Related papers: The parameterized quasinormal modes for modified T…
Motivated by the substantial instability of the fundamental and high-overtone quasinormal modes, recent developments regarding the notion of black hole pseudospectrum call for numerical results with unprecedented precision. This work…
We develop a novel technique through spectral decompositions to study the gravitational perturbations of a black hole, without needing to decouple the linearized field equations into master equations and separate their radial and angular…
We apply polynomial approximation methods -- known in the numerical PDEs context as spectral methods -- to approximate the vector-valued function that satisfies a linear system of equations where the matrix and the right hand side depend on…
We consider constrained partial differential equations of hyperbolic type with a small parameter $\varepsilon>0$, which turn parabolic in the limit case, i.e., for $\varepsilon=0$. The well-posedness of the resulting systems is discussed…
Starting with assumptions both simple and natural from "physical" point of view we present a direct construction of transformations preserving wide class of (anti)commutation relations which describe Euclidean/Minkowski superspace…
In the context of a gravity's rainbow, the asymptotic quasinormal modes of the scalar perturbation in the quantum modified Schwarzschild black holes are investigated. By using the monodromy method, we calculated and obtained the asymptotic…
We carry out the first computation of gravitational quasinormal modes of black holes with arbitrary rotation in a theory with higher-derivative corrections. Our analysis focuses on a recently identified quartic-curvature theory that…
This paper is devoted to the study of generalized subdifferentials of spectral functions over Euclidean Jordan algebras. Spectral functions appear often in optimization problems playing the role of "regularizer", "barrier", "penalty…
In this paper, we introduce a method known as polynomial frame approximation for approximating smooth, multivariate functions defined on irregular domains in $d$ dimensions, where $d$ can be arbitrary. This method is simple, and relies only…
The quantum-mechanical D-dimensional inverse square potential is analyzed using field-theoretic renormalization techniques. A solution is presented for both the bound-state and scattering sectors of the theory using cutoff and dimensional…
Einstein's General Relativity theory simplifies dramatically in the limit that the spacetime dimension D is very large. This could still be true in the gravity theory with higher derivative terms. In this paper, as the first step to study…
With the example of the spherically symmetric scalar wave equation on Minkowski space-time we demonstrate that a fully pseudospectral scheme (i.e. spectral with respect to both spatial and time directions) can be applied for solving…
Using an expansion in terms of the inverse multipole number and the WKB approach, we derive an analytic expression for generic parametrized spherically symmetric and asymptotically flat black holes described by the Rezzolla-Zhidenko…
There is a distinct possibility that current and future cosmological data can be used to constrain Einstein's theory of gravity on the very largest scales. To be able to do this in a model-independent way, it makes sense to work with a…
Generalizing the framework of an ultra-weak formulation for a hypersingular integral equation on closed polygons in [N. Heuer, F. Pinochet, arXiv 1309.1697 (to appear in SIAM J. Numer. Anal.)], we study the case of a hypersingular integral…
These notes provide an exposition on obtaining the well-known standard results of quasiregular maps on Riemannian manifolds, given the corresponding theory in the Euclidean setting. We recall several different approaches to first-order…
We calculate analytically the asymptotic form of quasi-normal modes of perturbations of arbitrary spin of a Schwarzschild black hole including first-order corrections. We use the Teukolsky equation which applies to both bosonic and…
We extend the renormalized quasiparticle description of the symmetric Anderson model in a magnetic field $H$, developed in earlier work, to the non-symmetric model. The renormalized parameters are deduced from the low energy NRG fixed point…
Quasinormal modes of rapidly rotating black holes are crucial in understanding the ringdown phase after a merger. While for Kerr black holes these modes have been known for a long time, their calculation has remained a challenge in…
In this paper we present a spectral decomposition of solutions to relativistic wave equations described on horizon penetrating hyperboloidal slices within a given Schwarzschild-black-hole background. The wave equa- tion in question is…