zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Magneto-dilatonic Bianchi-I cosmology: isotropization and singularity problems. (English) Zbl 1062.83090
Summary: We study the evolution of Bianchi-I spacetimes filled with a global unidirectional electromagnetic field $F_{\mu\nu}$ interacting with a massless scalar dilatonic field according to the law $\Psi(\varphi) F^{\mu\nu}F_{\mu\nu}$ where $\Psi(\varphi)>0$ is an arbitrary function. A qualitative study, among other results, shows that (i) the volume factor always evolves monotonically, (ii) there exist models that become isotropic at late times and (iii) the expansion generically starts from a singularity but there can be special models starting from a Killing horizon preceded by a static stage. All three features are confirmed for exact solutions found for the case usually considered, $\Psi=e^{2\lambda \varphi}$, $\lambda=\text{const}$. In particular, isotropizing models are found for $|\lambda|>1\sqrt 3$. In the special case $|\lambda|=1$, which corresponds to models of string origin, the string metric behaviour is studied and shown to be qualitatively similar to that of the Einstein frame metric. In the two appendices, we discuss and compare four different isotropization criteria for arbitrary Bianchi-I spacetimes and present their regularity conditions.

83F05Relativistic cosmology
83C75Space-time singularities, cosmic censorship, etc.
Full Text: DOI