Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 1302.4035

Evolution of the Carter constant for a resonant inspiral into a Kerr black hole: I. The scalar case

Soichiro Isoyama·Ryuichi Fujita·Hiroyuki Nakano·Norichika Sago·Takahiro Tanaka
View original source ↗Read source document ↗Export metadata ↓

Abstract

We discuss the inspiral of a small body around a Kerr black hole. When the time scale of the radiation reaction is sufficiently longer than its orbital period, the leading order orbital evolution is described only by the knowledge of the averaged evolution of the constants of motion, i.e., the energy, azimuthal angular momentum and the Carter constant. Although there is no conserved current composed of the perturbation field corresponding to the Carter constant, it has been shown that the averaged rate of change of the Carter constant can be given by a simple formula, when there exists a simultaneous turning point of the radial and polar oscillations. However, an inspiralling orbit may cross a "resonance" point, where the frequencies of the radial and polar orbital oscillations are in a rational ratio. At the resonance point, one cannot find a simultaneous turning point in general. Hence, even for the averaged rate of change of the Carter constant, a direct computation of the 'self-force", which is still challenging especially in the case of the Kerr background, seems to be necessary. In this paper, we present a method of computing the averaged rate of change of the Carter constant in a relatively simple manner at the "resonance" point.

Explore related subjects

gr-qcastro-ph.CO

Keep this discovery

BibTeXRIS

Soichiro Isoyama, Ryuichi Fujita, Hiroyuki Nakano, Norichika Sago, Takahiro Tanaka. 2013-02-17. Evolution of the Carter constant for a resonant inspiral into a Kerr black hole: I. The scalar case. https://doi.org/10.1093/ptep/ptt034

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↗