176 research outputs found
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 , 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 . 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
, 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 .Comment: 19 pages, LaTex, the final version to appear in J. Math. Phy
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 mass theorem in extended supergravities
Following the Witten-Nester formalism, we present a useful prescription using
Weyl spinors towards the positivity of mass. As a generalization of
arXiv:1310.1663, we show that some "positivity conditions" must be imposed upon
the gauge connections appearing in the supercovariant derivative acting on
spinors. A complete classification of the connection fulfilling the positivity
conditions is given. It turns out that these positivity conditions are indeed
satisfied for a number of extended supergravity theories. It is shown that the
positivity property holds for the Einstein-complex scalar system, provided that
the target space is Hodge-Kahler and the potential is expressed in terms of the
superpotential. In the Einstein-Maxwell-dilaton theory with a dilaton
potential, the dilaton coupling function and the superpotential are fixed by
the positive mass property. We also explore the gauged supergravity and
demonstrate that the positivity of the mass holds independently of the gaugings
and the deformation parameters.Comment: v2: 22 pages, typos fixed and refs added, a section discussing the
Einstein-Maxwell-dilaton theory added, an appendix classifies the connection
satisfying positivity conditions, accepted for publication in NP
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
- …