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.
In this chapter we presented only extremal configurations of intersecting branes. The natural further step to take would be to consider also non-extremal configurations of intersecting branes. There is however a subtlety: there could be a difference between intersections of non-extremal branes, and non-extremal intersections of otherwise extremal branes. If we focus on bound states (and thus not on configurations of well separated branes), it appears that a non-extremal configuration would be characterized for instance by @math charges and by its mass. There is only one additional parameter with respect to the extremal configurations. Physically, we could have hardly expected to have, say, as many non-extremality parameters as the number of branes in the bound state. Indeed, non-extremality can be roughly associated to the branes being in an excited state, and it would have thus been very unlikely that the excitations did not mix between the various branes in the bound state. Non-extremal intersecting brane solutions were found first in @cite_48 , and were derived from the equations of motion following a similar approach as here in @cite_81 @cite_16 .
@cite_48 @cite_81 @cite_16
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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. Abstract We present a general rule determining how extremal branes can intersect in a configuration with zero binding energy. The rule is derived in a model independent way and in arbitrary spacetime dimensions D by solving the equations of motion of gravity coupled to a dilaton and several different n -form field strengths. The intersection rules are all compatible with supersymmetry, although derived without using it. We then specialize to the branes occurring in type II string theories and in M-theory. We show that the intersection rules are consistent with the picture that open branes can have boundaries on some other branes. In particular, all the D-branes of dimension q , with 1 ≤ q ≤ 6, can have boundaries on the solitonic 5-brane.