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Related papers: Refined Error Estimates for the Riccati Equation w…

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We show that the Riccati--Pad\'{e} method is suitable for the calculation of the complex eigenvalues of the Schr\"{o}dinger equation with a repulsive exponential potential. The accuracy of the results is remarkable for realistic potential…

Mathematical Physics · Physics 2009-11-13 Paolo Amore , Francisco M. Fernandez

Recent measurements of gravitational-wave ringdown following the merger of binary black holes raise the prospect of precision black hole spectroscopy in the near future. To perform the most sensitive tests of the nature of black holes using…

General Relativity and Quantum Cosmology · Physics 2022-11-23 Asad Hussain , Aaron Zimmerman

Efficient and accurate low-rank approximation (LRA) methods are of great significance for large-scale data analysis. Randomized tensor decompositions have emerged as powerful tools to meet this need, but most existing methods perform poorly…

Machine Learning · Computer Science 2022-11-29 Yichun Qiu , Weijun Sun , Guoxu Zhou , Qibin Zhao

Post-adiabatic models of extreme- and intermediate-mass-ratio inspirals will require calculations of second-order gravitational self-force effects in the spacetime of a spinning, Kerr black hole. We take a step toward such calculations by…

General Relativity and Quantum Cosmology · Physics 2024-11-04 Patrick Bourg , Benjamin Leather , Marc Casals , Adam Pound , Barry Wardell

The analytical solutions reported in our previous paper are given as series of hypergeometric or Coulomb wave functions. By using them, we can get the Teukolsky functions analytically in a desired accuracy. For the computation, the deep…

General Relativity and Quantum Cosmology · Physics 2009-10-28 Shuhei Mano , Eiichi Takasugi

We investigate the relativistic scattering of spinning black holes using modern amplitude methods within a heavy-mass effective field theory formalism at third post-Minkowskian order. Using a systematic self-force expansion up to first…

High Energy Physics - Theory · Physics 2026-03-05 N. Emil J. Bjerrum-Bohr , Gang Chen , Konstantinos Papadimos , Yuexiang Zhang

Computable and sharp error bounds are derived for asymptotic expansions for linear differential equations having a simple turning point. The expansions involve Airy functions and slowly varying coefficient functions. The sharpness of the…

Classical Analysis and ODEs · Mathematics 2020-09-11 T. M. Dunster , A. Gil , J. Segura

In this work, we propose an efficient finite element method for solving fractional Sturm-Liouville problems involving either the Caputo or Riemann-Liouville derivative of order $\alpha\in(1,2)$ on the unit interval $(0,1)$. It is based on…

Numerical Analysis · Mathematics 2013-07-22 Bangti Jin , Raytcho Lazarov , Joseph Pasciak , William Rundell

We reduce the study of perturbations of rotating black holes in higher-derivative extensions of general relativity to a system of decoupled radial equations that stem from a set of universal Teukolsky equations. We detail a complete…

General Relativity and Quantum Cosmology · Physics 2023-07-25 Pablo A. Cano , Kwinten Fransen , Thomas Hertog , Simon Maenaut

We derive a geometrical version of the Regge-Wheeler and Zerilli equations, which allows us to study gravitational perturbations on an arbitrary spherically symmetric slicing of a Schwarzschild black hole. We explain how to obtain the…

General Relativity and Quantum Cosmology · Physics 2009-11-07 Olivier Sarbach , Manuel Tiglio

For the last decades, multiple international facilities have developed Radioactive-Ion Beams (RIB) to measure reaction processes including exotic nuclei. These measurements coupled with an accurate theoretical model of the reaction enable…

Nuclear Theory · Physics 2017-02-21 Chloë Hebborn , Pierre Capel

A key obstacle for theory-specific tests of general relativity is the lack of accurate black-hole solutions in beyond-Einstein theories, especially for moderate to high spins. We address this by developing a general framework--based on…

General Relativity and Quantum Cosmology · Physics 2026-01-19 Kelvin Ka-Ho Lam , Adrian Ka-Wai Chung , Nicolás Yunes

We present a Neumann series of spherical Bessel functions representation for solutions of the Sturm--Liouville equation in impedance form \[ (\kappa(x)u')' + \lambda \kappa(x)u = 0,\quad 0 < x < L, \] in the case where $\kappa \in…

Classical Analysis and ODEs · Mathematics 2026-01-09 Abigail G. Márquez-Hernández , Víctor A. Vicente-Benítez

We provide a posteriori error estimates for a discontinuous Galerkin scheme for the parabolic-elliptic Keller-Segel system in 2 or 3 space dimensions. The estimates are conditional, in the sense that an a posteriori computable quantity…

Numerical Analysis · Mathematics 2024-06-12 Jan Giesselmann , Kiwoong Kwon

The Arnoldi-Tikhonov method is a well-established regularization technique for solving large-scale ill-posed linear inverse problems. This method leverages the Arnoldi decomposition to reduce computational complexity by projecting the…

Numerical Analysis · Mathematics 2025-06-02 Davide Bianchi , Marco Donatelli , Davide Furchì , Lothar Reichel

We consider regular polynomial interpolation algorithms on recursively defined sets of interpolation points which approximate global solutions of arbitrary well-posed systems of linear partial differential equations. Convergence of the…

Numerical Analysis · Mathematics 2008-07-10 Joerg Kampen

We compute logarithmic corrections to the entropy of rotating extremal black holes using quantum entropy function i.e. Euclidean quantum gravity approach. Our analysis includes five dimensional supersymmetric BMPV black holes in type IIB…

High Energy Physics - Theory · Physics 2015-05-30 Ashoke Sen

In previous works, we developed a perturbative extrapolation formula to obtain gravitational waves at infinity from binary black hole simulations, based on the Regge-Wheeler-Zerilli formalism. In practice, this formula was basically derived…

General Relativity and Quantum Cosmology · Physics 2015-08-21 Hiroyuki Nakano

We derive the large time asymptotics of initially regular and localized solutions of the Teukolsky equation on the exterior of a subextremal Kerr black hole for any half integer spin. More precisely, we obtain the leading order term…

Analysis of PDEs · Mathematics 2023-02-15 Pascal Millet

Analytical series expansions for the bending of light in the equatorial plane of a Kerr black hole are presented in both the strong and weak deflection regimes. It is critical that these are known in analytical form so further analysis can…

General Relativity and Quantum Cosmology · Physics 2009-08-04 Savitri V. Iyer , Edward C. Hansen