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Thesis (Ph. D.)--Florida State University, 2006. / Advisor: Howard Baer, Florida State University, College of Arts and Sciences, Dept. of Physics. Title and description from dissertation home page (viewed Sept. 22, 2006). Document formatted into pages; contains xiii, 132 pages. Includes bibliographical references.

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This thesis examines exact solutions to gauged and ungauged supergravity theories in space-time dimensions D⩾5 as well as various instabilities of such solutions. I begin by using two solution generating techniques for five dimensional minimal ungauged supergravity, the first of which exploits the existence of a Killing spinor to generate supersymmetric solutions, which are time-like fibrations over four dimensional hyper-Kähler base spaces. I use this technique to construct a supersymmetric solution with the Atiyah-Hitchin metric as the base space. This solution has three independent parameters and possesses mass, angular momentum, electric charge and magnetic charge. Via an analysis of a congruence of null geodesics, I determine that the solution contains a region with naked closed time-like curves. The centre of the space-time is a conically singular pseudo-horizon that repels geodesics, otherwise known as a repulson. The region exterior to the closed time-like curves is outwardly geodesically complete and possesses an asymptotic region free of pathologies provided the angular momentum is chosen appropriately. The second solution generating technique exploits a hidden G2 symmetry in five dimensional minimal supergravity. I use this hidden symmetry approach to construct the most general black string solution in five dimensions, which is endowed with mass, angular momentum, linear momentum, electric charge and magnetic charge. This general black string satisfies the first law of thermodynamics, with the Bekenstein-Hawking entropy being reproduced via a microstate counting in terms of free M-branes in the decoupling limit. Furthermore it reduces to all previously known black string solutions in its various limits. A phase diagram for extremal black strings is produced to draw conclusions about extremal black rings, in particular why supersymmetric black rings exhibit a lower bound on the electric charge. The same phase diagram further suggests the existence of a new class of supersymmetric black rings, which are completely disconnected from the previously known class. A particular limit of this general black string is the magnetically charged black string, whose thermodynamic phase behaviour and perturbative stability were previously studied but not very well understood. I construct magnetically charged topological solitons, which I then show play an important role in the phase structure of these black strings. Topological solitons in Einstein-Maxwell gravity, however, were previously believed to generically correspond to unstable "bubbles of nothing" which expand to destroy the space-time. I show that the addition of a topological magnetic charge changes the stability properties of these Kaluza-Klein bubbles and that there exist perturbatively stable, static, magnetically charged bubbles which are the local vacuum and the end-point of Hawking evaporation of magnetic black strings. In gauged supergravity theories, bubbles of nothing are stabilised by the positive energy theorem for asymptotically anti-de Sitter space-times. For orbifold anti-de Sitter space-times in odd dimensions, a local vacuum state of the theory is just such a bubble, known as the Eguchi-Hanson soliton. I study the phase behaviour of orbifold Schwarzschild-anti-de Sitter black holes, thermal orbifold anti-de Sitter space-times, and thermal Eguchi-Hanson solitons from a gravitational perspective; general agreement is found between this analysis and the previous analysis from the gauge theory perspective via the AdS/CFT correspondence. I show that the usual Hawking-Page phase structure is recovered and that the main effect of the soliton in the phase space is to widen the range of large black holes that are unstable to decay despite the positivity of their specific heat. Furthermore, using topological arguments I show that the soliton and orbifold AdS geometry correspond to a confinement phase in the boundary gauge theory while the black hole corresponds to a deconfinement phase. An important instability for rotating asymptotically anti-de Sitter black holes is the superradiant instability. Motivated by arguments that the physical end point of this instability should describe a clump of scalar field co-rotating with the black hole, I construct asymptotically anti-de Sitter black hole solutions with scalar hair. Perturbative results, i.e. low amplitude boson stars and small radius black holes with low amplitude scalar hair, are presented in odd dimensions relevant to gauged supergravity theories, namely D=5,7. These solutions are neither stationary nor axisymmetric, allowing them to evade the rigidity theorem; instead the space-time plus matter fields are invariant under only a single helical Killing vector. These hairy black holes are argued to be stable within their class of scalar field perturbations but are ultimately unstable to higher order perturbative modes.

