Related papers: Riemann-Hilbert problems, Toeplitz operators and e…

For space-times with two spacelike isometries, we present infinite hierarchies of exact solutions of the Einstein and Einstein--Maxwell equations as represented by their Ernst potentials. This hierarchy contains three arbitrary rational…

We focus on the Clifford-algebra valued variable coefficients Riemann-Hilbert boundary value problems $\big{(}$for short RHBVPs$\big{)}$ for axially monogenic functions on Euclidean space $\mathbb{R}^{n+1},n\in \mathbb{N}$. With the help of…

We are solving the classical Riemann-Hilbert problem of rank N>1 on the extended complex plane punctured in 2m+2 points, for NxN quasi-permutation monodromy matrices. Following Korotkin we solve the Riemann-Hilbert problem in terms of the…

In this paper, we study the elliptic Weingarten surfaces of minimal type immersed in the warped product space $\mathbb{R} \times_{h} \mathbb{R}$, when $h$ is a $C^{1}$-function in $\mathbb{R}^{2}$ with radial symmetry. That is, surfaces…

Given a smooth manifold $M$ and a totally nonholonomic distribution $\Delta\subset TM$ of rank $d$, we study the effect of singular curves on the topology of the space of horizontal paths joining two points on $M$. Singular curves are…

We prove that on closed Riemannian manifolds with infinite abelian, but not cyclic, fundamental group, any isometry that is homotopic to the identity possesses infinitely many invariant geodesics. We conjecture that the result remains true…

Let $H\subset\mathbb{Z}^d$ be a half-space lattice, defined either relative to a fixed coordinate (e.g.\ $H = \mathbb{Z}^{d-1}\!\times\!\mathbb{Z}_+$), or relative to a linear order $\preceq$ on $\mathbb{Z}^d$, i.e.\ $H = \{j\in\mathbb{Z}^d…

The Einstein/Maxwell equations reduce in the stationary and axially symmetric case to a harmonic map with prescribed singularities phi: R^3\Sigma -> H^2_C, where Sigma is a subset of the axis of symmetry, and H^2_C is the complex hyperbolic…

Effects of inverse triad corrections and (point) holonomy corrections, occuring in loop quantum gravity, are considered on the properties of Reissner-Nordstr\"om black holes. The version of inverse triad corrections with unmodified…

In this paper matrix orthogonal polynomials in the real line are described in terms of a Riemann--Hilbert problem. This approach provides an easy derivation of discrete equations for the corresponding matrix recursion coefficients. The…

Tensor and scalar unparticle couplings to matter have been shown to enhance gravitational interactions and provide corrections to the Schwarzschild metric and associated black hole structure. We derive an exact solution to the Einstein…

This work addresses Riemann-Hilbert boundary value problems (RHBVPs) for null solutions to iterated perturbed Dirac operators over bi-axially symmetric domains in $\mathbb{R}^n$ with Clifford-algebra-valued variable coefficients. We first…

The Riemann -Rock theorem plays a central role in the theory of Riemann surfaces with applications to several branches in Mathematics and Physics. Suppose $X$ ia a compact Riemann surface of genus $g$ and $P \in X$. By the Riemann-Roch…

The well-known BTZ black hole solution of (2+1) Einstein's gravity, in the presence of a cosmological constant, is treated both at the classical and quantum level. Classically, the imposition of the two manifest local Killing fields of the…

This paper presents a close form solution in Reproducing Kernel Hilbert Space (RKHS) for the famed Wiener filter, which we called the functional Wiener filter(FWF). Instead of using the Wiener-Hopf factorization theory, here we define a new…

A throughout investigation is made of the exact black hole solution in five-dimensional warped conformal dilaton gravity, found in an earlier investigation. The singularities of the dynamical black hole spacetime are determined by the zeros…

By employing a novel generalization of the inverse scattering transform method known as the unified transform or Fokas method, it can be shown that the solution of certain physically significant boundary value problems for the elliptic…

Quasinormal modes of usual, four dimensional, Kerr black holes are described by certain solutions of a confluent Heun differential equation. In this work, we express these solutions in terms of the connection matrices for a Riemann-Hilbert…

Solving Einstein's constraint equations for the construction of black hole initial data requires handling the black hole singularity. Typically, this is done either with the excision method, in which the black hole interior is excised from…

By consideration of a Einstein-dilaton non-linear charged gravitating system, it has been shown that this theory is confronted with the problem of indeterminacy. It means that the number of independent differential equations is one less…