Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2210.02069

Quasi-Normal Modes from Bound States: The Numerical Approach

Sebastian H. Völkel
View original source ↗Read source document ↗Export metadata ↓

Abstract

It is known that the spectrum of quasi-normal modes of potential barriers is related to the spectrum of bound states of the corresponding potential wells. This property has been widely used to compute black hole quasi-normal modes, but it is limited to a few "approximate" potentials with certain transformation properties for which the spectrum of bound states must be known analytically. In this work we circumvent this limitation by proposing an approach that allows one to make use of potentials with similar transformation properties, but where the spectrum of bound states can also be computed numerically. Because the numerical calculation of bound states is usually more stable than the direct computation of the corresponding quasi-normal modes, the new approach is also interesting from a technical point of view. We apply the method to different potentials, including the P\"oschl-Teller potential for which all steps can be understood analytically, as well as potentials for which we are not aware of analytic results but provide independent numerical results for comparison. As a canonical test, all potentials are chosen to match the Regge-Wheeler potential of axial perturbations of the Schwarzschild black hole. We find that the new approximate potentials are more suitable to approximate the exact quasi-normal modes than the P\"oschl-Teller potential, particularly for the first overtone. We hope this work opens new perspectives to the computation of quasi-normal modes and finds further improvements and generalizations in the future.

Explore related subjects

gr-qcquant-ph

Keep this discovery

BibTeXRIS

Sebastian H. Völkel. 2022-10-05. Quasi-Normal Modes from Bound States: The Numerical Approach. https://doi.org/10.1103/physrevd.106.124009

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Electrovacuum Black Hole Uniqueness

We prove the black hole uniqueness conjecture in the axially symmetric, stationary, electrovacuum setting, subject to the refined asymptotic analysis of the associated singular harmonic maps, which includes an analyticity hypothesis at the axes. More precisely, it is shown that any asymptotically flat solution of the Einstein--Maxwell equations in this class, with more than one black hole horizon component is either: Majumdar--Papapetrou, up to a duality rotation, in which case all logarithmic angle defects vanish, or every finite axis rod logarithmic angle defect is strictly negative and hence every interaction force is strictly attractive. The proof extends the singular harmonic map method used for vacuum Kerr uniqueness in [18].

gr-qc↗
arXiv2026

Constraining Modified Mass-to-Horizon Cosmology Through Primordial Inflationary Observables

We investigate slow-roll inflation in a modified cosmological framework inspired by a generalized mass-to-horizon relation (MHR), $M=\gamma {c^2 L^n}/{G}$, where $n$ is a real parameter and $\gamma$ a dimensional constant. Using Padmanabhan's emergence paradigm, we derive the modified Friedmann equations for a flat FRW universe and analyze the dynamics of a canonical scalar field (inflaton) under the slow-roll approximation. We study the resulting inflationary phenomenology for power-law and Starobinsky potentials. For power-law potentials, the MHR modification fails to reconcile these models with current CMB constraints on $r$ and $n_s$. In contrast, Starobinsky inflation exhibits significant sensitivity to deviations from $n=1$. A perturbative analysis ($n=1+\Delta$) yields corrections to inflationary observables. We observe that the scalar power-spectrum normalization, under a fixed-Starobinsky prescription, imposes the stringent constraint $0.960 \lesssim n \lesssim 1.040$ for $N=60$ efolds. This is considerably tighter than spectral-index bounds. Our results establish inflation, particularly Starobinsky-like models, as a sensitive probe of generalized horizon thermodynamics and departures from standard MHR scaling.

gr-qc↗
arXiv2026

Improving the Sensitivity of Gravitational Wave Detection with Weighted Conformal Prediction

In the last decade, kilometre-scale interferometric gravitational-wave detectors have observed hundreds of compact binary mergers, the majority of which are binary black holes. However, the data are noise-dominated, and multiple independent search algorithms (pipelines) are used to enhance sensitivity and improve robustness. Rather than the standard approach of selecting the most significant pipeline output, we combine the outputs from all pipelines using a conformal prediction-based framework to provide statistically rigorous confidence estimates for candidate events. While combining pipelines improves sensitivity and ranking robustness, it requires a principled statistical framework that remains valid as data properties evolve across observing runs. A key challenge is distribution shifts between simulated datasets used for training and calibration and the real, unlabelled, observations used for testing, which can invalidate coverage guarantees and bias confidence estimates. In this work, we address this challenge by incorporating likelihood-ratio reweighting into our conformal prediction framework to account for covariate shift. Using mock datasets containing simulated signals, we demonstrate that weighted conformal prediction restores well-calibrated coverage under covariate shift and increases the confidence of events near the detection threshold, recovering true signals that would otherwise be missed.

gr-qc↗