We determine the conditions under which half-maximal matter coupled gauged supergravity in seven dimensions admits a chiral circle reduction to yield a matter coupled gauged supergravity in six dimensions with 8 real supersymmetry. Solving these conditions we nd that the SO(2; 2) and SO(3; 1) gauged 7D supergravities give a U(1)R, and the SO(2; 1) gauged 7D supergravity gives an Sp(1)R gauged chiral 6D supergravity coupled to certain matter multiplets. In the 6D models obtained, with or without gauging, we show that the scalar fields of the matter sector parametrize the coset SO(p + 1; 4)=SO(p + 1) SO(4), with the (p + 3) axions corresponding to its abelian isometries. We then derive the necessary and sufficient conditions for the existence of a Killing spinor in N = (1; 0) gauge 6D supergravity coupled to a single tensor multiplet, vector multiplets and hypermultiplets. We show that these conditions imply most of the eld equations. We also determine the remaining equations that need to be satised by an exact solution. In this framework, we nd a novel 1=8 supersymmetric dyonic string solution with nonvanishing hypermultiplet scalars. The activated scalars parametrize a 4 dimensional submanifold of a quaternionic hyperbolic ball. The key point is that we employ an identity map between this submanifold and the internal space transverse to the string worldsheet, thereby nding a higher dimensional generalization of Gell- Mann-Zweibach tear-drop solution.

In this dissertation, we systematically construct non-extremal charged rotating anti-de Sitter black hole solutions in four, five and seven dimensions. In four dimensions, we first obtain the rotating Kerr-Taub-NUT metric with four independent charges, as solutions of N = 2 supergravity coupled to three abelian vector multiplets by the solution generating technique. Then we generalise the four-dimensional rotating solutions to the solutions of gauged N = 4 supergravity with charges set pairwise equal. In five dimensions, the most general charged rotating black hole solution has three charge and two rotation parameters. We obtain several special cases of the general solution. To be specific, we obtain the first example of a non-extremal rotating black hole solution with two independent rotation parameters, which has two charge parameters set equal and the third vanishing. In another example, we obtain the nonextremal charged rotating black hole solution with three charge parameters set equal and non-equal rotation parameters. We are also able to construct the single-charge solution with two independent rotation parameters. In seven dimensions, we obtain the solution for non-extremal charged rotating black holes in gauged supergravity, in the case where the three rotation parameters are set equal. There are two independent charges, corresponding to gauge fields in the U(1) × U(1) abelian subgroup of the SO(5) gauge group.

We determine the conditions under which half-maximal matter coupled gauged supergravity in seven dimensions admits a chiral circle reduction to yield a matter coupled gauged supergravity in six dimensions with 8 real supersymmetry. Solving these conditions we nd that the SO(2; 2) and SO(3; 1) gauged 7D supergravities give a U(1)R, and the SO(2; 1) gauged 7D supergravity gives an Sp(1)R gauged chiral 6D supergravity coupled to certain matter multiplets. In the 6D models obtained, with or without gauging, we show that the scalar fields of the matter sector parametrize the coset SO(p + 1; 4) / SO(p + 1) X SO(4), with the (p + 3) axions corresponding to its abelian isometries. We then derive the necessary and sufficient conditions for the existence of a Killing spinor in N = (1; 0) gauge 6D supergravity coupled to a single tensor multiplet, vector multiplets and hypermultiplets. We show that these conditions imply most of the eld equations. We also determine the remaining equations that need to be satised by an exact solution. In this framework, we nd a novel 1=8 supersymmetric dyonic string solution with nonvanishing hypermultiplet scalars. The activated scalars parametrize a 4 dimensional submanifold of a quaternionic hyperbolic ball. The key point is that we employ an identity map between this submanifold and the internal space transverse to the string worldsheet, thereby nding a higher dimensional generalization of Gell- Mann-Zweibach tear-drop solution.

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Firstly, scalar quark mass matrices are calculated for a non-minimal SU₅ N=l supergravity theory with realistic fermion masses. The squark mixing matrices, analogues of the Kobayashi-Maskawa matrices for quarks, are also calculated and have significant off-diagonal entries. Thus, there are non-zero flavour-changing gaugino interactions between 'up' quarks and 'up' squarks in the non-minimal model. This is in contrast to the case for minimal SU₅ . It is shown that in the non-minimal model flavour-changing gluino interactions contribute to the proton decay modes p → μ⁺K⁰, ῡ_μK⁺ at about the same rate as the mode p → ῡ_μK⁺ mediated by Wino exchange. Contributions to the K_L-K_S mass difference from flavour-changing gluino and wino interactions are small. Secondly, for a finite N=2 globally supersymmetric theory it is shown that the set of finiteness-preserving soft operators previously derived by Parkes and West is incomplete. The complete set of 1-loop finite operators is derived by a graphical analysis, and it is shown that most of these preserve finiteness to all orders. The low-energy N=2 model of Del Aguila et al. is reviewed, and it is shown that new constraints on the τ-neutrino mass require an unnaturally high scale of supersymmebry breaking in the model.