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تسجيل مستخدم جديدBianchi cosmologies with $p$-form gauge fields
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In this paper the dynamics of free gauge fields in Bianchi type I-VII$_{h}$ space-times is investigated. The general equations for a matter sector consisting of a $p$-form field strength ($p,in,{1,3}$), a cosmological constant ($4$-form) and perfect fluid in Bianchi type I-VII$_{h}$ space-times are computed using the orthonormal frame method. The number of independent components of a $p$-form in all Bianchi types I-IX are derived and, by means of the dynamical systems approach, the behaviour of such fields in Bianchi type I and V are studied. Both a local and a global analysis are performed and strong global results regarding the general behaviour are obtained. New self-similar cosmological solutions appear both in Bianchi type I and Bianchi type V, in particular, a one-parameter family of self-similar solutions,Wonderland ($lambda$) appears generally in type V and in type I for $lambda=0$. Depending on the value of the equation of state parameter other new stable solutions are also found (The Rope and The Edge) containing a purely spatial field strength that rotates relative to the co-moving inertial tetrad. Using monotone functions, global results are given and the conditions under which exact solutions are (global) attractors are found.
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