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Application of linear hyperbolic PDE to linear quantum fields in curved spacetimes : especially black holes, time machines and a new semi-local vacuum concept

Bernard Kay (2000)

Journées équations aux dérivées partielles

Several situations of physical importance may be modelled by linear quantum fields propagating in fixed spacetime-dependent classical background fields. For example, the quantum Dirac field in a strong and/or time-dependent external electromagnetic field accounts for the creation of electron-positron pairs out of the vacuum. Also, the theory of linear quantum fields propagating on a given background curved spacetime is the appropriate framework for the derivation of black-hole evaporation (Hawking...

f ( R ) theories.

De Felice, Antonio, Tsujikawa, Shinji (2010)

Living Reviews in Relativity [electronic only]

Foliations of lightlike hypersurfaces and their physical interpretation

Krishan Duggal (2012)

Open Mathematics

This paper deals with a family of lightlike (null) hypersurfaces (H u) of a Lorentzian manifold M such that each null normal vector ℓ of H u is not entirely in H u, but, is defined in some open subset of M around H u. Although the family (H u) is not unique, we show, subject to some reasonable condition(s), that the involved induced objects are independent of the choice of (H u) once evaluated at u = constant. We use (n+1)-splitting Lorentzian manifold to obtain a normalization of ℓ and a well-defined...

Global Waves with Non-Positive Energy in General Relativity

Bachelot, Alain (2008)

Serdica Mathematical Journal

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...

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