Black hole Lasers powered by Axion SuperradianT instabilities BLASTs João G. Rosa Aveiro University with Tom Kephart (Vanderbilt University) Phys. Rev. Lett. 120, 231102 (2018) (Editors’ Suggestion) [arXiv:1709.06581 [gr-qc]] Café com Física, Universidade de Coimbra, 28 November 2018 Gr@v
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Black hole Lasers powered by Axion SuperradianT ... · (multi-field) inflation, curvaton, phase transitions PBH mass comparable to mass within Hubble horizon: δρ/ρ 0.1 M = c3t
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Black hole Lasers powered by Axion SuperradianT instabilities
BLASTs João G. Rosa
Aveiro University
with Tom Kephart (Vanderbilt University) Phys. Rev. Lett. 120, 231102 (2018) (Editors’ Suggestion)
[arXiv:1709.06581 [gr-qc]]
Café com Física, Universidade de Coimbra, 28 November 2018
Gr@v
Lasers and stimulated emission
Kerr black hole having a BLAST:
superradiant instability
stimulated axion decay
Outline
1. Black hole superradiance 2. Axions 3. Lasing in superradiant axion clouds 4. Primordial black hole lasers 5. Fast Radio Bursts 6. Summary & Future prospects
Black hole superradiance [Zeldovich (1966)]
ω < mΩ
R > 1
Ω
Low frequency waves can be amplified by scattering off a Kerr black hole:
ds2 = −1− 2Mr
Σ
dt2 +
Σ
∆dr2 + Σdθ2
+(r2 + a2)2 − a2 sin2 θ∆
Σsin2 θdφ2 − 4Mra sin2 θ
Σdtdφ
Kerr metric
Event horizon and Cauchy (inner) horizon:
(G = c = = 1)
J = aM ∆ = r2 + a2 − 2Mr Σ = r2 + a2 cos2 θ
r± = M ±
M2 − a2 0 ≤ a ≤ M
Black hole superradiance
Klein-Gordon equation in Kerr space-time:
Separation of variables:
gµν∇µ∇νΦ = 0
stationary and axisymmetric
Φ(t, r, θ,φ) = e−iωteimφS(θ)R(r)
spheroidal harmonics
Superradiance for scalar waves
Schrodinger-like equation
where
d2ψ
dr2∗+
ω2 − V (ω)
ψ = 0
ψ =
r2 + a2R , dr∗ =(r2 + a2)
∆dr
ergoregion
event horizon
Superradiance for scalar waves
I II
ψI = e−i(ω−mΩ)x , ψII = Ae−iωx +Beiωx
General solutions:
Boundary conditions:
Reflection coefficient:
ψI(0) = ψII(0) , ψI(0)− ψ
II(0) = αψI(0)
V (ω) = αδ(x)
+ mΩ(2ω −mΩ)(1−Θ(x))
R =
B
A
2
=α2 +m2Ω2
α2 + (2ω −mΩ)2> 1
Toy model for superradiance
ω < mΩ
I II V (ω) = αδ(x)
+ mΩ(2ω −mΩ)(1−Θ(x))
Toy model for superradiance
In the superradiant regime: • negative phase velocity: • positive group velocity:
Waves carry negative energy into the BH Energy and spin extraction from BH
kI = ω −mΩ < 0
vg = dω/dkI = 1
• Superradiant amplification for different waves:
– Scalar: 0.3%
– Electromagnetic: 4.4%
– Gravitational: 138%
• No superradiance for fermions
[Press & Teukolsky (1974)]
Superradiant amplification
[Press & Teukolsky (1972); Cardoso, Dias & Lemos (2004)]
• surround black hole with mirror
• multiple superradiant scatterings
• exponential amplification of signal
• extract large amount of energy and spin
• radiation pressure eventually destroys mirror
Black hole bombs
Massive fields can become bound to the black hole: “gravitational atoms”
[Arvanitaki et al. (2009)]
gravita6onal poten6al
Massive black hole bombs
I II
∞
ψI = e−i(ω−mΩ)x , ψII = A sin(ωx)
Bound states satisfy:
In the limit :
ω cot(ωL) + α = i(ω −mΩ)
L
ψI = e−i(ω−mΩ)x , ψII = A sin(ωx)
ωL 1 , α ω
ωR nπ
2L
ω = ωR + iΓ
Γ −ωR(ωR −mΩ)
α
Superradiant instability
Toy model for superradiant instabilities
Φ ∝ e−iωRteΓt
• Solve radial equation in both regions • Match asymptotic behaviour in overlap region
• Possible for small mass coupling:
r − r+ r+
Near region
Far region
Matching asymptotics method
r − r+ l/ω
αµ = GMµ/c 1
Gravitational Hydrogen-like spectrum
Note: matching not possible for extremal BH [JGR (2009)]
superradiant instability
[Detweiler (1980); Furuhashi & Nambu (2004)]
Gravitational “atoms”
ωn µc21−
α2µ
2n2
αµ ≡ GµMBH
c
Γ = −Cln(ωR −mΩ)α4l+5µ
r+ − r−r+ + r−
2l+1
(n, l,m)
αµ 1
Superradiant growth rate
n = 2, l = m = 1
[see review by Brito, Cardoso & Pani (2015)]
[Dolan (2007)]
Non-relativistic scalar clouds n = 2, l = m = 1
v2 (αµ/2)c
Γsa
24α9µ
c3
GM
4× 10−4a
µ
10−5 eV
αµ
0.03
8s−1 ,
r+ 0.1 αµ
0.03
µ
10−5 eV
−1 1 +
1− a2
cm
r0 =
µcαµ 66
αµ
0.03
−1 µ
10−5 eV
−1cmBohr radius:
Event horizon:
Superradiant growth rate:
Superradiant condition implies (for l=m=1):
For stellar mass black holes:
Can use superradiance to probe the low-energy BSM particle spectrum
Astrophysical black hole bombs
ω < Ω ⇒ αµ < 1/2
αµ 0.75
M
M⊙
µ
10−10 eV
CP-violation in Quantum Chromodynamics (QCD):
Neutron electric dipole moment:
Introduce dynamical axion field [Peccei & Quinn (1977)]:
L = −1
4FµνF
µν − θ
32π2Fµν F
µν
θ 10−10
Axions
L = −1
4FµνF
µν − 1
32π2
φ
FφFµν F
µν − 1
2∂µφ∂
µφ− V (φ)
Axion is a pseudo-NG boson of the U(1) Peccei-Quinn symmetry that gets potential from QCD instantons:
Axion can be very light: a
Axions
µ 10−5
Fφ
6× 1011 GeV
−1
eV
φ
V (φ)
[Weinberg; Wilczek (1978)]
The electromagnetic triangle anomaly leads to an axion-photon-photon interaction:
This leads to axion decay into photon pairs:
Axions can account for dark matter!
Axion-photon coupling
Lφγγ =αK
8πFφφFµν F
µν
τφ 3× 1032K−2 µ
10−5 eV
−5Gyr
Misalignment production:
- axion field initially displaced from origin - oscillates about origin after QCD transition - stable cold dark matter condensate
Fine-tuned initial conditions and other production mechanisms yield axion DM range: