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چكيده انگليسي :

دھ Cosmological solutions with charged black holes Master of Science Thesis in Farsi Departement of Mathematical Sciences Isfahan University of Technology Isfahan 84156 8311 IranSupervisor Dr Sayed Ghahreman Taherian2000 MSC 05C25 20B25 05C60Keywords Black holes Mathematical cosmology Backreaction Abstract In this thesis based on some articles of B Rashida et al we cosider the problem of constructing cosmologicalsolutions of the Einstein Maxwell equations that contain multiple charged black holes By considering the fieldequations as a set of constraint and evolution equations we construct exact initial data for N charged black holes ona hypersphere This corresponds to the maximum of expansion of a cosmological solution and provides sufficientinformation for a unique evolution We then consider the specific example of a universe that contains eight chargedblack holes and show that the existence of non zero electric charge reduces the scale of the cosmological region of thespace These solutions generalize the Majumdar Papapetrou solutions away from the extremal limit of charged blackholes and provide what we believe to be some of the first relativistic calculations of the effects of electric charge oncosmological back reaction The term back reaction is often used in cosmology to mean the effect that stucturehas on the large scale evolution of the universe and observations made within it The idea of black hole lattices as models for the large scale structure of the universe has been under scrutny for sev eral decades Some of the properties of these systems have been elucidated recently in the context of the problem ofcosmological back reaction We investigate here a fully relativistic evolution of these system We explicitly construct the first of these solutions by numerically integrating Einstein s equation in the case of aneight black hole lattice with the topology of S3 Then we have presented an analysis of an inhomogeneous cosmological model that consists of a lattice of regularlyarranged charged black holes at maximum of expansion This generalises existing work in the literature and providesinsight into the effect that electric charge has on cosmological physics We have found that the only solutions thatexist are those that have zero net charge We then applied this analysis to a specific model containing eight blackholes and found a relatively simply way of obtaining an uncharged universe overall by demanding that black holesexist in antipodal pairs and that each black hole has equal and opposite charge to its antipodal partner We then compared this model to an FLRW model with positive spatial curvature containing the same total mass indust We did this by comparing the scale between the two types of universe at maximum of expansion as a functionof the charge to mass ratio of the black holes We found that as the magnitude of the charge on the black holes wasincreased the discrepancy between lattice and FLRW was reduced with the largest discrepancy corresponding to thecase where there is no charge Lastly we investigated the size of the apparent horizon in this initial data as a functionof this charge to mass ratio We found that as the magnitude of the charge of the black holes is increased the size of the apparent horizon decreases and that in the limit where the black hole charges become extremal the apparent horizons recede to zero radius Wehave presented an analysis of an inhomogeneous cosmological model that consists of a lattice of regularly arranged charged black holes at maximum of expansion This generalises existing work in the literature and provides insightinto the effect that electric charge has on cosmological physics We have found that the only solutions that exist arethose that have zero net charge We then applied this analysis to a specific model containing eight black holes andfound a relatively simply way of obtaining an uncharged universe overall by demanding that black holes exist inantipodal pairs and that

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پاسخ هاي كيهان شناختي با سياه چاله هاي باردار

ميدان الكتريكي و ميدان الكترومغناطيسي , خميدگي , مقطع (برش) , تانسور ريچي , سياه چاله هاي باردار , كيهان شناسي