Download - ExDiP2010 9-12 Nov 2010 | KEK, Japan
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ExDiP2010 9-12 Nov 2010 | KEK, Japan
Instabilities of (very) compact objects
Vitor Cardoso (CENTRA/IST & Olemiss)
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Superradiant
Gregory-Laflamme
Spontaneous scalarization
Instabilities
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Why study instabilities
Learn if system exists in nature
Signals of bifurcation: to what ?
Practical applications
(gw emission, useful constraints on NS mass, etc)
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(Hill and Eaves, ‘08)
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BHs in GR are characterized by only three quantities:
mass, spin and electric charge
4D BHs have no hair and are stable
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Superradiant instabilitiesZel’dovich ’71; Press and Teukolsky ’72; Damour et al ’76;
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Ergo-region: asymptotic time-translation Kiling vector is space-like
* Penrose process
* Superradiance
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Waves incident upon a Kerr BH are amplified by superradiant scattering if m
Superradiant scattering Insert a mirror around the BH
Make a bomb!
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(Cardoso et al, ‘04)
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(Witek et al, ‘10)
Clearly, need improvements…
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Anti-de Sitter Massive fields
Small Kerr-AdS BHs are unstable
(Cardoso and Dias, ‘04; Kodama ’07;
Uchikata, Yoshida & Futamase, ’09)
Massive fields around Kerr are unstable
(Damour et al ‘76; Detweiler, ’80; Cardoso & Yoshida ’05; Dolan ‘07;
Ishibashi)
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(Cardoso & Yoshida ’05; Dolan ‘07)
Final state: gravitational atoms?(Arvanitaki & Dubovsky, ’10; Ishibashi, this afternoon)
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What about horizonless geometries?
Theorem (Friedman, 1978):
Every stationary, AF, horizonless spacetime with an ergoregion is unstable
Intuition: negative-energy states are amplified, no horizon to absorb them
(Vilenkin, ‘78)
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BH straw-
men:
NO definitive observational proof of the existence of EHs
• Gravastars (Mazur & Mottola ‘01)
• Boson Stars (Kaup ’68; Ruffini & Bonazzola ‘69)
• Wormholes (Morris & Thorne ‘88)
• Superspinars (Gimon & Horava ‘09)
But how strong is the instability?
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Kerr metric
(Teukolsky ’74)
The BH straw-man modelCardoso et al ’07; Barausse et al ’10
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Analytics
Matching condition
Perfect reflectionPerfect absorption
NO incomingwaves
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Results extend to compact gravastars, boson stars, etc
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No definitive observational proof for astrophysical BHs, ie., event horizons.
Straw-men for BHs, such as gravastars, boson stars, wormholes
and superspinars cannot be excluded at priori.
However, these objects develop ergoregions when rapidly rotating,
and become unstable, with timescales of order 1 sec - 1 week.
Thus, the ergoregion instability is a strong argument in favor of BHs:
it eliminates most straw-men
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Super-radiant instabilities in d
Kodama & Ishibashi ‘03
Cardoso & Yoshida ‘05
No stable bound orbits in these geometries passing through the ergosphere!
Cardoso et al, ‘09
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Black rings do have stable bound geodesics!
Igata, Ishihara,Takamori ’10
...are they unstable?
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Long-wavelength instabilities
Rayleigh 1878;Plateau 1873; Dyson 1893, Jeans 1902;
Chandrasekhar & Fermi 1953; Gregory & Laflamme 1993;
Lehner & Pretorius 2010
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Black string:
Perturb the BS (s-wave)
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Instabilities of black objects...and the Rayleigh-Plateau instability
(Plateau 1849, Rayleigh 1878)
Cardoso & O. J. C. Dias, ’06; K-I Maeda & Miyamoto, ‘08
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Instabilities of black objects...Rayleigh-Plateau instability end-state
Wagner et al, ‘09
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...Gregory-Laflamme instability end-state
Lehner & Pretorius, ‘10
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Fluid analogies capture behavior extremely well…
Generic CC violation?
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Ultra-spinning instabilitiesEmparan & Myers, ’03
Lengthscale in to (θ, ϕ) rotation plane
Lengthscale of Sd-4
Metric of black membrane
with fixed
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Ultra-spinning instabilitiesDias et al, ‘09
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Higher dimensions
See Yoshino’s talk for further details on this diagram
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Spontaneous scalarizationDamour & Farese 1992; Lima et al, ’10; Pani et al, in progress
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Awaking the vacuumLima et al, ’10
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Awaking the vacuumLima et al, ’10
What is the end-state? Collapse to BH? Mass shedding to escape forbidden region?
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Pani et al, to appear
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Weak-field gravitational tests highly constrain theory of
gravity
It turns out, they also constrain BH solutions…so high-redshift is
not the answer
However, compact stars could be na interesting testing
ground
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Instabilities of compact objects is a fascinating topic in GR
The event horizon is a stabilizing surface against ergoregion
instabilities
Higher dimensional objects are terribly difficult, but also
terribly exciting to study, with new insights and important
details emerging
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どうも有り難う
Thank you
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