Tunneling from the past horizon

We investigate a tunneling and emission process of a thin-shell from a Schwarzschild black hole, where the shell was initially located beyond the Einstein-Rosen bridge and finally appears at the right side of the Penrose diagram. In order to obtain such a solution, we should assume that the areal radius of the black hole horizon increases after the tunneling. Hence, there is a parameter range such that the tunneling rate is exponentially enhanced, rather than suppressed. We may have two interpretations regarding this. First, such a tunneling process from the past horizon is improbable by physical reasons; second, such a tunneling is possible in principle, but in order to obtain a stable Einstein-Rosen bridge, one needs to restrict the parameter spaces. If such a process is allowed, this can be a non-perturbative contribution to Einstein-Rosen bridges as well as eternal black holes.Comment: 13 pages, 6 figure

Fuzzy Euclidean wormholes in anti-de Sitter space

This paper is devoted to an investigation of Euclidean wormholes made by fuzzy instantons. We investigate the Euclidean path integral in anti-de Sitter space. In Einstein gravity, we introduce a scalar field with a potential. Because of the analyticity, there is a contribution of complex-valued instantons, so-called fuzzy instantons. If we have a massless scalar field, then we obtain Euclidean wormholes, where the probabilities become smaller and smaller as the size of the throat becomes larger and larger. If we introduce a non-trivial potential, then in order to obtain a non-zero tunneling rate, we need to tune the shape of the potential. With the $O(4)$ symmetry, after the analytic continuation to the Lorentzian time, the wormhole throat should expand to infinity. However, by adding mass, one may obtain an instant wormhole that should eventually collapse to the event horizon. The existence of Euclidean wormholes is related to the stability or unitarity issues of anti-de Sitter space. We are not conclusive yet, but we carefully comment on these physical problems.Comment: 20 pages, 9 figure

Fine gradings of complex simple Lie algebras and Finite Root Systems

A $G$-grading on a complex semisimple Lie algebra $L$, where $G$ is a finite abelian group, is called quasi-good if each homogeneous component is 1-dimensional and 0 is not in the support of the grading. Analogous to classical root systems, we define a finite root system $R$ to be some subset of a finite symplectic abelian group satisfying certain axioms. There always corresponds to $R$ a semisimple Lie algebra $L(R)$ together with a quasi-good grading on it. Thus one can construct nice basis of $L(R)$ by means of finite root systems. We classify finite maximal abelian subgroups $T$ in \Aut(L) for complex simple Lie algebras $L$ such that the grading induced by the action of $T$ on $L$ is quasi-good, and show that the set of roots of $T$ in $L$ is always a finite root system. There are five series of such finite maximal abelian subgroups, which occur only if $L$ is a classical simple Lie algebra

Can Sodium Abundances of A-Type Stars Be Reliably Determined from Na I 5890/5896 Lines?

An extensive non-LTE abundance analysis based on Na I 5890/5896 doublet lines was carried out for a large unbiased sample of ~120 A-type main-sequence stars (including 23 Hyades stars) covering a wide v_e sin i range of ~10--300 km/s, with an aim to examine whether the Na abundances in such A dwarfs can be reliably established from these strong Na I D lines. The resulting abundances ([Na/H]_{58}), which were obtained by applying the T_eff-dependent microturbulent velocities of \xi ~2--4 km/s with a peak at T_eff ~ 8000 K (typical for A stars), turned out generally negative with a large diversity (from ~-1 to ~0), while showing a sign of v_e sin i-dependence (decreasing toward higher rotation). However, the reality of this apparently subsolar trend is very questionable, since these [Na/H]_{58} are systematically lower by ~0.3--0.6 dex than more reliable [Na/H]_{61} (derived from weak Na I 6154/6161 lines for sharp-line stars). Considering the large \xi-sensitivity of the abundances derived from these saturated Na I D lines, we regard that [Na/H]_{58} must have been erroneously underestimated, suspecting that the conventional \xi values are improperly too large at least for such strong high-forming Na I 5890/5896 lines, presumably due to the depth-dependence of \xi decreasing with height. The nature of atmospheric turbulent velocity field in mid-to-late A stars would have to be more investigated before we can determine reliable sodium abundances from these strong resonance D lines.Comment: 14 pages, 8 figures, accepted for publication in Publ. Astron. Soc. Japan, Vol. 61, No. 5 (2009