Aspects Of 5D Supersymmetric Black Rings, Attractor And Dimensional Reduction

This thesis is mainly divided into two parts. The first part provides the investigation of the attractor mechanism of the black hole in the supergravity and the study of attrac-tor mechanism of supersymmetric black rings in five-dimensional supergravity, and it is the first time that one-order attractor flow equations of black rings is obtain. The second part is devoted to discuss non-liner sigma model and the supersymmetric solutions in the background of the dimensional reduction from five dimensions to three dimensions, and do some work on the study of the supersymmetric black rings in the target spaces by use of the coset space G2(2)/SO(4).Firstly, the history and recent progress of the attractor mechanism of black holes is reviewed. Next, we simply introduce the attractor mechanism in N=2, D=4 supergravity and multi-center attractor flow equations in the background of superstring. Meanwhile, in high dimensions, a black ring,which is different from topologically spherical black holes in four or lower dimensions, is introduced.Then, we introduce to how to use the real special geometry (very special geometry) to study the multi-center black ring solution in 5D N=2 supergravity, and show how to extend the black hole attractor to 5D black ring attractor, and obtain the first-order attractor flow equations for the general solutions of motion equations for N= 2 supergravity in five dimensional Gibbons-Hawking space. Meanwhile, we also get the constraint equaitons which determine the gauge fields. We analyze the first-order flow equations of black ring and find that the integrate of one of equations agrees precisely with the electronic central charge Ze. Moreover, taking the divergence of the other one, we can reproduce the second-order flow equation(which have been obtained by Kraus and Larsen). Also, the case of BMPV black hole, the limit of black ring, is discussed.In the last part of this thesis, first, we introduce the concept of Lie algebra of G2(2), then show how to reduce five dimensions minimal supergravity to four dimensions, fur- ther, to three dimensions. By use of the relation between the non-liner sigma model and the supersymmetric solutions, we study the supersymmetric black rings in the background of the coset space G2(2)/SO(4). With the R x U(1)×U(1) isometry of the stationary so-lutions, we reduce 5D supersymmetric black ring solutions to two dimensions and obtain a non-linear sigma model. Analyzing the algebra structure of G2(2)/SO(4), we obtain con-served flux and supersymmetry constraints of supersymmetric black rings. In the context of black rings, the conserved flux is dependent of angular coordinate. In order to obtain the charges independent of coordinates, we integrate these charge over S1. Analyzing the inte-gral results, we find the certain conserved charges corresponding with the electric charge Q and angular momentum Jψof supersymmetric black ring respectively. A special example, BMPV black hole, as the limit of the supersymmetric black ring solution, is studied, and the semi-classical wave function of black hole is discussed.