Gravity and black holes in four and five dimensions.

摘要

In this thesis we study several aspects of gravitational physics and black holes. We particularly focus on two areas of current research. The first involves finding a statistical description of black hole entropy within the gravitational picture. In this direction we work with the Mathur fuzzball proposal. The second area of study involves the construction and classification of black hole geometries in higher dimensional space-times.;In the second half of this work we investigate solution generating techniques for five dimensional space-times. We present a general method to add KK-monopole charge to any asymptotically flat, stationary, and axisymmetric solution of five dimensional General Relativity. The technique exploits the Maison formalism and the associated underlying SL(3, R ) invariance of the system. The key step involves identifying a particular element of the symmetry group which has the special property that its action changes asymptotically flat boundary conditions to KK-monopole asymptotics. Furthermore, we also develop a set of technical tools which allow us to apply the SL(3, R ) transformations to solutions produced by the Inverse Scattering method. As an example of our methods, we construct a new exact solution describing a static black ring in a KK-monopole background.;In the first half of this thesis we construct a family of asymptotically flat solutions carrying D1, D5 and momentum charges. These geometries describe the spectral flow of all the ground states of the D1-D5 system. After applying the spectral flow transformation in the near horizon region, the geometries are extended to asymptotically flat infinity by utilizing the general form of minimal supergravity solutions in six dimensions. By construction the solutions are a priori known to correspond to bound states of the three charges and as such can be interpreted as gravitational microstates of the 3-charge black hole. After giving the general form of the solution, we give an explicit example of the construction by considering in detail the geometry corresponding to a particular profile function.