)/(1 −s
2
).
© 2015 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
Wheeler’s famous conjecture that “black holes have no hair”
[1,2] predicts a simple and universal fate for all dynamical black-
hole
spacetimes [3]: the matter fields outside the horizon are ex-
pected
to be swallowed by the black hole or to be scattered away
to infinity, thus leaving behind a stationary “bald” Kerr–Newman
black hole [4–6]. The no-hair conjecture therefore suggests that,
within the framework of classical general relativity, black holes are
fundamental objects which possess only three conserved physical
parameters: mass M, charge Q , and angular momentum J .
The
no-hair conjecture predicts, in particular, that asymptoti-
cally
flat black holes cannot support static matter configurations in
their exterior regions. Early studies of the coupled Einstein-matter
*
Correspondence to: The Ruppin Academic Center, Emeq Hefer 40250, Israel.
E-mail
address: shaharhod@gmail.com.
equations have indeed ruled out the existence of regular black-
hole
solutions with static scalar hair [7], static spinor hair [8], and
static massive vector hair [9]. These early no-hair theorems have
therefore supported the simple physical picture suggested by the
no-hair conjecture [1,2].
However,
the somewhat surprising discovery of regular black-
hole
solutions [10] to the Einstein–Yang–Mills equations [11] has
revealed that coupled Einstein-matter systems may exhibit a more
complex behavior. The numerical discovery of these ‘colored’ black
holes [11], which provided the first genuine counterexample to the
no-hair conjecture, has motivated many researches to search for
other types of non-trivial hairy black-hole configurations. In fact,
it is by now well established that black holes can support vari-
ous
types of non-linear matter fields (that is, matter fields with
self-interaction terms) in their exterior regions [11–22].
The
hairy black-hole solutions discovered numerically in
[11–22] provide
compelling evidence that the no-hair conjecture,
in its original formulation [1,2], may be violated [23]. Accepting
http://dx.doi.org/10.1016/j.physletb.2015.10.039
0370-2693/
© 2015 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
.
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