گرانش و ساختارهاي علي در رويه هاي ﴿1+2﴾- بعدي

چكيده انگليسي :

Gravity and Causal Stracturs in 2 1 dementional Manifolds Delaram Mirfendereski d mirfendereski@ph iut ac ir 2012 03 11 Department of Physics Isfahan University of Technology Isfahan 84156 83111 IranDegree M Sc Language PersianSupervisor Dr F Loran loran@cc iut ac irAbstractThe de Sitter space is defined as a solution to Einstein equations with positive cosmological constant In this thesis we study 2 1 dimensional de Sitter manifolds whit signature embedded in a flatspace time with signature As the first step to realize symmetry group of the manifold one parameter subgroups of SO 3 1 symmetry group has been classified These subgroups divide intotwo distinct types permissible and impermissible The permissible types result in the metric tensorof embedding space in such a way that its determinate is compatible with the signature ofmetric On the other hand in impermissible type the determinate of metric tensor is positive whichis obviously incompatible with the signature of embedding space By realizing all permissible typesof the one parameter subgroups for SO 3 1 one can determine the isometries of the manifold Thegenerator of infinitesimal displacement along such directions is called a Killing vector One can com pactify the space along one of these isometries The norm of the Killing vector and other propertiesof embedding space determine whether it is possible to have a black hole solution or not The normof both of Killing vectors in de Sitter space show that it is impossible to find a black hole solutionby this way Whereas in anti de Sitter space which is defined by negative cosmological constant this process results in black hole solution One can show that this different behavior is an inheritanceof different embedding spaces The de Sitter manifold can be defined by different coordinates sys tems leads to metrics with different properties Beside the familiar metrics we introduce another onewhich is completely covered by global metric in 2 1 dimensions It means that the domain ofvalidity of this metric is a subset of the global one We called the common region which is coveredby both metrics as intersection region which is restricted by null geodesies It is not straightfor ward however to identify a coordinate transformation between these two metrics in this region Inaddition these two metrics show completely different properties As an example the global metric istime dependent because the spherical part of this metric expands monotonically in time But the othermetric is periodic in time and its volume vanishes periodically in spatial distances Also observers corresponding to these metrics make different judgments about longevity of the intersection region A local observer using the second metric can see the whole intersection region which exists forever But from the point of view of the global observer the intersection region disappears gradually bythe rate which depends on the position of the observer The causal structures and all these differencescan be shown in a Penrose diagrams It is specially an important example in de Sitter space becausebrings up the following question in the absence of coordinate transformation between two distinctmetrics how could the observers achieve a common perception about their surrounding events Asa practical example how the observer in one metric could determine his her wave function by usinga given wave function for another metric KeywordsAnti De Sitter space De Sitter Space and Different Metrics One parameter Subgroups of SO 2 2 SO 3 1 and SO 4 Isometries Identification BTZ Black Hole Intersection Region Thermodynam ics of Black Holes Black Hole and Cosmological Event Horizon

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گرانش و ساختارهاي علي در رويه هاي ﴿1+2﴾- بعدي

فضاي پاددوسيته , راستاهاي هم متري , فرآيند يكسان سازي , سياه چاله ي BT Z , نواحي هم پوشاني , افق هاي رويداد , سياه چاله و كيها نشناختي