A general dilaton gravity theory in 1+1 spacetime dimensions with a cosmological constant λ and a new dimensionless parameter ω, contains as special cases the constant curvature theory of Teitelboim and Jackiw, the theory equivalent to vacuum planar General Relativity, the first order string theory, and a two-dimensional purely geometrical theory. The equations of this general two-dimensional theory admit several different black holes with various types of singularities. The singularities can be spacelike, timelike or null, and there are even cases without singularities. Evaluation of the ADM mass, as a charge density integral, is possible in some situations, by carefully subtrating the black hole solution from the corresponding linear dilaton at infinity.

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Three dimensional black holes in a generalized dilaton gravity action theory are analysed. The theory is specified by two fields, the dilaton φ and the graviton g µν , and two parameters, the cosmological constant λ and the Brans-Dicke parameter ω. It contains seven different cases, of which one distinguishes as special cases, string theory, general relativity and a theory equivalent to four dimensional general relativity with one Killing vector. We study the causal structure and geodesic motion of null and timelike particles in the black hole geometries and find the ADM masses of the different solutions.

Recent work has shown that differential rotation, producing large scale drifts of fluid elements along stellar latitudes, is an unavoidable feature of r -modes in the nonlinear theory. We investigate the role of this differential rotation in the evolution of the l = 2 r -mode instability of a newly born, hot, rapidly rotating neutron star. It is shown that the amplitude of the r -mode saturates a few hundred seconds after the mode instability sets in. The saturation amplitude depends on the amount of differential rotation at the time the instability becomes active and can take values much smaller than unity. It is also shown that, independently of the saturation amplitude of the mode, the star spins down to rotation rates that are comparable to the inferred initial rotation rates of the fastest pulsars associated with supernova remnants. Finally, it is shown that, when the drift of fluid elements at the time the instability sets in is significant, most of the initial angular momentum of the star is transferred to the r -mode and, consequently, almost none is carried away by gravitational radiation.

We study the reheating process which takes place after the two periods of inflation that arise from a string-inspired cosmological model. Baryogenesis mechanisms and a possible solution for the magnetic monopole problem that are compatible with string-motivated inflationary scenarios are discussed.