Small Thermal Fluctuation on a Large Domain

Weak first-order phase transitions proceed with percolation of new phase. The kinematics of this process is clarified from the point of view of subcritical bubbles. We examine the effect of small subcritical bubbles around a large domain of asymmetric phase by introducing an effective geometry. The percolation process can be understood as a perpetual growth of the large domain aided by the small subcritical bubbles.Comment: 6 pages, latex, to be published in Progress of Theoretical Physic

Positive energy theorem implies constraints on static steller models

Using the positive energy theorem, we derive some constraints on static steller models in asymptotically flat spacetimes in a general setting without imposing spherical symmetry. We show that there exist no regular solutions under certain conditions on the equation of state. As the contraposition, we obtain some constraints on the pressure and adiabatic index.Comment: 7 pages, final version accepted for publication in Prog. Theore. Phy

Timelike Infinity and Asymptotic Symmetry

By extending Ashtekar and Romano's definition of spacelike infinity to the timelike direction, a new definition of asymptotic flatness at timelike infinity for an isolated system with a source is proposed. The treatment provides unit spacelike 3-hyperboloid timelike infinity and avoids the introduction of the troublesome differentiability conditions which were necessary in the previous works on asymptotically flat spacetimes at timelike infinity. Asymptotic flatness is characterized by the fall-off rate of the energy-momentum tensor at timelike infinity, which makes it easier to understand physically what spacetimes are investigated. The notion of the order of the asymptotic flatness is naturally introduced from the rate. The definition gives a systematized picture of hierarchy in the asymptotic structure, which was not clear in the previous works. It is found that if the energy-momentum tensor falls off at a rate faster than $\sim t^{-2}$, the spacetime is asymptotically flat and asymptotically stationary in the sense that the Lie derivative of the metric with respect to \ppp_t falls off at the rate $\sim t^{-2}$. It also admits an asymptotic symmetry group similar to the Poincar\'e group. If the energy-momentum tensor falls off at a rate faster than $\sim t^{-3}$, the four-momentum of a spacetime may be defined. On the other hand, angular momentum is defined only for spacetimes in which the energy-momentum tensor falls off at a rate faster than $\sim t^{-4}$.Comment: 19 pages, LaTex, the final version to appear in J. Math. Phy