Mathematical general relativity: a sampler - INSPIRE

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Mathematical general relativity: a sampler

Apr, 2010

87 pages

e-Print:

1004.1016 [gr-qc]

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Abstract: (arXiv)

We provide an introduction to selected recent advances in the mathematical understanding of Einstein's theory of gravitation.

Note:

Some updates. A shortened version, to appear in the Bulletin of the AMS, is available online at http://www.ams.org/journals/bull/0000-000-00/S0273-0979-2010-01304-5

general relativity
vector: Killing
causality
boundary condition
cosmic censorship
black hole
space-time: Schwarzschild
space-time: Taub-NUT
gravitation: surface
space-time: Bianchi

References(321)

Figures(8)

Hawking's local rigidity theorem without analyticity

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

e-Print:
- 0902.1173

Near-constant mean curvature solutions of the Einstein constraint equations with non-negative Yamabe metrics

James Isenberg
(
- Oregon U., Dept. Math.
)
,
Adam Clausen
(
- Lawrence U.
)
,
Paul T. Allen
(
- Potsdam, Max Planck Inst.
)

- Class.Quant.Grav. 25 (2008) 075009
•
e-Print:
- 0710.0725
•
DOI:
- 10.1088/0264-9381/25/7/075009

The Global existence problem in general relativity

Lars Andersson
(
- Royal Inst. Tech., Stockholm
)

e-Print:
- gr-qc/9911032

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

Local existence of dynamical and trapping horizons

Lars Andersson
(
- Potsdam, Max Planck Inst. and
- Miami U., Dept. Math. CS
)
,
Marc Mars
(
- Salamanca U.
)
,
Walter Simon
(
- Salamanca U.
)

- Phys.Rev.Lett. 95 (2005) 111102
•
e-Print:
- gr-qc/0506013
•
DOI:
- 10.1103/PhysRevLett.95.111102

Curvature estimates for stable marginally trapped surfaces

Lars Andersson
(
- Potsdam, Max Planck Inst. and
- Miami U.
)
,
Jan Metzger
(
- Potsdam, Max Planck Inst.
)

- J.Diff.Geom. 84 (2010) 2, 231-265
•
e-Print:
- gr-qc/0512106

The Area of horizons and the trapped region

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•
e-Print:
- 0708.4252
•
DOI:
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Elliptic hyperbolic systems and the Einstein equations

Lars Andersson
(
- Miami U., Dept. Math. CS
)
,
Vincent Moncrief
(
- Yale U.
)

- Annales Henri Poincare 4 (2003) 1-34
•
e-Print:
- gr-qc/0110111
•
DOI:
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Future complete vacuum space-times

Lars Andersson
(
- Miami U., Dept. Math. CS
)
,
Vincent Moncrief
(
- Yale U.
)

e-Print:
- gr-qc/0303045

Quiescent cosmological singularities

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•
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•
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Some uniqueness results for dynamical horizons

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•
e-Print:
- gr-qc/0503109
•
DOI:
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Isolated and dynamical horizons and their applications

Abhay Ashtekar
(
- Penn State U. and
- Santa Barbara, KITP and
- Potsdam, Max Planck Inst. and
- Schrodinger Inst., Vienna
)
,
Badri Krishnan
(
- Potsdam, Max Planck Inst. and
- Schrodinger Inst., Vienna
)

- Living Rev.Rel. 7 (2004) 10
•
e-Print:
- gr-qc/0407042
•
DOI:
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Background independent quantum gravity: A Status report

Abhay Ashtekar
(
)
,
Jerzy Lewandowski
(
- Warsaw U. and
- Penn State U. and
- Potsdam, Max Planck Inst. and
- Schrodinger Inst., Vienna
)

- Class.Quant.Grav. 21 (2004) R53
•
e-Print:
- gr-qc/0404018
•
DOI:
- 10.1088/0264-9381/21/15/R01

Analogue gravity

Carlos Barcelo
(
- IAA, Granada
)
,
Stefano Liberati
(
- INFN, Trieste and
- SISSA, Trieste
)
,
Matt Visser
(
- Victoria U., Wellington
)

- Living Rev.Rel. 8 (2005) 12,
- Living Rev.Rel. 14 (2011) 3
•
e-Print:
- gr-qc/0505065
•
DOI:
- 10.12942/lrr-2005-12

Analog gravity from field theory normal modes?

Carlos Barcelo
(
- Washington U., St. Louis
)
,
Stefano Liberati
(
- Maryland U.
)
,
Matt Visser
(
- Washington U., St. Louis
)

- Class.Quant.Grav. 18 (2001) 3595-3610
•
e-Print:
- gr-qc/0104001
•
DOI:
- 10.1088/0264-9381/18/17/313

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Phase space for the Einstein equations

Robert Bartnik
(
- Canberra U.
)

e-Print:
- gr-qc/0402070

On Maximal hypersurfaces in asymptotically flat space-times

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•
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On the numerical integration of Einstein's field equations

- Phys.Rev.D 59 (1998) 024007
•
e-Print:
- gr-qc/9810065
•
DOI:
- 10.1103/PhysRevD.59.024007

Killing initial data

Robert Beig
(
- Vienna U.
)
,
Piotr T. Chrusciel
(
- Tours U.
)

- Class.Quant.Grav. 14 (1997) A83-A92
•
e-Print:
- gr-qc/9604040
•
DOI:
- 10.1088/0264-9381/14/1A/007

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