Geodesic
Global Waves with Non-Positive Energy in General Relativity
Serdica Mathematical Journal, Tome 34 (2008) no. 1, pp. 127-154.

Voir la notice de l'article provenant de la source Bulgarian Digital Mathematics Library

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]
Keywords: Global Cauchy Problem, Causality, Superradiance, Time Machine, Black-hole, Scattering 
@article{SMJ2_2008_34_1_a5,
     author = {Bachelot, Alain},
     title = {Global {Waves} with {Non-Positive} {Energy} in {General} {Relativity}},
     journal = {Serdica Mathematical Journal},
     pages = {127--154},
     publisher = {mathdoc},
     volume = {34},
     number = {1},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SMJ2_2008_34_1_a5/}
}
TY  - JOUR
AU  - Bachelot, Alain
TI  - Global Waves with Non-Positive Energy in General Relativity
JO  - Serdica Mathematical Journal
PY  - 2008
SP  - 127
EP  - 154
VL  - 34
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SMJ2_2008_34_1_a5/
LA  - en
ID  - SMJ2_2008_34_1_a5
ER  - 
%0 Journal Article
%A Bachelot, Alain
%T Global Waves with Non-Positive Energy in General Relativity
%J Serdica Mathematical Journal
%D 2008
%P 127-154
%V 34
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SMJ2_2008_34_1_a5/
%G en
%F SMJ2_2008_34_1_a5
Bachelot, Alain. Global Waves with Non-Positive Energy in General Relativity. Serdica Mathematical Journal, Tome 34 (2008) no. 1, pp. 127-154. http://geodesic.mathdoc.fr/item/SMJ2_2008_34_1_a5/