Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1301.7595

Stationary Bound States of Dirac Particles in the Schwarzschild Gravitational Field

M. A. Vronsky·M. V. Gorbatenko·N. S. Kolesnikov·V. P. Neznamov·E. Yu. Popov·I. I. Safronov
View original source ↗Read source document ↗Export metadata ↓

Abstract

Nondecaying bound states of elementary spin-half particles are validated and calculated numerically for the Schwarzschild gravitational field using a self-conjugate Hamiltonian with a flat scalar product for any value of the gravitational coupling constant. Hilbert condition g_{00}>0 leads to a boundary condition such that components of the vector of current density of Dirac particles are zero near the "event horizon". At small values of the coupling constant, the energy spectrum is close to the hydrogen-like spectrum. Based on the results of this study, we can assume that there exists a new type of collapsars, for which the Hawking radiation mechanism is not present. From the standpoint of cosmology, if the value of the gravitational coupling constant is small, alpha<<1, the new type of nonradiating relict collapsars can manifest itself only through gravitation. Thus, they are good candidates for the role of "dark matter" carriers. In the wide range of admissible masses, there can exist collapsars of a new type with the masses of hypothesized WIMP particles, which are treated as representatives of "dark matter" in numerous scenarios of the expansion of the universe. The results of this study can lead to revisiting some concepts of the standard cosmological model related to the evolution of the universe and interaction of collapsars with surrounding matter.

Explore related subjects

gr-qc

Keep this discovery

BibTeXRIS

M. A. Vronsky, M. V. Gorbatenko, N. S. Kolesnikov, V. P. Neznamov, E. Yu. Popov, I. I. Safronov. 2013-01-31. Stationary Bound States of Dirac Particles in the Schwarzschild Gravitational Field. https://arxiv.org/abs/1301.7595

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↗