Instabilities of extremal rotating black holes in higher dimensions - INSPIRE

DataBETA

Instabilities of extremal rotating black holes in higher dimensions

Stefan Hollands
(
- Leipzig U.
)
,
Akihiro Ishibashi
(
- Kinki U., Osaka
)

Aug 4, 2014

54 pages

Published in:

Commun.Math.Phys. 339 (2015) 3, 949-1002

Published: Aug 13, 2015

e-Print:

1408.0801 [hep-th]

DOI:

10.1007/s00220-015-2410-0

View in:

reference search20 citations

Citations per year

Abstract: (Springer)

Recently, Durkee and Reall have conjectured a criterion for linear instability of rotating, extremal, asymptotically Minkowskian black holes in

{d\ge 4}

dimensions, such as the Myers–Perry black holes. They considered a certain elliptic operator,

{\mathcal{A}}

, acting on symmetric trace-free tensors intrinsic to the horizon. Based in part on numerical evidence, they suggested that if the lowest eigenvalue of this operator is less than the critical value −1/4 ( called “effective BF-bound”), then the black hole is linearly unstable. In this paper, we prove an extended version of their conjecture. Our proof uses a combination of methods such as (1) the “canonical energy method” of Hollands–Wald, (2) algebraically special properties of the near horizon geometries associated with the black hole, (3) the Corvino–Schoen technique, and (4) semiclassical analysis. Our method of proof is also applicable to rotating, extremal asymptotically Anti-deSitter black holes. In that case, we find additional instabilities for ultra-spinning black holes. Although we explicitly discuss in this paper only extremal black holes, we argue that our results can be generalized to near extremal black holes.

Note:

52pp, LateX, 8 figures, v2: title changed, references added, extended discussion of the near extremal case, numerous minor revisions

black hole: rotation
black hole: Myers-Perry
stability: rotation
stability: linear
horizon: geometry
higher-dimensional

References(68)

Figures(0)

[1]

Lectures on Holographic Superfluidity and Superconductivity

Christopher P. Herzog
(
- Princeton U.
)

- J.Phys.A 42 (2009) 343001
•
e-Print:
- 0904.1975
•
DOI:
- 10.1088/1751-8113/42/34/343001

[2]

Lectures on holographic methods for condensed matter physics

Sean A. Hartnoll
(
- Harvard U.
)

- Class.Quant.Grav. 26 (2009) 224002
•
e-Print:
- 0903.3246
•
DOI:
- 10.1088/0264-9381/26/22/224002

[3]

Black Holes in Higher Dimensions

- Living Rev.Rel. 11 (2008) 6
•
e-Print:
- 0801.3471
•
DOI:
- 10.12942/lrr-2008-6

[4]

Stability of a Schwarzschild singularity

Tullio Regge
(
- Turin U. and
- Princeton U.
)
,
John A. Wheeler
(
- Turin U. and
- Princeton U.
)

- Phys.Rev. 108 (1957) 1063-1069
•
DOI:
- 10.1103/PhysRev.108.1063

[5]

Effective potential for even parity Regge-Wheeler gravitational perturbation equations

Frank J. Zerilli
(
- North Carolina U.
)

- Phys.Rev.Lett. 24 (1970) 737-738
•
DOI:
- 10.1103/PhysRevLett.24.737

[6]

Gauge-invariant perturbations of Reissner-Nordstrom black holes

Vincent Moncrief
(
- Utah U.
)

- Phys.Rev.D 12 (1975) 1526-1537
•
DOI:
- 10.1103/PhysRevD.12.1526

[7]

Stability of higher dimensional Schwarzschild black holes

- Prog.Theor.Phys. 110 (2003) 901-919
•
e-Print:
- hep-th/0305185
•
DOI:
- 10.1143/PTP.110.901

[8]

Perturbations of a rotating black hole. 1. Fundamental equations for gravitational electromagnetic and neutrino field perturbations

Saul A. Teukolsky
(
- Caltech
)

- Astrophys.J. 185 (1973) 635-647
•
DOI:
- 10.1086/152444

[9]

Mode Stability of the Kerr Black Hole

Bernard F. Whiting
(
- North Carolina U.
)

- J.Math.Phys. 30 (1989) 1301
•
DOI:
- 10.1063/1.528308

[10]

Black Holes in Higher Dimensional Space-Times

Robert C. Myers
(
- Princeton U.
)
,
M.J. Perry
(
- Princeton U.
)

- Annals Phys. 172 (1986) 304
•
DOI:
- 10.1016/0003-4916(86)90186-7

[11]

Rotating black holes in higher dimensions with a cosmological constant

G.W. Gibbons
(
- Cambridge U., DAMTP
)
,
H. Lu
(
- Texas A-M
)
,
Don N. Page
(
- Texas A-M and
- Alberta U.
)
,
C.N. Pope
(
- Texas A-M
)

- Phys.Rev.Lett. 93 (2004) 171102
•
e-Print:
- hep-th/0409155
•
DOI:
- 10.1103/PhysRevLett.93.171102

