# Global Waves with Non-Positive Energy in General Relativity

Serdica Mathematical Journal (2008)

- Volume: 34, Issue: 1, page 127-154
- ISSN: 1310-6600

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topBachelot, Alain. "Global Waves with Non-Positive Energy in General Relativity." Serdica Mathematical Journal 34.1 (2008): 127-154. <http://eudml.org/doc/281370>.

@article{Bachelot2008,

abstract = {2000 Mathematics Subject Classification: 35Lxx, 35Pxx, 81Uxx, 83Cxx.The theory of the waves equations has a long history since M.
Riesz and J. Hadamard. It is impossible to cite all the important results in
the area, but we mention the authors related with our work: J. Leray [34]
and Y. Choquet-Bruhat [9] (Cauchy problem), P. Lax and R. Phillips [33]
(scattering theory for a compactly supported perturbation), L. H¨ ormander
[27] and J-M. Bony [7] (microlocal analysis). In all these domains, V. Petkov
has made fundamental contributions, mainly in microlocal analysis, scattering theory, dynamical zeta functions (see in particular the monography [42]).
In this paper we present a survey of some recent results on the global
existence and the asymptotic behaviour of waves, when the conserved energy
is not definite positive. This unusual situation arises in important cosmological models of the General Relativity where the gravitational curvature
is very strong. We consider the case of the closed time-like curves (violation
of the causality) [1], and the charged black-holes (superradiance) [3]},

author = {Bachelot, Alain},

journal = {Serdica Mathematical Journal},

keywords = {Global Cauchy Problem; Causality; Superradiance; Time Machine; Black-hole; Scattering; Global Cauchy problem; causality; superradiance; time machine; black hole scattering},

language = {eng},

number = {1},

pages = {127-154},

publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},

title = {Global Waves with Non-Positive Energy in General Relativity},

url = {http://eudml.org/doc/281370},

volume = {34},

year = {2008},

}

TY - JOUR

AU - Bachelot, Alain

TI - Global Waves with Non-Positive Energy in General Relativity

JO - Serdica Mathematical Journal

PY - 2008

PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences

VL - 34

IS - 1

SP - 127

EP - 154

AB - 2000 Mathematics Subject Classification: 35Lxx, 35Pxx, 81Uxx, 83Cxx.The theory of the waves equations has a long history since M.
Riesz and J. Hadamard. It is impossible to cite all the important results in
the area, but we mention the authors related with our work: J. Leray [34]
and Y. Choquet-Bruhat [9] (Cauchy problem), P. Lax and R. Phillips [33]
(scattering theory for a compactly supported perturbation), L. H¨ ormander
[27] and J-M. Bony [7] (microlocal analysis). In all these domains, V. Petkov
has made fundamental contributions, mainly in microlocal analysis, scattering theory, dynamical zeta functions (see in particular the monography [42]).
In this paper we present a survey of some recent results on the global
existence and the asymptotic behaviour of waves, when the conserved energy
is not definite positive. This unusual situation arises in important cosmological models of the General Relativity where the gravitational curvature
is very strong. We consider the case of the closed time-like curves (violation
of the causality) [1], and the charged black-holes (superradiance) [3]

LA - eng

KW - Global Cauchy Problem; Causality; Superradiance; Time Machine; Black-hole; Scattering; Global Cauchy problem; causality; superradiance; time machine; black hole scattering

UR - http://eudml.org/doc/281370

ER -

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