On the linear stability of the extreme Kerr black hole under axially symmetric perturbations

Dain, Sergio; de Austria, Ivan Gentile

doi:10.1088/0264-9381/31/19/195009

On the linear stability of the extreme Kerr black hole under axially symmetric perturbations

Feb 12, 2014

30 pages

Published in:

Class.Quant.Grav. 31 (2014) 19, 195009

Published: Sep 18, 2014

e-Print:

1402.2848 [gr-qc]

DOI:

10.1088/0264-9381/31/19/195009

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Abstract: (IOP)

We prove that for axially symmetric linear gravitational perturbations of the extreme Kerr black hole, there exists a positive definite and conserved energy. This provides a basic criteria for linear stability in axial symmetry. In the particular case of Minkowski, using this energy we also prove the pointwise boundedness of the perturbation in a remarkably simple way.

Note:

35 pages. 2 figures. Relevant improvement in the presentation in section 2.2

04.20.Ex
04.20.Dw
04.70.Bw
stability
extreme Kerr black hole

References(47)

Figures(2)

[1]

Hidden symmetries and decay for the wave equation on the Kerr spacetime

Lars Andersson
(
- Edinburgh U., Sch. Math. and
- Edinburgh U.
)
,
Pieter Blue
(
- Edinburgh U., Sch. Math. and
- Edinburgh U.
)

e-Print:
- 0908.2265

[2]

Rotating, stationary, axially symmetric spacetimes with collisionless matter

- Commun.Math.Phys. 329 (2014) 787-808
•
e-Print:
- 1212.5028
•
DOI:
- 10.1007/s00220-014-1904-5

[3]

Stability and Instability of Extreme Reissner-Nordström Black Hole Spacetimes for Linear Scalar Perturbations I

Stefanos Aretakis
(
- Cambridge U.
)

- Commun.Math.Phys. 307 (2011) 17-63
•
e-Print:
- 1110.2007
•
DOI:
- 10.1007/s00220-011-1254-5

[4]

Stability and Instability of Extreme Reissner-Nordström Black Hole Spacetimes for Linear Scalar Perturbations II

Stefanos Aretakis
(
- Cambridge U.
)

- Annales Henri Poincare 12 (2011) 1491-1538
•
e-Print:
- 1110.2009
•
DOI:
- 10.1007/s00023-011-0110-7

[5]

Decay of Axisymmetric Solutions of the Wave Equation on Extreme Kerr Backgrounds

Stefanos Aretakis
(
- Cambridge U.
)

- J.Funct.Anal. 263 (2012) 2770-2831,
- J. Functional Analysis 263 (2012) 2770-2831
•
e-Print:
- 1110.2006
•
DOI:
- 10.1016/j.jfa.2012.08.015

[6]

Horizon Instability of Extremal Black Holes

Stefanos Aretakis
(
)

- Adv.Theor.Math.Phys. 19 (2015) 507-530
•
e-Print:
- 1206.6598
•
DOI:
- 10.4310/ATMP.2015.v19.n3.a1

[7]

Nonlinear instability of scalar fields on extremal black holes

Stefanos Aretakis
(
- Princeton U., Math. Dept. and
- Princeton, Inst. Advanced Study
)

- Phys.Rev.D 87 (2013) 084052
•
e-Print:
- 1304.4616
•
DOI:
- 10.1103/PhysRevD.87.084052

[8]

Phase space for the Einstein equations

Robert Bartnik
(
- Canberra U.
)

e-Print:
- gr-qc/0402070

[9]

A remark about wave equations on the extreme Reissner-Nordström black hole exterior

- Class.Quant.Grav. 30 (2013) 065001
•
e-Print:
- 1212.0729
•
DOI:
- 10.1088/0264-9381/30/6/065001

[10]

Axisymmetric Black Hole Has Only Two Degrees of Freedom

B. Carter
(
- Cambridge U., Inst. of Astron.
)

- Phys.Rev.Lett. 26 (1971) 331-333
•
DOI:
- 10.1103/PhysRevLett.26.331

[11]

An Axisymmetric gravitational collapse code

Matthew W. Choptuik
(
- British Columbia U.
)
,
Eric W. Hirschmann
(
- Brigham Young U.
)
,
Steven L. Liebling
(
- Long Island U., Southampton
)
,
Frans Pretorius
(
- Caltech
)

- Class.Quant.Grav. 20 (2003) 1857-1878
•
e-Print:
- gr-qc/0301006
•
DOI:
- 10.1088/0264-9381/20/9/318

[12]

Asymptotic properties of linear field equations in Minkowski space

D. Christodoulou
,
S. Klainerman

- Commun.Pure Appl.Math. 43 (1990) 137-199

[13]

The Global Nonlinear Stability of the Minkowski Space, volume 41 of Princeton Mathematical series. Princeton University Press, Princeton, NJ

D. Christodoulou
,
S. Klainerman

[14]

Lectures on black holes and linear waves

- Clay Math.Proc. 17 (2013) 97-205
•
e-Print:
- 0811.0354

[15]

A new Physical-space Approach to Decay for the Wave Equation With Applications to Black Hole Spacetimes

- ,
- ,
- XVIth International Congress on Mathematical Physics, P. Exner (ed.), World Scientific, London, 2009, pp. 421-433
•
e-Print:
- 1010.5137
•
DOI:
- 10.1142/9789814304634_0032