CFT Duals for Extreme Black Holes

It is argued that the general four-dimensional extremal Kerr-Newman-AdS-dS black hole is holographically dual to a (chiral half of a) two-dimensional CFT, generalizing an argument given recently for the special case of extremal Kerr. Specifically, the asymptotic symmetries of the near-horizon region of the general extremal black hole are shown to be generated by a Virasoro algebra. Semiclassical formulae are derived for the central charge and temperature of the dual CFT as functions of the cosmological constant, Newton's constant and the black hole charges and spin. We then show, assuming the Cardy formula, that the microscopic entropy of the dual CFT precisely reproduces the macroscopic Bekenstein-Hawking area law. This CFT description becomes singular in the extreme Reissner-Nordstrom limit where the black hole has no spin. At this point a second dual CFT description is proposed in which the global part of the U(1) gauge symmetry is promoted to a Virasoro algebra. This second description is also found to reproduce the area law. Various further generalizations including higher dimensions are discussed.Comment: 18 pages; v2 minor change

Volumes of polytopes in spaces of constant curvature

We overview the volume calculations for polyhedra in Euclidean, spherical and hyperbolic spaces. We prove the Sforza formula for the volume of an arbitrary tetrahedron in $H^3$ and $S^3$. We also present some results, which provide a solution for Seidel problem on the volume of non-Euclidean tetrahedron. Finally, we consider a convex hyperbolic quadrilateral inscribed in a circle, horocycle or one branch of equidistant curve. This is a natural hyperbolic analog of the cyclic quadrilateral in the Euclidean plane. We find a few versions of the Brahmagupta formula for the area of such quadrilateral. We also present a formula for the area of a hyperbolic trapezoid.Comment: 22 pages, 9 figures, 58 reference

THEORY AND PRACTICE IN THE DEVELOPMENT OF TWO-DISC DISTRIBUTING DEVICES FOR SEED PREPARATION

One way of preserving grain from harvest to emergence is to prepare the seed for sowing. It is known as seed dressing. Single-disc chamber seed dressers are the most widely used, but at maximum flow rates the quality of the treatment is significantly reduced. Therefore, the purpose of the study was to develop a treatment chamber distributor to improve the quality of seed dressing in cereal crops. To solve this problem, it was necessary to develop a double-disc distributing device which is capable to improve the quality of treatment, to carry out a theoretical justification of its application, as well as to give a preliminary evaluation of the device use under laboratory conditions. For this reason, a double-disc distributing device has been developed. It is capable of redistributing the seed flow between the lower solid disc and the upper annular disc when changing the flow rate. Classical mechanics and mathematics were the basis of theoretical research. As a result, we have determined the forces exerting on the seed, the differential equations of motion of a constrained material particle and the motion of the seed on rotating discs in analytical form of a two-disc distributing device consisting of upper annular and lower solid discs with polymer spreaders, and the critical speed of the drive shaft 13,5 s-1, which determines the moment of the seed sliding on discs. The actual angular velocity (56.5 s-1) was found to be 4.2 times greater than the critical velocity of 13.5 s-1, which is sufficient to produce a uniform flow of seeds with discs directed towards the deflectors. The evaluation of the application of the developed device under laboratory conditions provides a maximum seed supply of 5.84 kg/s, a non-uniformity of 3.1 %, and a seed crushing of 0.04% by the dresser. This has a positive effect on the seed dressing quality

Exact Exploration and Hanging Algorithms ⋆

Abstract. Recent analysis of sequential algorithms resulted in their axiomatization and in a representation theorem stating that, for any sequential algorithm, there is an abstract state machine (ASM) with the same states, initial states and state transitions. That analysis, however, abstracted from details of intra-step computation, and the ASM, produced in the proof of the representation theorem, may and often does explore parts of the state unexplored by the algorithm. We refine the analysis, the axiomatization and the representation theorem. Emulating a step of the given algorithm, the ASM, produced in the proof of the new representation theorem, explores exactly the part of the state explored by the algorithm. That frugality pays off when state exploration is costly. The algorithm may be a high-level specification, and a simple function call on the abstraction level of the algorithm may hide expensive interaction with the environment. Furthermore, the original analysis presumed that state functions are total. Now we allow state functions, including equality, to be partial so that a function call may cause the algorithm as well as the ASM to hang. Since the emulating ASM does not make any superfluous function calls, it hangs only if the algorithm does. [T]he monotony of equality can only lead us to boredom. —Francis Picabia