Symmetries and conformal bridge in Schwarschild-(A)dS black hole mechanics

We show that the Schwarzschild-(A)dS black hole mechanics possesses a hidden symmetry under the three-dimensional Poincaré group. This symmetry shows up after having gauge-fixed the diffeomorphism invariance in the symmetry-reduced homogeneous Einstein-Λ model and stands as a physical symmetry of the system. It dictates the geometry both in the black hole interior and exterior regions, as well as beyond the cosmological horizon in the Schwarzschild-dS case. It follows that one can associate a set of non-trivial conserved charges to the Schwarzschild-(A)dS black hole which act in each causally disconnected regions. In T-region, they act on fields living on spacelike hypersurface of constant time, while in R-regions, they act on time-like hypersurface of constant radius. We find that while the expression of the charges depend explicitly on the location of the hypersurface, the charge algebra remains the same at any radius in R-regions (or time in T-regions). Finally, the analysis of the Casimirs of the charge algebra reveals a new solution-generating map. The $$ \mathfrak{sl}\left(2,\mathrm{\mathbb{R}}\right) $$ sl 2 ℝ Casimir is shown to generate a one-parameter family of deformation of the black hole geometry labelled by the cosmological constant. This gives rise to a new conformal bridge allowing one to continuously deform the Schwarzschild-AdS geometry to the Schwarzschild and the Schwarzschild-dS solutions.

Shape Dynamics of the TT¯ Deformation

I will show how the flow triggered by deforming two-dimensional conformal field theories on a torus by the TT¯ operator is identical to the evolution generated by the (radial) quantum Shape Hamiltonian in 2 + 1 dimensions. I will discuss how the gauge invariances of the Shape Dynamics, i.e., volume-preserving conformal invariance and diffeomorphism invariance along slices of constant radius are realized as Ward identities of the deformed quantum field theory. I will also comment about the relationship between the reduction to shape space on the gravity side and the solvability of the irrelevant operator deformation of the conformal field theory

Perturbations of the Gravitational Energy in the TEGR: Quasinormal Modes of the Schwarzschild Black Hole

We calculate the gravitational energy spectrum of the perturbations of a Schwarzschild black hole described by quasinormal modes, in the framework of the teleparallel equivalent of general relativity (TEGR). We obtain a general formula for the gravitational energy enclosed by a large surface of constant radius r, in the region m<<r<<∞, where m is the mass of the black hole. Considering the usual asymptotic expression for the perturbed metric components, we arrive at finite values for the energy spectrum. The perturbed energy depends on the two integers n and l that describe the quasinormal modes. In this sense, the energy perturbations are discretized. We also obtain a simple expression for the decrease of the flux of gravitational radiation of the perturbations.

Modeling fluid outflow from a channel consisting of three different segments

The topic of the article is modeling fluid outflow from a channel consisting of three different segments. The subject of research is the outflow of fluid from a channel consisting of three different sections. The article discusses the parameters of the fluid flow in the channel segments of the converging flow section, the section of a constant radius and expanding flow section. Research methods are based on Newton's rheological law; the continuity equation and the Navier-Stokes equation, which are the basic equations of fluid flow; and on the method of mathematical modeling and analytical method of solution. Expressions of hydrodynamic parameters for each segment, with a successively located converging section, a section of a constant radius, and expanding flow sections, are determined in the article by analytical method. Analytical expressions are obtained for the pressure and average flow rate of the fluid in the channel where there are converging rectilinear inlet flow area, cylindrical average area, and expanding rectilinear outlet flow area. The solutions obtained make it possible to determine the flow parameters in the zone of the vibration baffle of pipeline transport of such a geometry that damps vibrations caused by the flow; in the transition sections of the channels of hydraulic drives and in other channels of the fluid flow, which are set to improve the hydrodynamic parameters of the flow.

Surfaces of congruent sections on cylinders

Introduction. The definition of surfaces of congruent sections was first formulated in the work written by I.I. Kotov. These and several other types of surfaces, generated by the motion of a curve, belonged to the class of kinematic surfaces. Such kinematic surfaces as those of plane parallel displacement, surfaces of rotation, Monge surfaces, cyclic surfaces with ge-nerating circles having constant radius, rotative and spiroidal surfaces, helical some helix-shaped surfaces can be included into the class of surfaces that have congruent sections. Materials and methods. Using I.I. Kotov’s methodology, the authors first derived parametrical and vector equations for eight surfaces of congruent pendulum type cross sections of circular, elliptic, and parabolic cylinders and several helix-shaped surfaces. Circles, ellipses, and parabolas, located in the plane of the generating curve of a guiding cylinder or in the planes of a bundle that passes through the longitudinal axis of a cylinder, generate plane curves. Ellipses, analyzed in the article, can be easily converted into circles and this procedure can increase the number of shapes analyzed here. Results. Formulas are provided in the generalized form, so the shape of a plane generating curve can be arbitrary. Some surfaces of congruent sections are determined by two varieties of parametric equations. In one case, the central angle of the guiding cylindrical surface was used as an independent parameter, but in the other case, one of rectangular coordinates of the cylinder’s guiding curve served as an independent parameter. Two types of surfaces are analyzed: 1) when local axes of generating curves remain parallel in motion; 2) when these axes rotate. Conclusions. The analysis of the sources and the results, recommendations and proposals for application of surfaces, having congruent sections, is made with a view to their use in architecture and technology. The list of references has 27 positions, and it shows that the surfaces considered in this paper are being analyzed by architects, engineers, and geometricians both in Russia and abroad.

Based on DLVO Theory: A Theoretical Model of Boundary Condition for Heavy Oil in Low-Temperature Transportation

The low-temperature transportation, a process of gathering and transportation at ultrahigh water content, can incline the energy consumption and elevate the efficiency of the surface gathering system. Here we found that there is the risk of wall sticking of heavy oil in the low-temperature transportation.In this work, a theoretical model of boundary condition for heavy oil in low-temperature transportation based on DLVO theory was proposed to predict the wall sticking occurrence temperature. The outcomes of modeling results had a good agreement in comparison with experiment results (error values: 0.1°C~1.5°C).Moreover, the interaction mechanism of wall sticking was correlated well with the Hamaker constant, radius of oil droplets, Ζeta potential, and Debye length.

Large Eddy Simulation of Laminar and Turbulent Shock/Boundary Layer Interactions in a Transonic Passage

Shock/boundary layer interactions (SBLI) are a fundamental fluid mechanics problem relevant in a wide range of applications including transonic rotors in turbomachinery. This paper uses wall-resolved large eddy simulation (LES) to examine the interaction of normal shocks with laminar and turbulent inflow boundary layers in transonic flow. The calculations were performed using GENESIS, a high-order, unstructured LES solver. The geometry created for this study is a transonic passage with a convergent-divergent nozzle that expands the flow to the desired Mach number upstream of the shock and then introduces constant radius curvature to simulate local airfoil camber. The Mach numbers in the divergent section of the transonic passage simulate single stage commercial fan blades. The results predicted with the LES calculations show significant differences between laminar and turbulent SBLI in terms of shock structure, boundary layer separation and transition, and aerodynamic losses. For laminar flow into the shock, significant flow separation and low-frequency unsteadiness occur, while for turbulent flow into the shock, both the boundary layer loss and the low-frequency unsteadiness are reduced.