ExDiP Nov 2010 | KEK, Japan Instabilities of (very) compact objects Vitor Cardoso (CENTRA/IST & Olemiss) 

Superradiant  Gregory-Laflamme  Spontaneous scalarization Instabilities

Why study instabilities Learn if system exists in nature Signals of bifurcation: to what ? Practical applications (gw emission, useful constraints on NS mass, etc)

(Hill and Eaves, ‘08)

BHs in GR are characterized by only three quantities: mass, spin and electric charge 4D BHs have no hair and are stable

Superradiant instabilities Zel’dovich ’71; Press and Teukolsky ’72; Damour et al ’76;

Ergo-region: asymptotic time-translation Kiling vector is space-like * Penrose process * Superradiance

Waves incident upon a Kerr BH are amplified by superradiant scattering if Superradiant scattering Insert a mirror around the BH Make a bomb!

(Cardoso et al, ‘04)

(Witek et al, ‘10) Clearly, need improvements…

Anti-de SitterMassive 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)

(Cardoso & Yoshida ’05; Dolan ‘07) Final state: gravitational atoms? (Arvanitaki & Dubovsky, ’10; Ishibashi, this afternoon)

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)

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?

Kerr metric (Teukolsky ’74) ‏ The BH straw-man model Cardoso et al ’07; Barausse et al ’10

Analytics Matching condition Perfect reflection Perfect absorption NO incoming waves

Results extend to compact gravastars, boson stars, etc

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

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

Black rings do have stable bound geodesics! Igata, Ishihara,Takamori ’10...are they unstable?

Long-wavelength instabilities Rayleigh 1878;Plateau 1873; Dyson 1893, Jeans 1902; Chandrasekhar & Fermi 1953; Gregory & Laflamme 1993; Lehner & Pretorius 2010

Black string: Perturb the BS (s-wave)

Instabilities of black objects...and the Rayleigh-Plateau instability (Plateau 1849, Rayleigh 1878) Cardoso & O. J. C. Dias, ’06; K-I Maeda & Miyamoto, ‘08

Instabilities of black objects...Rayleigh-Plateau instability end-state Wagner et al, ‘09

...Gregory-Laflamme instability end-state Lehner & Pretorius, ‘10

Fluid analogies capture behavior extremely well… Generic CC violation?

Ultra-spinning instabilities Emparan & Myers, ’03 Lengthscale in to (θ, ϕ ) rotation plane Lengthscale of S d-4 Metric of black membrane with fixed

Ultra-spinning instabilities Dias et al, ‘09

Higher dimensions See Yoshino’s talk for further details on this diagram

Spontaneous scalarization Damour & Farese 1992; Lima et al, ’10; Pani et al, in progress

Awaking the vacuum Lima et al, ’10

What is the end-state? Collapse to BH? Mass shedding to escape forbidden region?

Pani et al, to appear

 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

 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

どうも有り難う Thank you

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