Abstract
In this paper, we provide a simple and modern discussion of rotational super-radiance based on quantum field theory. We work with an effective theory valid at scales much larger than the size of the spinning object responsible for superradiance. Within this framework, the probability of absorption by an object at rest completely determines the superradiant amplification rate when that same object is spinning. We first discuss in detail superradiant scattering of spin 0 particles with orbital angular momentum ℓ = 1, and then extend our analysis to higher values of orbital angular momentum and spin. Along the way, we provide a simple derivation of vacuum friction — a “quantum torque” acting on spinning objects in empty space. Our results apply not only to black holes but to arbitrary spinning objects. We also discuss superradiant instability due to formation of bound states and, as an illustration, we calculate the instability rate Γ for bound states with massive spin 1 particles. For a black hole with mass M and angular velocity Ω, we find Γ ∼ (GM μ)7Ω when the particle’s Compton wavelength 1/μ is much greater than the size GM of the spinning object. This rate is parametrically much larger than the instability rate for spin 0 particles, which scales like (GM μ)9Ω. This enhanced instability rate can be used to constrain the existence of ultralight particles beyond the Standard Model.
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References
Y.B. Zel’Dovich, Generation of waves by a rotating body, JETP Lett. 14 (1971) 180.
Y.B. Zel’Dovich, Amplification of cylindrical electromagnetic waves reflected from a rotating body, Sov. Phys. JETP 35 (1972) 1085.
C.W. Misner, Stability of kerr black holes against scalar perturbations, Bull. Am. Phys. Soc. 17 (1972) 472.
A.A. Starobinsky, Amplification of waves reflected from a rotating “black hole”, Sov. Phys. JETP 37 (1973) 28 [INSPIRE].
A.A. Starobinsky and S.M. Churilov, Amplification of electromagnetic and gravitational waves scattered by a rotating black hole, Zh. Eksp. Teor. Fiz 65 (1973) 3.
S.A. Teukolsky and W.H. Press, Perturbations of a rotating black hole. III — Interaction of the hole with gravitational and electromagnet ic radiation, Astrophys. J. 193 (1974) 443 [INSPIRE].
W.H. Press and S.A. Teukolsky, Floating Orbits, Superradiant Scattering and the Black-hole Bomb, Nature 238 (1972) 211 [INSPIRE].
R.D. Blandford and R.L. Znajek, Electromagnetic extractions of energy from Kerr black holes, Mon. Not. Roy. Astron. Soc. 179 (1977) 433 [INSPIRE].
J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
V. Cardoso and O.J.C. Dias, Small Kerr-anti-de Sitter black holes are unstable, Phys. Rev. D 70 (2004) 084011 [hep-th/0405006] [INSPIRE].
A. Arvanitaki, S. Dimopoulos, S. Dubovsky, N. Kaloper and J. March-Russell, String Axiverse, Phys. Rev. D 81 (2010) 123530 [arXiv:0905.4720] [INSPIRE].
A. Arvanitaki and S. Dubovsky, Exploring the String Axiverse with Precision Black Hole Physics, Phys. Rev. D 83 (2011) 044026 [arXiv:1004.3558] [INSPIRE].
A. Arvanitaki, M. Baryakhtar and X. Huang, Discovering the QCD Axion with Black Holes and Gravitational Waves, Phys. Rev. D 91 (2015) 084011 [arXiv:1411.2263] [INSPIRE].
A. Arvanitaki, M. Baryakhtar, S. Dimopoulos, S. Dubovsky and R. Lasenby, Black Hole Mergers and the QCD Axion at Advanced LIGO, Phys. Rev. D 95 (2017) 043001 [arXiv:1604.03958] [INSPIRE].
A. Arvanitaki, P.W. Graham, J.M. Hogan, S. Rajendran and K. Van Tilburg, Search for light scalar dark matter with atomic gravitational wave detectors, arXiv:1606.04541 [INSPIRE].
J.D. Bekenstein and M. Schiffer, The Many faces of superradiance, Phys. Rev. D 58 (1998) 064014 [gr-qc/9803033] [INSPIRE].
R. Brito, V. Cardoso and P. Pani, Superradiance, Lect. Notes Phys. 906 (2015) 1 [arXiv:1501.06570] [INSPIRE].
S.A. Teukolsky, The Kerr Metric, Class. Quant. Grav. 32 (2015) 124006 [arXiv:1410.2130] [INSPIRE].
L.V. Delacrétaz, S. Endlich, A. Monin, R. Penco and F. Riva, (Re-)Inventing the Relativistic Wheel: Gravity, Cosets and Spinning Objects, JHEP 11 (2014) 008 [arXiv:1405.7384] [INSPIRE].
