ExDiP2010 9-12 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 instabilitiesZel’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 m

Superradiant scattering Insert a mirror around the BH

Make a bomb!

(Cardoso et al, ‘04)

(Witek et al, ‘10)

Clearly, need improvements…

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)

(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 modelCardoso et al ’07; Barausse et al ’10

Analytics

Matching condition

Perfect reflectionPerfect absorption

NO incomingwaves

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 instabilitiesEmparan & Myers, ’03

Lengthscale in to (θ, ϕ) rotation plane

Lengthscale of Sd-4

Metric of black membrane

with fixed

Ultra-spinning instabilitiesDias et al, ‘09

Higher dimensions

See Yoshino’s talk for further details on this diagram

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

Awaking the vacuumLima et al, ’10

Awaking the vacuumLima 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

Extensions