Kei-Ichi Maeda

We examine the effect of local matter on the chaotic behavior of a relativistic test particle in non-vacuum static axisymmetric spacetimes. We find that the sign of the sectional curvature in the geodesic deviation equation defined by the Riemann curvature does not always become a good tool to judge the occurrence of chaos in the non-vacuum case. However, we show that the locally unstable region ( LU region ) defined by the Weyl curvature can provide information about chaos even in non-vacuum spacetime as well as in vacuum spacetime. Since the Weyl tensor affects only the shear part of the geodesic congruence, it works effectively to stretch some directions of geodesic congruence, which helps to cause the chaotic behavior of geodesics. Actually, the orbit moving around an unstable periodic orbit (UPO) becomes strongly chaotic if it passes through an LU region, which means that the LU region can be used as a good tool to know in which situation the chaos by homoclinic mixing occurs around a UPO.

First-order cosmological phase transitions are considered in the models with an $O(3)$-symmetric scalar field, in the high temperature limit. It is shown that a global monopole can be produced at the center of a bubble when the bubble is nucleated.

We discuss black holes in an effective theory derived from a superstring model, which includes a dilaton field, a gauge field and the Gauss-Bonnet term. Assuming U(1) or SU(2) symmetry for the gauge field, we find four types of spherically symmetric solutions, i.e., a neutral, an electrically charged, a magnetically charged and a ``colored'' black hole, and discuss their thermodynamical properties and fate via the Hawking evaporation process. For neutral and electrically charged black holes, we find critical point and a singular end point. Below the mass corresponding to the critical point, nosolution exists, while the curvature on the horizon diverges and anaked singularity appears at the singular point. A cusp structure in the mass-entropy diagram is found at the critical point and black holes on the branch between the critical and singular points become unstable. For magnetically charged and ``colored" black holes, the solution becomes singular just at the end point with a finite mass. Because the black hole temperature is always finite even at the critical point or the singular point, we may conclude that the evaporation process will not be stopped even at the critical point or the singular point, and the black hole will move to a dynamical evaporation phase or a naked singularity will appear.

The nucleation and evolution of bubbles are investigated in the model of an $O(3)$-symmetric scalar field coupled to gravity in the high temperature limit. It is shown that, in addition to the well-known bubble of which the inside region is true vacuum, there exists another decay channel at high temperature which is described by a new solution such that a false vacuum region like a global monopole remains at the center of a bubble. The value of the Euclidean action of this bubble is higher than that of the ordinary bubble; however, the production rate of it can be considerable for a certain range of scalar potentials.

We study the motion of test particle in static axisymmetric vacuum spacetimes and discuss two criteria for strong chaos to occur: (1) a local instability measured by the Weyl curvature, and (2) a tangle of a homoclinic orbit, which is closely related to an unstable periodic orbit in general relativity. We analyze several static axisymmetric spacetimes and find that the first criterion is a sufficient condition for chaos, at least qualitatively. Although some test particles which do not satisfy the first criterion show chaotic behavior in some spacetimes, these can be accounted for the second criterion.

In this paper we examine the classical evolution of a cosmological model derived from the low-energy tree-level limit of a generic string theory. The action contains the metric, dilaton, central charge and an antisymmetric tensor field. We show that with a homogeneous and isotropic metric, allowing spatial curvature, there is a formal equivalence between this system and a scalar field minimally coupled to Einstein gravity in a spatially flat metric. We refer to this system as the shifted frame and using it we describe the full range of cosmological evolution that this model can exhibit. We show that generic solutions begin (or end) with a singularity. As the system approaches a singularity the dilaton becomes becomes large and loop corrections will become important.