相关论文: Refined Error Estimates for the Riccati Equation w…

A method is presented for obtaining rigorous error estimates for approximate solutions of the Riccati equation, with real or complex potentials. Our main tool is to derive invariant region estimates for complex solutions of the Riccati…

Analytic solutions of the Teukolsky equation in Kerr geometries are presented in the form of series of hypergeometric functions and Coulomb wave functions. Relations between these solutions are established. The solutions provide a very…

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…

An accurate closed-form expression is provided to predict the bending angle of light as a function of impact parameter for equatorial orbits around Kerr black holes of arbitrary spin. This expression is constructed by assuring that the…

We study gravitational perturbations on the near-horizon region of extremal and near-extremal rotating black holes in a general higher-derivative extension of Einstein gravity. We find a decoupled modified Teukolsky equation that rules the…

An approach for solving a variety of inverse coefficient problems for the Sturm-Liouville equation -y''+q(x)y={\lambda}y with a complex valued potential q(x) is presented. It is based on Neumann series of Bessel functions representations…

In this paper, we consider weakly regular Sturm-Liouville eigenproblems with unbounded potential at both endpoints of the domain. We propose a Galerkin spectral matrix method for its solution and we study the error in the eigenvalue…

Perturbations of Kerr spacetime are typically studied with the Teukolsky formalism, in which a pair of invariant components of the perturbed Weyl tensor are expressed in terms of separable modes that satisfy ordinary differential equations.…

A variety of inverse Sturm-Liouville problems is considered, including the two-spectrum inverse problem, the problem of recovering the potential from the Weyl function, as well as the recovery from the spectral function. In all cases the…

The Teukolsky Master Equation is the basic tool for study of perturbations of the Kerr metric in linear approximation. It admits separation of variables, thus yielding the Teukolsky Radial Equation and the Teukolsky Angular Equation. We…

We use Heun type solutions given in \cite{Suzuki} for the radial Teukolsky equation, written in the background metric of the Kerr-Newman-de Sitter geometry, to calculate the quasinormal frequencies for polynomial solutions and the…

For initial value problems associated with operator-valued Riccati differential equations posed in the space of Hilbert--Schmidt operators existence of solutions is studied. An existence result known for algebraic Riccati equations is…

We revisit the quasinormal-mode/greybody factor correspondence for Kerr black holes in the eikonal limit and develop a systematic WKB-based formulation by recasting the radial Teukolsky equation into a Schr\"odinger-type equation with a…

We have developed a numerical method for evolving perturbations of rotating black holes. Solutions are obtained by integrating the Teukolsky equation written as a first-order in time, coupled system of equations, in a form that explicitly…

We develop a formalism to treat higher order (nonlinear) metric perturbations of the Kerr spacetime in a Teukolsky framework. We first show that solutions to the linearized Einstein equation with nonvanishing stress tensor can be decomposed…

We present the computation of logarithmic corrections to near-extremal black hole entropy from one-loop Euclidean gravity path integral around the near-horizon geometry. We extract these corrections employing a suitably modified heat kernel…

So-called functional error estimators provide a valuable tool for reliably estimating the discretization error for a sum of two convex functions. We apply this concept to Tikhonov regularization for the solution of inverse problems for…

In this paper, we shall derive a spectral matrix method for the approximation of the eigenvalues of (weakly) regular and singular Sturm-Liouville problems in normal form with an unbounded potential at the left endpoint. The method is…

We establish boundedness and polynomial decay results for the Teukolsky system in the exterior spacetime of very slowly rotating and strongly charged sub-extremal Kerr-Newman black holes, with a focus on axially symmetric solutions. The key…

We compute one-loop corrections to the euclidean gravitational path integral of near-extremal (anti-)de Sitter-Kerr black hole in terms of the connection coefficients of the Heun equation describing the black hole linear perturbations in…