Superradiance effects in General Relativity Introduction to - PowerPoint PPT Presentation

Superradiance effects in General Relativity Introduction to Gravitational Waves Emmanuele Picciau A.A. 2017/2018

Summary • What is superradiance? • Superradiance in a flat spacetime • Superradiance in astrophysics • Superradiant instabilities • Emission of GWs • GWs vs Kerr BHs • Conclusions

What is superradiance? Superradiance is the radiation enhancement effect based on the dissipation of a physical system. Superradiance examples:  Sonic «boom»  Cherenkov emission  Coherent emitters  Rotational superradiance

What is superradiance? Sonic «boom» Superradiance amplification of sound waves

What is superradiance? Cherenkov radia iation Superradiance amplification of electromagnetic waves

What is superradiance? Coherent emit itters If there are N emitters the intensity of the radiation is: ∝ 𝑂 for incoherent regime ∝ 𝑂 2 for coherent regime

What is superradiance? Rotational superradiance In 1971 Zel’dovich showed that when radiation scatter off rotating absorbing surface it could increase its amplitude if ω : frequency of the radiation Ω : orbital velocity of the body m: azimutal number Y. B. Zel'dovich Pis'ma Zh. Eksp. Teor. Fiz. 14 (1971) 270 [JETP Lett. 14, 180 (1971)]

Superradiance in flat spacetime One of the first examples of superradiance is known as the Kle lein in paradox A particle beam propagating in a region with a potential barrier V can emerge without exponential damping Klein, O. Z. Physik (1929) 53: 157. https://doi.org/10.1007/BF01339716

Superradiance in flat spacetime The paradox is today resolved by the creation of pair ir particle-antiparticle le Klein-Gordon and Dirac equations are not 1-particle equations, but relativistic field equations

Superradiance in flat spacetime Bosonic scattering Fermionic scatterin ing Where:

Superradiance in flat spacetime For bosons the solution of the problem is so, under the condition is possible to have superradiant amplification of the reflected current

Superradiance in astrophysics Let’s consider a scalar field 𝜚 around a spinning body In a coordinate system in which the medium is at rest: 𝛽 : absorption parameter

Superradiance in astrophysics Superradia iance from stars V. Cardoso, R. Brito, and J. L. Rosa, Superradiance in stars; arXiv:1505.05509

Superradiance instabilities In astrophysics superradiance amplification of radiation comes by the extraction of energy from massive objects This effect could be the cause of instabilities of systems  CFS instability  Black Hole bombs  Effect of massive bosonic field

Superradiance instabilities CFS in instabil ility The instability occurs when a mode that is retrograde in the frame corotating with the star appears as prograde to a inertial frame. S. Chandrasekhar, “Solutions of two problems in the theory of gravitational radiation ,” Phys.Rev.Lett. 24 (1970) 611-615

Superradiance instabilities Bla lack Hole le bombs If we have a scalar perturbing a rotating axis-symmetric black hole Let’s imagine to enclose the black hole in a reflecting mirror W. H. Press and S. A. Teukolsky, Nature 238, 211 (1972)

Superradiance instabilities In Instabilit ity from bosonic massiv ive fie ield ld «Nature provide its own mirrors»

Superradiance instabilities In Instabilit ity from bosonic massiv ive fie ield ld If the imaginary part becomes positive can be defined an instability time scale In this case the field could growth as P. Pani et al. Perturbations of slowly rotating black holes: massive vector fields in the Kerr metric, Phys.Rev. D86 (2012) 104017, arXiv:1209.0773

Superradiance instabilities In Instabilit ity from bosonic massiv ive fie ield ld Superradiant instability for the fundamental mode (l=m=1) as a function of the coupling M μ s and for several spinning BHs

Emission of GWs Evolution of f in instabilities In the instabilities time scale τ a cloud of bosons could grow near the BH Backreaction on the geometry caused by bosons is neglected

Emission of GWs Emission of f en energy and angular momentum Using Teukolsky formalism R. Brito, V. Cardoso, and P. Pani, “Black holes as particle detectors: evolution of superradiant instabilities," arXiv:1411.0686

Emission of GWs Bosenova and emission of f GWs Hirotaka Yoshino and Hideo Kodama 2015 Class. Quantum Grav. 32 214001

GWs VS Kerr BHs Scattering and absorption of f gr gravitational pla lane waves by rotating BHs BHs S. R. Dolan, “Scattering and Absorption of Gravitational Plane Waves by Rotating Black Holes," Class.Quant.Grav. 25 (2008) 235002, arXiv:0801.3805

Conclusions We have seen how superradiance effects could modify the dynamics of classical and quantum physical systems.  The amplification of waves extracts energy from dissipative systems.  Instabilities due to the superradiance have a lot of consequences about physics beyond the Standard Model  Superradiant effects for GWs could probe Kerr BHs and their parameters

Thanks for the attention