The thesis begins with an introduction to M-theory (at a graduate student's level), starting from perturbative string theory and proceeding to dualities, D-branes and finally Matrix theory. The following chapter treats, in a self-contained way, of general classical p-brane solutions. Black and extremal branes are reviewed, along with their semi-classical thermodynamics. We then focus on intersecting extremal branes, the intersection rules being derived both with and without the explicit use of supersymmetry. The last three chapters comprise more advanced aspects of brane physics, such as the dynamics of open branes, the little theories on the world-volume of branes and how the four dimensional Schwarzschild black hole can be mapped to an extremal configuration of branes, thus allowing for a statistical interpretation of its entropy. The original results were already reported in hep-th 9701042, hep-th 9704190, hep-th 9710027 and hep-th 9801053.
It should also not be underestimated that the derivation of the intersecting solutions presented in this chapter is a thorough consistency check of all the dualities acting on, and between, the supergravity theories. It is straightforward to check that, starting from one definite configuration, all its dual configurations are also found between the solutions presented here (with the exception of the solutions involving waves and KK monopoles). In this line of thoughts, we presented a recipe for building five and four dimensional extreme supersymmetric black holes. Some of these black holes were used in the literature to perform a microscopic counting of their entropy, as in @cite_191 @cite_61 for the 5-dimensional ones. Actually, the only (5 dimensional) black holes in the U-duality orbit' that were counted were the ones containing only D-branes and KK momentum. It is still an open problem to directly count the microscopic states of the same black hole but in a different M-theoretic formulation.
@cite_191 @cite_61
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Abstract We present non-extreme generalisations of intersecting p -brane solutions of eleven-dimensional supergravity which upon toroidal compactification reduce to non-extreme static black holes in dimensions D = 4, D = 5 and 6 ⩽ D ⩽ 9, parameterised by four, three and two charges, respectively. The D = 4 black holes are obtained either from a non-extreme configuration of three intersecting five-branes with a boost along the common string or from a non-extreme intersecting system of two two-branes and two five-branes. The D = 5 black holes arise from three intersecting two-branes or from a system of an intersecting two-brane and five-brane with a boost along the common string. The five-brane and two-brane with a boost along one direction reduce to black holes in D = 6 and D = 9, respectively, while a D = 7 black hole can be interpreted in terms of a non-extreme configuration of two intersecting two-branes. We discuss the expressions for the corresponding masses and entropies. We construct new supersymmetric solutions of D = 11 supergravity describing n orthogonally “overlapping” membranes and fivebranes for n = 2,…,8. Overlapping branes arise after separating intersecting branes in a direction transverse to all of the branes. The solutions, which generalize known intersecting brane solutions, preserve at least 2−n of the supersymmetry. Each pairwise overlap involves a membrane overlapping a membrane in a 0-brane, a fivebrane overlapping a fivebrane in a 3-brane or a membrane overlapping a fivebrane in a string. After reducing n overlapping membranes to obtain n overlapping D-2-branes in D = 10, T-duality generates new overlapping D-brane solutions in type IIA and type IIB string theory. Uplifting certain type IIA solutions leads to the D = 11 solutions. Some of the new solutions reduce to dilaton black holes in D = 4. Additionally, we present a D = 10 solution that describes two D-5-branes overlapping in a string. T-duality then generates further D = 10 solutions and uplifting one of the type IIA solutions gives a new D = 11 solution describing two fivebranes overlapping in a string. We construct the most general supersymmetric configuration of @math -branes and @math -branes on a 6-torus. It contains arbitrary numbers of branes at relative @math angles. The corresponding supergravity solutions are constructed and expressed in a remarkably simple form, using the complex geometry of the compact space. The spacetime supersymmetry of the configuration is verified explicitly, by solution of the Killing spinor equations, and the equations of motion are verified too. Our configurations can be interpreted as a 16-parameter family of regular extremal black holes in four dimensions. Their entropy is interpreted microscopically by counting the degeneracy of bound states of @math -branes. Our result agrees in detail with the prediction for the degeneracy of BPS states in terms of the quartic invariant of the E(7,7) duality group. Abstract Strominger and Vafa have used D-brane technology to identify and precisely count the degenerate quantum states responsible for the entropy of certain extremal, BPS-saturated black holes. Here we give a Type-II D-brane description of a class of extremal and non-extremal five-dimensional Reissner-Nordstrom solutions and identify a corresponding set of degenerate D-brane configurations. We use this information to do a string theory calculation of the entropy, radiation rate and “Hawking” temperature. The results agree perfectly with standard Hawking results for the corresponding nearly extremal Reissner-Nordstrom black holes. Although these calculations suffer from open-string strong coupling problems, we give some reasons to believe that they are nonetheless qualitatively reliable. In this optimistic scenario there would be no “information loss” in black hole quantum evolution.