Related papers: Natural polynomials for Kerr quasi-normal modes
We consider the 4-dimensional $\mathcal{N}=1$ Lie superconformal algebra and search for completely "symmetric" (in the graded sense) 3-index invariant tensors. The solution we find is unique and we show that the corresponding invariant…
We demonstrate that a system of bi-orthogonal polynomials and their associated functions corresponding to a regular semi-classical weight on the unit circle constitute a class of general classical solutions to the Garnier systems by…
We discuss a new ringdown frequency mode for vacuum perturbations of the Kerr black hole. We evolve initial data for the vacuum radial Teukolsky equation using a near horizon approximation, and find a frequency mode analogous to that found…
This paper is devoted to the construction of polynomial 2-surfaces which possess a polynomial area element. In particular we study these surfaces in the Euclidean space $\mathbb R^3$ (where they are equivalent to the PN surfaces) and in the…
We construct a linear basis for the polynomial eigenfunctions of a family of deformed Calogero-Moser-Sutherland operators naturally associated with hypergeometric polynomials. In our construction the eigenfunctions are obtained as linear…
In this paper we introduce a basic representation for the confluent Cherednik algebras $\mathcal H_{\rm V}$, $\mathcal H_{\rm III}$, $\mathcal H_{\rm III}^{D_7}$ and $\mathcal H_{\rm III}^{D_8}$ defined in arXiv:1307.6140. To prove…
There is a well-known, intuitive geometric correspondence between high-frequency QNMs of Schwarzschild black holes and null geodesics that reside on the light-ring : the real part of the mode's frequency relates to the geodesic's orbital…
The security of multivariate cryptosystems and digital signature schemes relies on the hardness of solving a system of polynomial equations over a finite field. Polynomial system solving is also currently a bottleneck of index-calculus…
Lassalle and Nekrasov discovered in the 1990s a surprising correspondence between the rational Calogero-Moser system with a harmonic term and its trigonometric version. We present a conceptual explanation of this correspondence using the…
The Regge-Wheeler equation describes axial perturbations of Schwarzschild metric in linear approximation. Teukolsky Master Equation describes perturbations of Kerr metric in the same approximation. We present here unified description of all…
A characteristic polynomial is an important invariant in the field of hyperplane arrangement. For the Linial arrangement of any irreducible root system, Postnikov and Stanley conjectured that all roots of the characteristic polynomial have…
This article analyzes well-definedness and regularity of renormalized powers of Ornstein-Uhlenbeck processes and uses this analysis to establish local existence, uniqueness and regularity of strong solutions of stochastic Ginzburg-Landau…
Polynomials $Q_n(z)$, $n=0,1,\ldots,$ that are multi-orthogonal with respect to a Nikishin system of $p\geq 1$ compactly supported measures over the star-like set of $p+1$ rays $S_+:=\{z\in \mathbb{C}: z^{p+1}\geq 0 \}$ are investigated. We…
The quasinormal modes (QNMs) of a black hole spacetime are the free, decaying oscillations of the spacetime, and are well understood in the case of Kerr black holes. We discuss a method for computing the QNMs of spacetimes which are…
A new bi-parametric $su(1,1)$ algebraization of the Heun class of equations is explored. This yields additional quasi-polynomial solutions of the form $\{z^{\alpha}P_N(z): \ \alpha \in \mathbb{C}, \ N \in \mathbb{N}_0\}$ to the General Heun…
This paper is to evaluate certain Catalan-Hankel Pfaffians by the theory of skew orthogonal polynomials. Due to different kinds of hypergeometric orthogonal polynomials underlying the Askey scheme, we explicitly construct the classical skew…
Two numerical methods are developed to reduce the solution of the radial Schr\"odinger equation for proposed heavy quark-antiquark interactions, into the solution of the eigenvalue problem for the infinite system of tridiagonal matrices.…
Despite recent progress, the complete understanding of the perturbations of charged, rotating black holes as described by the Kerr-Newman metric remains an open and fundamental problem in relativity. In this study, we explore the existence…
A fundamental open problem in algebraic combinatorics is to find a positive combinatorial formula for Kronecker coefficients, which are multiplicities of the decomposition of the tensor product of two \S_r-irreducibles into irreducibles.…
We consider the Klein-Gordon equation on a class of Lorentzian manifolds with Cauchy surface of bounded geometry, which is shown to include examples such as exterior Kerr, Kerr-de Sitter and Kerr-Kruskal spacetimes. In this setup, we give…