The Closed Orbit Controllability Criterium

We prove that every closed "general" trajectory of the control system $\Sigma_M$ has an open neighborhood on which $\Sigma_M$ is controllable if 1) this orbit contains some point where the Lie algebra rank condition ($LARC$) is satisfied, and 2) the set of control vectors is "involved" at $q$. In particular, for the control systems $\Sigma_M$ on the compact connected manifold $M^n$ with an open control set this gives the following "Closed Orbit Controllability Criterium": The dynamical system $\Sigma_M$ of the considered type is controllable on $M^n$ if and only if for an arbitrary point $q$ of $M^n$ there exists a closed trajectory of the control system going through this point. We also present examples which show that our conditions are necessary.Comment: 16 pag

Remarks on non-singular black holes

We briefly discuss non-singular black hole models, with the main focus on the properties of non-singular evaporating black holes. Such black holes possess an apparent horizon, however the event horizon may be absent. In such a case, the information from the black hole interior may reach the external observer after the complete evaporation of the black hole. This model might be used for the resolution of the information loss puzzle. However, as we demonstrate, in a general case the quantum radiation emitted from the black hole interior, calculated in the given black hole background, is very large. This outburst of the radiation is exponentially large for models with the redshift function $\alpha=1$. We show that it can be suppressed by including a non-trivial redshift function. However, even this suppression is not enough to guarantee self-consistency of the model. This problem is a manifestation of a general problem, known as the "mass inflation". We briefly comment on possible ways to overcome this problem in the models of non-singular evaporating black holes.Comment: 10 pages, Extended version of the plenary talk given at a Joint Meeting: 13th International Conference on Gravitation, Astrophysics, and Cosmology 15th Italian-Korean Symposium on Relativistic Astrophysics, Seoul, July 03--07, 201

Binarity of the Nearby 30 Myr Old Solar Analog HIP 16853 in the Tucana-Horologium Stream

A robust unconstrained orbital solution is obtained for the G2 V star HIP 16853 = HD 22705 at 42 pc, which is a probable member of the 28-30 Myr old Tucana-Horologium stream of post-T Tauri stars. The solution yields an apparent semimajor axis of 5.1 ± 0.7 mas, a period of 201 ± 2 days, and an inclination of 80° ± 7°. Assuming a mass of 1 M_⊙ for the primary, the close companion is only 0.4 M_⊙, which implies a spectral type M0.5 at this age. The expected maximum separation (a) between the companions is 18 mas, which makes this system amenable for high-resolution observations. The wide companion HIP 16853 B at 14" is investigated as a possible tertiary component but rejected on account of the near-infrared photometric data inconsistent with the well-defined H-R diagram of the Tucana-Horologium group