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

DataBETA

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

Oct, 2010

12 pages

Part of On recent developments in theoretical and experimental general relativity, astrophysics and relativistic field theories. Proceedings, 12th Marcel Grossmann Meeting on General Relativity, Paris, France, July 12-18, 2009. Vol. 1-3, 132-189

Contribution to:

- ICMP09
, 421-432
,
- MG 12
, 132-189

Published: 2010

e-Print:

1010.5137 [gr-qc]

DOI:

View in:

ADS Abstract Service

reference search75 citations

Citations per year

Abstract: (World Scientific)

We present a new general method for proving global decay of energy through a suitable spacetime foliation, as well as pointwise decay, starting from an integrated local energy decay estimate. The method is quite robust, requiring only physical space techniques, and circumvents use of multipliers or commutators with weights growing in t. In particular, the method applies to a wide class of perturbations of Minkowski space as well as to Schwarzschild and Kerr black hole exteriors.

Note:

48 pages, 5 figures, to appear in Proceedings of the 12 Marcel Grossmann Meeting

The wave equation
Black holes
General relativity

References(42)

Figures(0)

Uniqueness of smooth stationary black holes in vacuum: Small perturbations of the Kerr spaces

S. Alexakis
(
- MIT
)
,
A.D. Ionescu
(
- Wisconsin U., Madison
)
,
S. Klainerman
(
- Princeton U.
)

- Commun.Math.Phys. 299 (2010) 89-127
•
e-Print:
- 0904.0982
•
DOI:
- 10.1007/s00220-010-1072-1

- Commun.Math.Phys. 288 199

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

The Wave Equation on Extreme Reissner-Nordstrom Black Hole Spacetimes: Stability and Instability Results

Stefanos Aretakis
(
- Cambridge U.
)

e-Print:
- 1006.0283

Decay of the Maxwell Field on the Schwarzschild Manifold

Pieter Blue
(
- Potsdam, Max Planck Inst.
)

- J.Hyperbol.Diff.Equat. 5 (2008) 04, 807-856
•
DOI:
- 10.1142/S0219891608001714

Semilinear wave equations on the Schwarzschild manifold. 1. Local decay estimates

- Adv.Diff.Eq. 8 (2003) 595-614
•
e-Print:
- gr-qc/0310091

Errata for `Global existence and scattering for the nonlinear Schrodinger equation on Schwarzschild manifolds', `Semilinear wave equations on the Schwarzschild manifold I: Local decay estimates', and `The Wave equation on the Schwarzschild metric. II. Local decay for the spin 2 Regge Wheeler equation'

P. Blue
,
A. Soffer

e-Print:
- gr-qc/0608073

- Commun.Math.Phys. 268 481

Global structure of the Kerr family of gravitational fields

Brandon Carter
(
- Cambridge U., DAMTP
)

- Phys.Rev. 174 (1968) 1559-1571
•
DOI:
- 10.1103/PhysRev.174.1559

Hamilton-Jacobi and Schrodinger separable solutions of Einstein's equations

B. Carter
(
- Cambridge U. (main)
)

- Commun.Math.Phys. 10 (1968) 4, 280-310
•
DOI:
- 10.1007/BF03399503

- Commun.Pure Appl.Math. 43 137

- Commun.Pure Appl.Math. 52 859

The Wave equation on Schwarzschild-de Sitter spacetimes

e-Print:
- 0709.2766

e-Print:
- 0710.0171

A Proof of the uniform boundedness of solutions to the wave equation on slowly rotating Kerr backgrounds

- Invent.Math. 185 (2011) 467-559
•
e-Print:
- 0805.4309
•
DOI:
- 10.1007/s00222-010-0309-0

Lectures on black holes and linear waves

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

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:
- 0910.4957

Decay of solutions of the wave equation in the Kerr geometry

Felix Finster
(
- Regensburg U.
)
,
Niky Kamran
(
- McGill U., Math. Stat.
)
,
Joel Smoller
(
- Michigan U., Math. Dept.
)
,
Shing-Tung Yau
(
- Harvard U., Dept. Math.
)

- Commun.Math.Phys. 264 (2006) 465-503
•
e-Print:
- gr-qc/0504047
•
DOI:
- 10.1007/s00220-006-1525-8

- Commun.Math.Phys. 38 47

Ultimately Schwarzschildean Spacetimes and the Black Hole Stability Problem

Gustav Holzegel
(
- Princeton U., Math. Dept.
)

e-Print:
- 1010.3216

Linear Stability of Schwarzschild Under Perturbations Which Are Nonvanishing on the Bifurcation Two Sphere

Bernard S. Kay
(
- Zurich U.
)
,
Robert M. Wald
(
- Chicago U., EFI
)

- Class.Quant.Grav. 4 (1987) 893-898,
- Class. Quantum Grav. 4 ( 1987) 893-898
•
DOI:
- 10.1088/0264-9381/4/4/022

Gravitational field of a spinning mass as an example of algebraically special metrics

Roy P. Kerr
(
- Texas U.
)

- Phys.Rev.Lett. 11 (1963) 237-238
•
DOI:
- 10.1103/PhysRevLett.11.237

- Helv.Phys.Acta 72 272

- J.Math.Mech. 12 55

Improved decay for solutions to the linear wave equation on a Schwarzschild black hole

Jonathan Luk
(
- Unlisted
)

- Annales Henri Poincare 11 (2010) 805-880
•
e-Print:
- 0906.5588
•
DOI:
- 10.1007/s00023-010-0043-6

1-25 of 42
1
2
25 / page