R.A. Porto, Post-Newtonian corrections to the motion of spinning bodies in NRGR, Phys. Rev. D 73 (2006) 104031 [gr-qc/0511061] [INSPIRE].
M. Levi and J. Steinhoff, Spinning gravitating objects in the effective field theory in the post-Newtonian scheme, JHEP 09 (2015) 219 [arXiv:1501.04956] [INSPIRE].
W.D. Goldberger and I.Z. Rothstein, Dissipative effects in the worldline approach to black hole dynamics, Phys. Rev. D 73 (2006) 104030 [hep-th/0511133] [INSPIRE].
R.A. Porto, Absorption effects due to spin in the worldline approach to black hole dynamics, Phys. Rev. D 77 (2008) 064026 [arXiv:0710.5150] [INSPIRE].
P. Pani, V. Cardoso, L. Gualtieri, E. Berti and A. Ishibashi, Perturbations of slowly rotating black holes: massive vector fields in the Kerr metric, Phys. Rev. D 86 (2012) 104017 [arXiv:1209.0773] [INSPIRE].
T. Papenbrock and H.A. Weidenmueller, Effective Field Theory for Finite Systems with Spontaneously Broken Symmetry, Phys. Rev. C 89 (2014) 014334 [arXiv:1307.1181] [INSPIRE].
I. Low and A.V. Manohar, Spontaneously broken space-time symmetries and Goldstone’s theorem, Phys. Rev. Lett. 88 (2002) 101602 [hep-th/0110285] [INSPIRE].
C.G. Callan Jr., S.R. Coleman, J. Wess and B. Zumino, Structure of phenomenological Lagrangians. 2., Phys. Rev. 177 (1969) 2247 [INSPIRE].
S.R. Coleman, J. Wess and B. Zumino, Structure of phenomenological Lagrangians. 1., Phys. Rev. 177 (1969) 2239 [INSPIRE].
D.V. Volkov, Phenomenological Lagrangians, Fiz. Elem. Chast. Atom. Yadra 4 (1973) 3 [INSPIRE].
V.I. Ogievetsky, Nonlinear realizations of internal and space-time symmetries, in X-th winter school of theoretical physics in Karpacz, Poland (1974).
A.J. Hanson and T. Regge, The Relativistic Spherical Top, Annals Phys. 87 (1974) 498 [INSPIRE].
A.P. Balachandran, G. Marmo, B.S. Skagerstam and A. Stern, Spinning Particles in General Relativity, Phys. Lett. 89B (1980) 199 [INSPIRE].
W.D. Goldberger and I.Z. Rothstein, An Effective field theory of gravity for extended objects, Phys. Rev. D 73 (2006) 104029 [hep-th/0409156] [INSPIRE].
D. Lopez Nacir, R.A. Porto, L. Senatore and M. Zaldarriaga, Dissipative effects in the Effective Field Theory of Inflation, JHEP 01 (2012) 075 [arXiv:1109.4192] [INSPIRE].
S. Endlich and R. Penco, Effective field theory approach to tidal dynamics of spinning astrophysical systems, Phys. Rev. D 93 (2016) 064021 [arXiv:1510.08889] [INSPIRE].
S. Endlich, A. Nicolis, R.A. Porto and J. Wang, Dissipation in the effective field theory for hydrodynamics: First order effects, Phys. Rev. D 88 (2013) 105001 [arXiv:1211.6461] [INSPIRE].
S.M. Rytov, Y.A. Kravtsov and V.I. Tatarskii, Principles of statistical radiophysics 3. Elements of random fields, Springer-Verlag Berlin Heidelberg (1989).
M.F. Maghrebi, R.L. Jaffe and M. Kardar, Spontaneous emission by rotating objects: A scattering approach, Phys. Rev. Lett. 108 (2012) 230403 [arXiv:1202.1485] [INSPIRE].
M.F. Maghrebi, R. Golestanian and M. Kardar, Scattering approach to the dynamical Casimir effect, Phys. Rev. D 87 (2013) 025016 [arXiv:1210.1842] [INSPIRE].
M.F. Maghrebi, R.L. Jaffe and M. Kardar, Nonequilibrium quantum fluctuations of a dispersive medium: Spontaneous emission, photon statistics, entropy generation and stochastic motion, Phys. Rev. A 90 (2014) 012515 [INSPIRE].
D. Arteaga, Quasiparticle excitations in relativistic quantum field theory, Annals Phys. 324 (2009) 920 [arXiv:0801.4324] [INSPIRE].
