Further evidence for the non-existence of a unified hoop conjecture

The hoop conjecture, introduced by Thorne almost five decades ago, asserts that black holes are characterized by the mass-to-circumference relation $$4\pi {\mathcal {M}}/{\mathcal {C}}\ge 1$$ 4 π M / C ≥ 1 , whereas horizonless compact objects are characterized by the opposite inequality $$4\pi {\mathcal {M}}/{\mathcal {C}}<1$$ 4 π M / C < 1 (here $${\mathcal {C}}$$ C is the circumference of the smallest ring that can engulf the self-gravitating compact object in all azimuthal directions). It has recently been proved that a necessary condition for the validity of this conjecture in horizonless spacetimes of spatially regular charged compact objects is that the mass $${\mathcal {M}}$$ M be interpreted as the mass contained within the engulfing sphere (and not as the asymptotically measured total ADM mass). In the present paper we raise the following physically intriguing question: is it possible to formulate a unified version of the hoop conjecture which is valid for both black holes and horizonless compact objects? In order to address this important question, we analyze the behavior of the mass-to-circumference ratio of Kerr–Newman black holes. We explicitly prove that if the mass $${\mathcal {M}}$$ M in the hoop relation is interpreted as the quasilocal Einstein–Landau–Lifshitz–Papapetrou and Weinberg mass contained within the black-hole horizon, then these charged and spinning black holes are characterized by the sub-critical mass-to-circumference ratio $$4\pi {\mathcal {M}}/{\mathcal {C}}<1$$ 4 π M / C < 1 . Our results provide evidence for the non-existence of a unified version of the hoop conjecture which is valid for both black-hole spacetimes and spatially regular horizonless compact objects.

Адсорбция атомов Ga и Cl и молекулы GaCl на карбиде кремния: модельный подход

Within the scope of the Haldane – Anderson model metallic and ionic contri-butions to the adsorption energy are calculated for the Ga and Cl atoms ad-sorbed on the C- and Si-faces of p- and n-SiC substrates. It is shown firstly that for all considered cases we obtain that ionic contribution is greater than metallic contribution. Secondly, in the case of adsorption on the p-SiC sub-strate value of the model of adsorption energy for Ga is greater than for Cl while in the case of adsorption on the n-SiC opposite inequality is realized. For the description of the GaCl adsorption on SiC substrate simple ionic model is put forward. Comparison with the results of other authors demonstrates valid-ity of the proposed models.

Numerical simulation of near-Alfven MHD flows relaxation with a longitudinal magnetic field

Stationary magnetohydrodynamics flows in nozzle-type channels in the presence of a longitudinal magnetic field are divided into three significantly different classes: super-Alfven flows in which the longitudinal plasma velocity is higher than the Alfven velocity calculated by a longitudinal magnetic field, sub-Alfven flows – with the opposite inequality, and Alfven flows in which the longitudinal plasma velocity coincides with the Alfven velocity over the entire length of the channel and the plasma density has a constant value. In the present work, stationary Alfven and close to Alfven magnetohydrodynamic flows obtained by using a numerical modeling of their relaxation processes in coaxial channels in the presence of a longitudinal magnetic field are considered.

A Final Result on the Oscillation of Solutions of the Linear Discrete Delayed EquationΔx(n)=−p(n)x(n−k)with a Positive Coefficient

A linear(k+1)th-order discrete delayed equationΔx(n)=−p(n)x(n−k)wherep(n)a positive sequence is considered forn→∞. This equation is known to have a positive solution if the sequencep(n)satisfies an inequality. Our aim is to show that, in the case of the opposite inequality forp(n), all solutions of the equation considered are oscillating forn→∞.