We construct a five-dimensional, asymptotically Gödel, three-charge black hole via dimensional reduction of an asymptotically plane wave, rotating D1-D5-brane solution of type IIB supergravity. This latter is itself constructed via the solution generating procedure of Garfinkle and Vachaspati, applied to the standard rotating D1-D5-brane solution. Taking all charges to be equal gives a "BMPV Gödel black hole", which is closely related to that recently found by Herdeiro. We emphasise, however, the importance of our ten-dimensional microscopic description in terms of branes. We discuss various properties of the asymptotically Gödel black hole, including the physical bound on the rotation of the hole, the existence of closed timelike curves, and possible holographic protection of chronology.

Recently, it has been proposed that the deformed matrix model describes a twodimensional type 0A extremal black hole. In this paper, the thermodynamics of 0A charged non-extremal black holes is investigated. We observe that the free energy of the deformed matrix model to leading order in 1/q can be seen to agree to that of the extremal black hole. We also speculate on how the deformed matrix model is able to describe the thermodynamics of non-extremal black holes.

We study the relation between c = 1 matrix models at self-dual radii and topological strings on non-compact Calabi-Yau manifolds. Particularly the special case of the deformed matrix model is investigated in detail. Using recent results on the equivalence of the partition function of topological strings and that of four dimensional BPS black holes, we are able to calculate the entropy of the black holes, using matrix models. In particular, we show how to deal with the divergences that arise as a result of the non-compactness of the Calabi-Yau. The main result is that the entropy of the black hole at zero temperature coincides with the canonical free energy of the matrix model, up to a proportionality constant given by the self-dual temperature of the matrix model.

We explore the possibility of obtaining inflation in weakly coupled heterotic string theory, where the model dependent axions are responsible for driving inflation. This model can be considered as a certain extrapolation of m 2 φ 2 -inflation, and is an attempt to explicitly realize the so called N-flation proposal in string theory. The instanton generated potential for the axions essentially has two parameters; a natural mass scale M and the string coupling g s . For isotropic compactifications leading to of order O(10 4 ) axions in the four dimensional spectrum we find that with (M, g s ) ≃ (M GU T , 0.5) the observed temperature fluctuations in the CMB are correctly reproduced. We assume an initially random distribution for the vevs of the axions. The spectral index, n s , is generically more red than for m 2 φ 2 -inflation. The greater the vevs, the more red the spectral index becomes. Allowing for a wide range of vevs 55 e-foldings from the end of inflation, we find 0.946 n s 0.962. The tensor-to-scalar ratio, r, is more sensitive to the vevs, but typically smaller than in m 2 φ 2 -inflation. Furthermore, in the regime where the leading order theory is valid, r is bounded by r < 0.10. The spectral index and the tensor-to-scalar ratio are correlated. For example, n s ≃ 0.951 corresponds to r ≃ 0.036.

We discuss thermalization in de Sitter space and argue, from two different points of view, that the typical time needed for thermalization is of order R 3 /l 2 pl , where R is the radius of the de Sitter space in question. This time scale gives plenty of room for non-thermal deviations to survive during long periods of inflation. We also speculate in more general terms on the meaning of the time scale for finite quantum systems inside isolated boxes, and comment on the relation to the Poincaré recurrence time.