A. Calogeracos and G.E. Volovik, Rotational quantum friction in superfluids: Radiation from object rotating in superfluid vacuum, JETP Lett. 69 (1999) 281 [cond-mat/9901163] [INSPIRE].
A. Manjavacas and F.J.G. de Abajo. Vacuum friction in rotating particles, Phys. Rev. Lett. 105 (2010) 113601 [arXiv:1009.4107].
A. Manjavacas and F.J.G. de Abajo, Thermal and vacuum friction acting on rotating particles, Phys. Rev. A 82 (2010) 063827 [Erratum ibid. A 87 (2013) 019904].
Y. Takahashi and H. Umezawa, Thermo field dynamics, Int. J. Mod. Phys. B 10 (1996) 1755 [INSPIRE].
M. Le Bellac. Thermal Field Theory, Cambridge University Press (2011).
S. Weinberg. The quantum theory of fields. Vol. 1: Foundations, Cambridge University Press (1995).
D.N. Page, Particle Emission Rates from a Black Hole: Massless Particles from an Uncharged, Nonrotating Hole, Phys. Rev. D 13 (1976) 198 [INSPIRE].
W.G. Unruh, Absorption Cross-Section of Small Black Holes, Phys. Rev. D 14 (1976) 3251 [INSPIRE].
K.S. Thorne, Multipole Expansions of Gravitational Radiation, Rev. Mod. Phys. 52 (1980) 299 [INSPIRE].
J.G. Rosa and S.R. Dolan, Massive vector fields on the Schwarzschild spacetime: quasi-normal modes and bound states, Phys. Rev. D 85 (2012) 044043 [arXiv:1110.4494] [INSPIRE].
J.M. Cornwall, D.N. Levin and G. Tiktopoulos, Derivation of Gauge Invariance from High-Energy Unitarity Bounds on the s Matrix, Phys. Rev. D 10 (1974) 1145 [Erratum ibid. D 11 (1975) 972] [INSPIRE].
C.E. Vayonakis, Born Helicity Amplitudes and Cross-Sections in Nonabelian Gauge Theories, Lett. Nuovo Cim. 17 (1976) 383 [INSPIRE].
M.E. Peskin and D.V. Schroeder, An Introduction to quantum field theory, Addison-Wesley (1995).
K. Hinterbichler, Theoretical Aspects of Massive Gravity, Rev. Mod. Phys. 84 (2012) 671 [arXiv:1105.3735] [INSPIRE].
L.D. Landau, V.B. Berestetskii, E.M. Lifshitz and L.P. Pitaevskii, Course of Theoretical Physics: Relativistic Quantum Theory, volume 4, Pergamon Press (1971).
K. Glampedakis, S.J. Kapadia and D. Kennefick, Superradiance-tidal friction correspondence, Phys. Rev. D 89 (2014) 024007 [arXiv:1312.1912] [INSPIRE].
W.D. Goldberger, Les Houches lectures on effective field theories and gravitational radiation, hep-ph/0701129 [INSPIRE].
R.A. Porto, The effective field theorist’s approach to gravitational dynamics, Phys. Rept. 633 (2016) 1 [arXiv:1601.04914] [INSPIRE].
S.L. Detweiler, Klein-Gordon equation and rotating black holes, Phys. Rev. D 22 (1980) 2323 [INSPIRE].
J.J. Sakurai and J. Napolitano, Modern quantum mechanics, 2nd edition, Pearson (2014).
I.M. Ternov, V.R. Khalilov, G.A. Chizhov and A.B. Gaina, Finite motion of massive particles in the Kerr and Schwarzschild fields, Sov. Phys. J. 21 (1978) 1200 [INSPIRE].
J. Winter, Tensor spherical harmonics, Lett. Math. Phys. 6 (1982) 91.
D.V. Gal’tsov, G.V. Pomerantseva and G.A. Chizhov, Behavior of massive vector particles in a Schwarzschild field, Sov. Phys. J. 27 (1984) 697 [INSPIRE].
J.N. Goldberg, A.J. MacFarlane, E.T. Newman, F. Rohrlich and E.C.G. Sudarshan, Spin s spherical harmonics and edth, J. Math. Phys. 8 (1967) 2155 [INSPIRE].
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Endlich, S., Penco, R. A modern approach to superradiance. J. High Energ. Phys. 2017, 52 (2017). https://doi.org/10.1007/JHEP05(2017)052
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DOI: https://doi.org/10.1007/JHEP05(2017)052