BlackHawk：普适黑洞蒸发光谱计算工具
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BlackHawk是一个开源的C语言程序，它在Open Access的背景下为研究人员提供了计算任意黑洞分布霍金辐射光谱的强大工具。霍金辐射是基于量子力学和广义相对论的一个理论概念，预测了黑洞并非完全吞噬所有物质，而是会以微弱的粒子形式通过事件视界逸出，这些粒子被称为“霍金辐射”。BlackHawk的设计目标是帮助科学家们深入了解这一现象，特别是对于那些不稳定或者寿命较长的粒子，如光子、电子、甚至是可能的重粒子，其初级和次级光谱的产生及其随时间的变化。
程序的核心功能包括处理各种类型的黑洞分布，无论是质量分布、旋转分布还是电荷分布，都能准确地计算出相应黑洞的霍金辐射特征。用户可以通过BlackHawk提供的接口输入不同的参数，如黑洞的质量、自旋和温度等，然后得到精确的辐射光谱结果。此外，该程序还支持对不同阶段的黑洞演化进行模拟，这在理解黑洞生命周期以及它们如何与宇宙背景相互作用方面具有重要意义。
BlackHawk的开发团队由来自法国多个知名机构的研究人员组成，包括里昂大学、巴黎索邦大学和高等师范学院的物理学家，以及CERN（欧洲核子研究中心）。他们在论文《Eur.Phys.J.C (2019) 79: 693》中详细介绍了这个项目的开发过程、原理和应用，该论文也被引用为SpecialArticle-Tools for Experiment and Theory，表明BlackHawk不仅是一个实用的工具，也是理论物理研究的重要支撑。
通过访问https://blackhawk.hepforge.org，用户可以直接下载并使用BlackHawk程序，进行相关的黑洞蒸发光谱计算。这对于学术界来说，无疑拓宽了探索宇宙深处黑洞奥秘的可能性，同时也促进了跨学科的合作，推动了理论物理学和天体物理学领域的前沿研究。
Eur. Phys. J. C (2019) 79 :693 Page 5 of 26 693
2.3.2 Kerr Black Holes
For Kerr BHs, a new phenomenon arises. The rotation of
the BH enhances the emission of particles with high angular
momentum, and with a projection m of that angular momen-
tum aligned with the BH spin, thus effectively extracting
angular momentum from the BH [42]. The equation for the
Page factor f (M, a
∗
) becomes [24,43,44]
f (M, a
∗
) ≡−M
2
dM
dt
= M
2
+∞
0
E
2π
dof
Γ
s
(E, M, a
∗
)
e
E
/T
± 1
dE, (21)
and the differential equation describing the angular momen-
tum J is [24,43,44]
3
g(M, a
∗
) ≡−
M
a
∗
dJ
dt
=−
M
a
∗
+∞
0
dof
m
2π
Γ
s
(E, M, a
∗
)
e
E
/T
± 1
dE. (22)
Once the f (M, a
∗
) and g(M, a
∗
) Page factors are obtained,
the evolution of a
∗
is straightforwardly obtained through
da
∗
dt
=
d( J/M
2
)
dt
=
1
M
2
dJ
dt
− 2
J
M
3
dM
dt
= a
∗
2 f (M, a
∗
) − g(M, a
∗
)
M
3
. (23)
The computation of the f (M, a
∗
) and g(M, a
∗
) Page fac-
tors in BlackHawk is described in Appendix B.2.
2.3.3 Exotic Black Holes
Exotic BHs listed in Sect. 2.2.3 can have a modified evolu-
tion as compared to the Schwarzschild and Kerrcases,fortwo
main reasons. First, since their greybody factors and temper-
ature are different, the f and g parameters are expected to be
different as well and the master Eq. (18) will give a different
emission rate. Second, these BHs can possess other scalar
degrees of freedom, such as a U (1) charge (e.g. the electric
charge in Reissner–Nordström BHs [25]), which experience
a specific evolution. Evolution equations for these additional
charges have to be derived, and would be similar to Eqs. (21)
and (22). The implementation of beyond-standard BHs in
BlackHawk is described in Sect. 9.5.
3
Same remark as above, we have in our conventions an opposite sign
for g.
2.4 Hadronization
The elementary particles emitted by BHs are not the final
products of the HR. Some of them are unstable, others only
exist in hadrons. A particle physics code has to be used in
order to evolve the elementary particles into final products.
We used HERWIG [45] and PYTHIA [46] for this purpose.
The final particles, hereby denoted as “secondary Hawk-
ing particles” (the elementary being the “primary Hawking
particles”), depend on the cosmological context in which they
are emitted. For Big-Bang Nucleosynthesis (BBN) studies,
an estimation of the reaction rates imposes to keep the parti-
cles with a lifetimelonger than ∼ 10
−8
s[47]. These particles
are listed in the Table 2 of Appendix C.
The time-dependent comoving density of Hawking sec-
ondary particle j emitted by a distribution of BHs per units
of time and energy is computed with the integral
d
2
n
j
dtdE
=
i
d
2
n
i
dtdE
·
dN
i
j
dE
dE
, (24)
where the sum is taken over Hawking primary particles i,
and Sect. Appendix B.3 describes how hadronization tables
dN
i
j
(E
, E) have been computed to transform the primary
spectra into secondary spectra in BlackHawk.
3 Content and compilation
This section describes the structure and file content of the
code and explains its usage. BlackHawk is written in C
and has been tested under Linux, Mac and Windows (using
Cygwin64). It can be obtained from
blackhawk.hepforge.org
3.1 Main directory
The main directory contains:
– the source codes BlackHawk_*.c containing the
main routines,
– a pre-built parameter file parameters.txt,
– a compilation file Makefile,
–aREADME.txt file containing general information
about the code,
– four folders src/, results/, manual/ and
scripts/ that are described in the following.
3.2 src/ sub-folder
This folder contains:
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