Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2608.11379

Analysis of the equations of motion of fictitious matter in embedding theory

A. J. Ziyatdinov·S. A. Paston
View original source ↗Read source document ↗Export metadata ↓

Abstract

Embedding theory is a possible modification of general relativity that provides a framework for explaining the observed effects typically attributed to dark matter. The idea of this modification is to consider our spacetime as a four-dimensional surface in a ten-dimensional flat ambient space. The equations of motion in embedding theory can be reformulated as a set of Einstein equations with the contribution of some additional fictitious matter and of equations describing this matter. We analyze static solutions of these equations, which are reduced to fictitious-matter configurations of the wall, string, and ball types. The string case is ultimately described by the Liouville equation, and the ball case is described by its three dimensional analogue. For the string case, we show that as the density contribution decreases at infinity, all solutions to the Liouville equation are rotationally symmetric. For the case of the ball, we show that under the assumption of spherical symmetry, there exists a unique one-parameter family of solutions that are smooth at the center.

Explore related subjects

gr-qc

Keep this discovery

BibTeXRIS

A. J. Ziyatdinov, S. A. Paston. 2026-08-11. Analysis of the equations of motion of fictitious matter in embedding theory. https://doi.org/10.1134/s0040577926060140

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↗