Aspects of nonlinear effect on black hole superradiance
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Springer
Received: October 24, Revised: December 21, Accepted: January 6, Published: January 21,
2019 2019 2020 2020
Hajime Fukudaa,b,c and Kazunori Nakayamaa,d a
Department of Physics, Faculty of Science, The University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan b Theoretical Physics Group, Lawrence Berkeley National Laboratory, 1 Cyclotron Rd, Berkeley, CA 94720, U.S.A. c Berkeley Center for Theoretical Physics, Department of Physics, University of California, 366 LeConte Hall, Berkeley, CA 94720, U.S.A. d Kavli IPMU (WPI), The University of Tokyo, Kashiwa, Chiba 277-8583, Japan
E-mail: [email protected], [email protected] Abstract: Under some conditions, light boson fields grow exponentially around a rotating black hole, called the superradiance instability. We discuss effects of nonlinear interactions of the boson on the instability. In particular, we focus on the effect of the particle production and show that the growth of the boson cloud may be saturated much before the black hole spin is extracted by the boson cloud, while the nonlinear interactions also induce the boson emission. For application, we revisit the superradiant instability of the standard model photon, axion and hidden photon. Keywords: Beyond Standard Model, Black Holes ArXiv ePrint: 1910.06308
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP01(2020)128
JHEP01(2020)128
Aspects of nonlinear effect on black hole superradiance
Contents 1 Introduction
1
2 Nonlinear effects on superradiant instability 2.1 Rough sketch 2.2 Time evolution of black hole
3 3 4 6 6 9 10 12
4 Conclusions and discussion
15
A Schwinger pair production A.1 Schwinger pair production rate A.2 Comparison with superradiance rate
16 16 17
B Radiation due to nonlinearity B.1 Scalar radiation B.2 Vector radiation
20 20 21
1
Introduction
There may exist light scalar fields in theories beyond the standard model [1] and many ideas are proposed to find signatures of such light particles including terrestrial experiments and astrophysical observations. One of the ideas is to see the effects of light particles on the black hole physics. As we briefly review below, light bosons around a rotating black hole (or Kerr black hole) may experience a so-called superradiant instability and the boson cloud may be formed. It can significantly affect the evolution of the black hole through the extraction of its mass and spin by the boson cloud, which can be severely constrained by observations. Theoretical and phenomenological aspects of black hole superradiance are found in refs. [2–28]. A massive scalar field φ with its mass µ around a black hole satisfies the Klein-Gordon equation ( − µ2 )φ = 0.
–1–
(1.1)
JHEP01(2020)128
3 Examples 3.1 Standard Model photon around primordial black hole 3.2 Axion with cosine potential 3.3 Hidden photon with Higgs mechanism 3.4 Scalar with four-point interaction
Under the Kerr metric, the solution to this equation of the form φ ∝ e−iωt+imϕ is found, where m is a
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