Perturbation analysis for massless spin fields in accelerating Kerr-Newman-(anti-)de Sitter black holes

We obtain the wave equation of the perturbation theory governing massless fields of spin 0, 1/2, 1, 3/2 and 2 in accelerating Kerr–Newman–(anti-)de Sitter black holes. We show that the wave equation is separable and the radial and angular equations can both be transformed into Heun’s equation. We approximate Heun’s equation and analyze the solution of radial function near the event horizon. It is worth pointing out that all the field equations collapse to a unique equation which means it can provide a possible way for the analog research between the gravitational field and those other fields.

Quantization of the charge in Coulomb plus harmonic potential

We consider two models where the wave equation can be reduced to the effective Schrödinger equation whose potential contains both harmonic and the Coulomb terms, ω2r2 – a/r. The equation reduces to the biconfluent Heun’s equation, and we find that the charge as well as the energy must be quantized and state dependent. We also find that two quantum numbers are necessary to count radial degrees of freedom and suggest that this is a general feature of differential equation with higher singularity like the Heun’s equation.

Gravitational domain wall and stability with some symmetry algebra

In this paper, first, we will try to introduce the gravitational domain wall as a physical system. In the second step, we also introduce the Hun differential equation as a mathematical tools. We factorize the known Heun’s equation as form of operators [Formula: see text], [Formula: see text] and [Formula: see text]. Then we compare the differential equation of gravitational domain wall with corresponding Hun equation. In that case the above-mentioned operators can be obtained for the gravitational system by the comparing process. Finally, we employ such operators and achieve the corresponding symmetry algebra with the usual commutation relation of operators to each other. Here, by having such operators, we investigate the stability of system.

On Symmetrical Deformation of Toroidal Shell with Circular Cross-Section

By introducing a variable transformation $\xi=\frac{1}{2}(\sin \theta+1)$, the symmetrical deformation equation of elastic toroidal shells is successfully transferred into a well-known equation, namely Heun's equation of ordinary differential equation, whose exact solution is obtained in terms of Heun's functions. The computation of the problem can be carried out by symbolic software that is able to with the Heun's function, such as Maple. The Gauss curvature of the elastic toroidal shells shows that the internal portion of the toroidal shells has better bending capacity than the outer portion, which might be useful for the design of metamaterials with toroidal shells cells. Through numerical comparison study, the mechanics of elastic toroidal shells is sensitive to the radius ratio. By slightly adjustment of the ratio might get a desired high performance shell structure.

Chiral symmetry and Heun’s equation

We show that the current quark mass should vanish to be consistent with the QCD color confinement: a bag model leads us to Heun’s equation, which requests that not only the energy but also the string tension should be quantized. This is due to the presence of higher-order singularity which requests higher regularity condition demanding that parameters of the theory should be related to one another. As a result, the Hadron spectrum is consistent with the Regge trajectory only when quark mass vanishes. Therefore, in this model, the chiral symmetry is a consequence of the confinement.

On Symmetrical Deformation of Toroidal Shell with Circular Cross-Section

By introducing a variable transformation $\xi=\frac{1}{2}(\sin \theta+1)$, the complicated deformation equation of toroidal shell is successfully transferred into a well-known equation, namely Heun's equation of ordinary differential equation, whose exact solution is obtained in terms of Heun's functions. The computation of the problem can be carried out by symbolic software that is able to with the Heun's function, such as Maple. The geometric study of the Gauss curvature shows that the internal portion of the toroidal shell has better bending capacity than the outer portion, which might be useful for the design of metamaterials with toroidal shell cells.

Novel Representation of the General Fuchsian and Heun Equations and their Solutions

In the present article we introduce and study a novel type of solutions to the general Heun's equation. Our approach is based on the symmetric form of the Heun's differential equation yielded by development of the Papperitz-Klein symmetric form of the Fuchsian equations with an arbitrary number N≥4 of regular singular points. We derive the symmetry group of these equations which turns to be a proper extension of the Mobius group. We also introduce and study new series solutions of the proposed in the present paper symmetric form of the general Heun's differential equation (N=4) which treats simultaneously and on an equal footing all singular points.