[12]

A Rotating black ring solution in five-dimensions

Roberto Emparan
(
- CERN
)
,
Harvey S. Reall
(
- Queen Mary, U. of London
)

- Phys.Rev.Lett. 88 (2002) 101101
•
e-Print:
- hep-th/0110260
•
DOI:
- 10.1103/PhysRevLett.88.101101

[13]

Black ring with two angular momenta

A.A. Pomeransky
(
- Novosibirsk, IYF
)
,
R.A. Sen'kov
(
- Novosibirsk, IYF
)

e-Print:
- hep-th/0612005

[14]

Classification of the Weyl tensor in higher dimensions

A. Coley
(
- Dalhousie U., Math. Dept.
)
,
R. Milson
(
- Dalhousie U., Math. Dept.
)
,
Vojtech Pravda
(
- Prague, Math. Inst.
)
,
A. Pravdova
(
- Prague, Math. Inst.
)

- Class.Quant.Grav. 21 (2004) L35-L42
•
e-Print:
- gr-qc/0401008
•
DOI:
- 10.1088/0264-9381/21/7/L01

[15]

Generalization of the Geroch-Held-Penrose formalism to higher dimensions

Mark Durkee
(
- Cambridge U., DAMTP
)
,
Vojt Pravda
(
- Prague, Math. Inst.
)
,
Alena Pravdova
(
- Prague, Math. Inst.
)
,
Harvey S. Reall
(
- Cambridge U., DAMTP
)

- Class.Quant.Grav. 27 (2010) 215010
•
e-Print:
- 1002.4826
•
DOI:
- 10.1088/0264-9381/27/21/215010

[16]

Type D Einstein spacetimes in higher dimensions

Vojtech Pravda
(
- Prague, Math. Inst.
)
,
Alena Pravdova
(
- Prague, Math. Inst.
)
,
Marcello Ortaggio
(
- Trento U. and
- INFN, Trento
)

- Class.Quant.Grav. 24 (2007) 4407-4428
•
e-Print:
- 0704.0435
•
DOI:
- 10.1088/0264-9381/24/17/009

[17]

Perturbations of near-horizon geometries and instabilities of Myers-Perry black holes

- Phys.Rev.D 83 (2011) 104044
•
e-Print:
- 1012.4805
•
DOI:
- 10.1103/PhysRevD.83.104044

[18]

Perturbations of higher-dimensional spacetimes

- Class.Quant.Grav. 28 (2011) 035011
•
e-Print:
- 1009.0015
•
DOI:
- 10.1088/0264-9381/28/3/035011

[19]

An instability of higher-dimensional rotating black holes

Oscar J.C. Dias
(
- Cambridge U., DAMTP
)
,
Pau Figueras
(
- Durham U.
)
,
Ricardo Monteiro
(
- Cambridge U., DAMTP
)
,
Harvey S. Reall
(
- Cambridge U., DAMTP
)
,
Jorge E. Santos
(
- Cambridge U., DAMTP
)

- JHEP 05 (2010) 076
•
e-Print:
- 1001.4527
•
DOI:
- 10.1007/JHEP05(2010)076

[20]

Instability and new phases of higher-dimensional rotating black holes

Oscar J.C. Dias
(
- Cambridge U., DAMTP
)
,
Pau Figueras
(
- Durham U. and
- Durham U., Dept. of Math.
)
,
Ricardo Monteiro
(
- Cambridge U., DAMTP
)
,
Jorge E. Santos
(
- Cambridge U., DAMTP
)
,
Roberto Emparan
(
- ICREA, Barcelona and
- Barcelona U., Dept. Fund. Phys.
)

- Phys.Rev.D 80 (2009) 111701
•
e-Print:
- 0907.2248
•
DOI:
- 10.1103/PhysRevD.80.111701

[21]

Near-horizon symmetries of extremal black holes

Hari K. Kunduri
(
- Nottingham U.
)
,
James Lucietti
(
- Durham U., Dept. of Math.
)
,
Harvey S. Reall
(
- Nottingham U.
)

- Class.Quant.Grav. 24 (2007) 4169-4190
•
e-Print:
- 0705.4214
•
DOI:
- 10.1088/0264-9381/24/16/012

[22]

Extremal vacuum black holes in higher dimensions

- Phys.Rev.D 78 (2008) 044042
•
e-Print:
- 0803.2998
•
DOI:
- 10.1103/PhysRevD.78.044042

[23]

A Classification of near-horizon geometries of extremal vacuum black holes

- J.Math.Phys. 50 (2009) 082502
•
e-Print:
- 0806.2051
•
DOI:
- 10.1063/1.3190480

[24]

Classification of near-horizon geometries of extremal black holes

- Living Rev.Rel. 16 (2013) 8
•
e-Print:
- 1306.2517
•
DOI:
- 10.12942/lrr-2013-8

[25]

Decay for solutions of the wave equation on Kerr exterior spacetimes I-II: The cases |a| << M or axisymmetry

e-Print:
- 1010.5132

1-25 of 68
1
2
3
25 / page